Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.2% → 83.0%

Time: 34.4s

Alternatives: 28

Speedup: 0.5×

• 58.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - t \cdot a\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \cdot t_3 + \left(x \cdot t_1 + t_2\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, t_1, \mathsf{fma}\left(j, t_3, t_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y z) (* t a)))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (- (* t c) (* y i))))
   (if (<= (+ (* j t_3) (+ (* x t_1) t_2)) INFINITY)
     (fma x t_1 (fma j t_3 t_2))
     (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = (t * c) - (y * i);
	double tmp;
	if (((j * t_3) + ((x * t_1) + t_2)) <= ((double) INFINITY)) {
		tmp = fma(x, t_1, fma(j, t_3, t_2));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * z) - Float64(t * a))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(j * t_3) + Float64(Float64(x * t_1) + t_2)) <= Inf)
		tmp = fma(x, t_1, fma(j, t_3, t_2));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(j * t$95$3), $MachinePrecision] + N[(N[(x * t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(x * t$95$1 + N[(j * t$95$3 + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 91.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 91.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 91.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 91.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 91.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 91.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 91.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 91.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 91.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 91.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 91.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 91.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 91.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 91.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 91.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 91.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 40.7%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 62.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 62.9%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 62.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 62.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 62.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 62.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 62.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 62.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 68.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 68.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 68.5%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 68.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 68.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 68.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 68.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 68.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 2: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* j (- (* t c) (* y i)))
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c)))))))
   (if (<= t_1 INFINITY)
     t_1
     (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 91.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 40.7%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 62.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 62.9%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 62.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 62.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 62.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 62.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 62.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 62.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 68.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 68.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 68.5%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 68.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 68.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 68.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 68.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 68.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq \infty:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 3: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+180}:\\ \;\;\;\;t_3 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1600000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-221}:\\ \;\;\;\;t_3 + t_1\\ \mathbf{elif}\;x \leq 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* b (- (* a i) (* z c)))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -1.75e+180)
     (- t_3 (* c (* z b)))
     (if (<= x -1.46e+85)
       (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a))))
       (if (<= x -1600000000000.0)
         (+ (* a (- (* b i) (* x t))) (* z (- (* x y) (* b c))))
         (if (<= x 4.6e-262)
           t_2
           (if (<= x 1.45e-221)
             (+ t_3 t_1)
             (if (<= x 1e-47)
               t_2
               (+ t_3 (- (* a (* b i)) (* y (* i j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.75e+180) {
		tmp = t_3 - (c * (z * b));
	} else if (x <= -1.46e+85) {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	} else if (x <= -1600000000000.0) {
		tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)));
	} else if (x <= 4.6e-262) {
		tmp = t_2;
	} else if (x <= 1.45e-221) {
		tmp = t_3 + t_1;
	} else if (x <= 1e-47) {
		tmp = t_2;
	} else {
		tmp = t_3 + ((a * (b * i)) - (y * (i * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-1.75d+180)) then
        tmp = t_3 - (c * (z * b))
    else if (x <= (-1.46d+85)) then
        tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
    else if (x <= (-1600000000000.0d0)) then
        tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)))
    else if (x <= 4.6d-262) then
        tmp = t_2
    else if (x <= 1.45d-221) then
        tmp = t_3 + t_1
    else if (x <= 1d-47) then
        tmp = t_2
    else
        tmp = t_3 + ((a * (b * i)) - (y * (i * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.75e+180) {
		tmp = t_3 - (c * (z * b));
	} else if (x <= -1.46e+85) {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	} else if (x <= -1600000000000.0) {
		tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)));
	} else if (x <= 4.6e-262) {
		tmp = t_2;
	} else if (x <= 1.45e-221) {
		tmp = t_3 + t_1;
	} else if (x <= 1e-47) {
		tmp = t_2;
	} else {
		tmp = t_3 + ((a * (b * i)) - (y * (i * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (b * ((a * i) - (z * c)))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.75e+180:
		tmp = t_3 - (c * (z * b))
	elif x <= -1.46e+85:
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
	elif x <= -1600000000000.0:
		tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)))
	elif x <= 4.6e-262:
		tmp = t_2
	elif x <= 1.45e-221:
		tmp = t_3 + t_1
	elif x <= 1e-47:
		tmp = t_2
	else:
		tmp = t_3 + ((a * (b * i)) - (y * (i * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.75e+180)
		tmp = Float64(t_3 - Float64(c * Float64(z * b)));
	elseif (x <= -1.46e+85)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	elseif (x <= -1600000000000.0)
		tmp = Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (x <= 4.6e-262)
		tmp = t_2;
	elseif (x <= 1.45e-221)
		tmp = Float64(t_3 + t_1);
	elseif (x <= 1e-47)
		tmp = t_2;
	else
		tmp = Float64(t_3 + Float64(Float64(a * Float64(b * i)) - Float64(y * Float64(i * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t_1 + (b * ((a * i) - (z * c)));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.75e+180)
		tmp = t_3 - (c * (z * b));
	elseif (x <= -1.46e+85)
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	elseif (x <= -1600000000000.0)
		tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)));
	elseif (x <= 4.6e-262)
		tmp = t_2;
	elseif (x <= 1.45e-221)
		tmp = t_3 + t_1;
	elseif (x <= 1e-47)
		tmp = t_2;
	else
		tmp = t_3 + ((a * (b * i)) - (y * (i * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+180], N[(t$95$3 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.46e+85], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1600000000000.0], N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-262], t$95$2, If[LessEqual[x, 1.45e-221], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[x, 1e-47], t$95$2, N[(t$95$3 + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.7499999999999999e180

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 75.7%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in j around 0 84.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(z \cdot b\right)} \]

   if -1.7499999999999999e180 < x < -1.46e85

   1. Initial program 58.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 76.3%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 82.3%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 82.3%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 82.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 82.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 82.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 82.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 82.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 82.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 82.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 82.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 82.3%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 82.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 82.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 82.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 82.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 82.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   if -1.46e85 < x < -1.6e12

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 71.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 78.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 86.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   if -1.6e12 < x < 4.6000000000000002e-262 or 1.44999999999999997e-221 < x < 9.9999999999999997e-48

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   if 4.6000000000000002e-262 < x < 1.44999999999999997e-221

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 77.2%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   if 9.9999999999999997e-48 < x

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 76.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 77.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 77.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 77.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 77.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 77.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 77.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 77.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 77.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around 0 75.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + a \cdot \left(i \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+180}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1600000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 10^{-47}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + \left(a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\right)\\ \end{array} \]

Alternative 4: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_5 := t_4 + t_2\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+180}:\\ \;\;\;\;t_4 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1100000000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-221}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (+ t_1 t_2))
        (t_4 (* x (- (* y z) (* t a))))
        (t_5 (+ t_4 t_2)))
   (if (<= x -1.02e+180)
     (- t_4 (* c (* z b)))
     (if (<= x -1.2e+84)
       (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a))))
       (if (<= x -1100000000000.0)
         t_5
         (if (<= x 4.6e-262)
           t_3
           (if (<= x 1.45e-221) (+ t_4 t_1) (if (<= x 2.6e-105) t_3 t_5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_1 + t_2;
	double t_4 = x * ((y * z) - (t * a));
	double t_5 = t_4 + t_2;
	double tmp;
	if (x <= -1.02e+180) {
		tmp = t_4 - (c * (z * b));
	} else if (x <= -1.2e+84) {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	} else if (x <= -1100000000000.0) {
		tmp = t_5;
	} else if (x <= 4.6e-262) {
		tmp = t_3;
	} else if (x <= 1.45e-221) {
		tmp = t_4 + t_1;
	} else if (x <= 2.6e-105) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t_1 + t_2
    t_4 = x * ((y * z) - (t * a))
    t_5 = t_4 + t_2
    if (x <= (-1.02d+180)) then
        tmp = t_4 - (c * (z * b))
    else if (x <= (-1.2d+84)) then
        tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
    else if (x <= (-1100000000000.0d0)) then
        tmp = t_5
    else if (x <= 4.6d-262) then
        tmp = t_3
    else if (x <= 1.45d-221) then
        tmp = t_4 + t_1
    else if (x <= 2.6d-105) then
        tmp = t_3
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_1 + t_2;
	double t_4 = x * ((y * z) - (t * a));
	double t_5 = t_4 + t_2;
	double tmp;
	if (x <= -1.02e+180) {
		tmp = t_4 - (c * (z * b));
	} else if (x <= -1.2e+84) {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	} else if (x <= -1100000000000.0) {
		tmp = t_5;
	} else if (x <= 4.6e-262) {
		tmp = t_3;
	} else if (x <= 1.45e-221) {
		tmp = t_4 + t_1;
	} else if (x <= 2.6e-105) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t_1 + t_2
	t_4 = x * ((y * z) - (t * a))
	t_5 = t_4 + t_2
	tmp = 0
	if x <= -1.02e+180:
		tmp = t_4 - (c * (z * b))
	elif x <= -1.2e+84:
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
	elif x <= -1100000000000.0:
		tmp = t_5
	elif x <= 4.6e-262:
		tmp = t_3
	elif x <= 1.45e-221:
		tmp = t_4 + t_1
	elif x <= 2.6e-105:
		tmp = t_3
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t_1 + t_2)
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_5 = Float64(t_4 + t_2)
	tmp = 0.0
	if (x <= -1.02e+180)
		tmp = Float64(t_4 - Float64(c * Float64(z * b)));
	elseif (x <= -1.2e+84)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	elseif (x <= -1100000000000.0)
		tmp = t_5;
	elseif (x <= 4.6e-262)
		tmp = t_3;
	elseif (x <= 1.45e-221)
		tmp = Float64(t_4 + t_1);
	elseif (x <= 2.6e-105)
		tmp = t_3;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t_1 + t_2;
	t_4 = x * ((y * z) - (t * a));
	t_5 = t_4 + t_2;
	tmp = 0.0;
	if (x <= -1.02e+180)
		tmp = t_4 - (c * (z * b));
	elseif (x <= -1.2e+84)
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	elseif (x <= -1100000000000.0)
		tmp = t_5;
	elseif (x <= 4.6e-262)
		tmp = t_3;
	elseif (x <= 1.45e-221)
		tmp = t_4 + t_1;
	elseif (x <= 2.6e-105)
		tmp = t_3;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + t$95$2), $MachinePrecision]}, If[LessEqual[x, -1.02e+180], N[(t$95$4 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e+84], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1100000000000.0], t$95$5, If[LessEqual[x, 4.6e-262], t$95$3, If[LessEqual[x, 1.45e-221], N[(t$95$4 + t$95$1), $MachinePrecision], If[LessEqual[x, 2.6e-105], t$95$3, t$95$5]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.02e180

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 75.7%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in j around 0 84.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(z \cdot b\right)} \]

   if -1.02e180 < x < -1.2e84

   1. Initial program 55.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 55.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 55.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 55.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 55.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 55.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 55.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 55.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 55.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 74.6%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 80.3%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 80.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 80.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 80.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 80.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 80.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 80.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 80.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 80.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 80.3%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 80.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 80.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 80.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 80.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 80.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   if -1.2e84 < x < -1.1e12 or 2.5999999999999999e-105 < x

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 77.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 75.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   if -1.1e12 < x < 4.6000000000000002e-262 or 1.44999999999999997e-221 < x < 2.5999999999999999e-105

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around 0 77.7%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   if 4.6000000000000002e-262 < x < 1.44999999999999997e-221

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 77.2%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+180}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1100000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 5: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+178}:\\ \;\;\;\;t_4 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -2020000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-221}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4 + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (+ t_1 t_2))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= x -1.9e+178)
     (- t_4 (* c (* z b)))
     (if (<= x -2.25e+84)
       (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a))))
       (if (<= x -2020000000000.0)
         (+ (* a (- (* b i) (* x t))) (* z (- (* x y) (* b c))))
         (if (<= x 4.6e-262)
           t_3
           (if (<= x 1.45e-221)
             (+ t_4 t_1)
             (if (<= x 3.3e-105) t_3 (+ t_4 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_1 + t_2;
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.9e+178) {
		tmp = t_4 - (c * (z * b));
	} else if (x <= -2.25e+84) {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	} else if (x <= -2020000000000.0) {
		tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)));
	} else if (x <= 4.6e-262) {
		tmp = t_3;
	} else if (x <= 1.45e-221) {
		tmp = t_4 + t_1;
	} else if (x <= 3.3e-105) {
		tmp = t_3;
	} else {
		tmp = t_4 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t_1 + t_2
    t_4 = x * ((y * z) - (t * a))
    if (x <= (-1.9d+178)) then
        tmp = t_4 - (c * (z * b))
    else if (x <= (-2.25d+84)) then
        tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
    else if (x <= (-2020000000000.0d0)) then
        tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)))
    else if (x <= 4.6d-262) then
        tmp = t_3
    else if (x <= 1.45d-221) then
        tmp = t_4 + t_1
    else if (x <= 3.3d-105) then
        tmp = t_3
    else
        tmp = t_4 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_1 + t_2;
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.9e+178) {
		tmp = t_4 - (c * (z * b));
	} else if (x <= -2.25e+84) {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	} else if (x <= -2020000000000.0) {
		tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)));
	} else if (x <= 4.6e-262) {
		tmp = t_3;
	} else if (x <= 1.45e-221) {
		tmp = t_4 + t_1;
	} else if (x <= 3.3e-105) {
		tmp = t_3;
	} else {
		tmp = t_4 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t_1 + t_2
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.9e+178:
		tmp = t_4 - (c * (z * b))
	elif x <= -2.25e+84:
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
	elif x <= -2020000000000.0:
		tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)))
	elif x <= 4.6e-262:
		tmp = t_3
	elif x <= 1.45e-221:
		tmp = t_4 + t_1
	elif x <= 3.3e-105:
		tmp = t_3
	else:
		tmp = t_4 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t_1 + t_2)
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.9e+178)
		tmp = Float64(t_4 - Float64(c * Float64(z * b)));
	elseif (x <= -2.25e+84)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	elseif (x <= -2020000000000.0)
		tmp = Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (x <= 4.6e-262)
		tmp = t_3;
	elseif (x <= 1.45e-221)
		tmp = Float64(t_4 + t_1);
	elseif (x <= 3.3e-105)
		tmp = t_3;
	else
		tmp = Float64(t_4 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t_1 + t_2;
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.9e+178)
		tmp = t_4 - (c * (z * b));
	elseif (x <= -2.25e+84)
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	elseif (x <= -2020000000000.0)
		tmp = (a * ((b * i) - (x * t))) + (z * ((x * y) - (b * c)));
	elseif (x <= 4.6e-262)
		tmp = t_3;
	elseif (x <= 1.45e-221)
		tmp = t_4 + t_1;
	elseif (x <= 3.3e-105)
		tmp = t_3;
	else
		tmp = t_4 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+178], N[(t$95$4 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.25e+84], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2020000000000.0], N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-262], t$95$3, If[LessEqual[x, 1.45e-221], N[(t$95$4 + t$95$1), $MachinePrecision], If[LessEqual[x, 3.3e-105], t$95$3, N[(t$95$4 + t$95$2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.89999999999999999e178

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 75.7%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in j around 0 84.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(z \cdot b\right)} \]

   if -1.89999999999999999e178 < x < -2.2499999999999999e84

   1. Initial program 58.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 76.3%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 82.3%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 82.3%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 82.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 82.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 82.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 82.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 82.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 82.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 82.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 82.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 82.3%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 82.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 82.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 82.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 82.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 82.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   if -2.2499999999999999e84 < x < -2.02e12

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 71.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 78.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 86.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   if -2.02e12 < x < 4.6000000000000002e-262 or 1.44999999999999997e-221 < x < 3.2999999999999999e-105

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around 0 77.7%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   if 4.6000000000000002e-262 < x < 1.44999999999999997e-221

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 77.2%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   if 3.2999999999999999e-105 < x

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 77.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 75.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -2020000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 6: 65.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.06 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-38}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -6e+255)
     t_2
     (if (<= b -1.06e+110)
       (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a))))
       (if (<= b -6.4e-38)
         (+ t_1 t_2)
         (if (<= b 1.5e+75)
           (+ (* x (- (* y z) (* t a))) t_1)
           (+ (* z (- (* x y) (* b c))) (* i (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6e+255) {
		tmp = t_2;
	} else if (b <= -1.06e+110) {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	} else if (b <= -6.4e-38) {
		tmp = t_1 + t_2;
	} else if (b <= 1.5e+75) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-6d+255)) then
        tmp = t_2
    else if (b <= (-1.06d+110)) then
        tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
    else if (b <= (-6.4d-38)) then
        tmp = t_1 + t_2
    else if (b <= 1.5d+75) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = (z * ((x * y) - (b * c))) + (i * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6e+255) {
		tmp = t_2;
	} else if (b <= -1.06e+110) {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	} else if (b <= -6.4e-38) {
		tmp = t_1 + t_2;
	} else if (b <= 1.5e+75) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -6e+255:
		tmp = t_2
	elif b <= -1.06e+110:
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
	elif b <= -6.4e-38:
		tmp = t_1 + t_2
	elif b <= 1.5e+75:
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -6e+255)
		tmp = t_2;
	elseif (b <= -1.06e+110)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	elseif (b <= -6.4e-38)
		tmp = Float64(t_1 + t_2);
	elseif (b <= 1.5e+75)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(i * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -6e+255)
		tmp = t_2;
	elseif (b <= -1.06e+110)
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	elseif (b <= -6.4e-38)
		tmp = t_1 + t_2;
	elseif (b <= 1.5e+75)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+255], t$95$2, If[LessEqual[b, -1.06e+110], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.4e-38], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[b, 1.5e+75], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.00000000000000035e255

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 66.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 66.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 66.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 66.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 66.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 66.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 83.1%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -6.00000000000000035e255 < b < -1.06000000000000005e110

   1. Initial program 58.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 51.5%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 83.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 83.5%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 83.5%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 83.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 83.5%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 83.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 83.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 83.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 87.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 87.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 87.7%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 87.7%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 87.7%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 87.7%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 87.7%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 87.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   if -1.06000000000000005e110 < b < -6.39999999999999955e-38

   1. Initial program 83.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 83.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around 0 80.5%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   if -6.39999999999999955e-38 < b < 1.5e75

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 72.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 72.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 73.2%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   if 1.5e75 < b

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 56.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 60.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 67.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in t around 0 76.6%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+255}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.06 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-38}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 7: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -8300000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+175}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= x -8300000000000.0)
     t_2
     (if (<= x -4.5e-151)
       t_1
       (if (<= x 6.8e-261)
         (* i (- (* a b) (* y j)))
         (if (<= x 7e-112)
           t_1
           (if (<= x 3.6e+18)
             t_3
             (if (<= x 9.5e+52)
               t_2
               (if (<= x 7.8e+81)
                 t_3
                 (if (<= x 7.4e+175) (* y (- (* x z) (* i j))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -8300000000000.0) {
		tmp = t_2;
	} else if (x <= -4.5e-151) {
		tmp = t_1;
	} else if (x <= 6.8e-261) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 7e-112) {
		tmp = t_1;
	} else if (x <= 3.6e+18) {
		tmp = t_3;
	} else if (x <= 9.5e+52) {
		tmp = t_2;
	} else if (x <= 7.8e+81) {
		tmp = t_3;
	} else if (x <= 7.4e+175) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = b * ((a * i) - (z * c))
    if (x <= (-8300000000000.0d0)) then
        tmp = t_2
    else if (x <= (-4.5d-151)) then
        tmp = t_1
    else if (x <= 6.8d-261) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 7d-112) then
        tmp = t_1
    else if (x <= 3.6d+18) then
        tmp = t_3
    else if (x <= 9.5d+52) then
        tmp = t_2
    else if (x <= 7.8d+81) then
        tmp = t_3
    else if (x <= 7.4d+175) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -8300000000000.0) {
		tmp = t_2;
	} else if (x <= -4.5e-151) {
		tmp = t_1;
	} else if (x <= 6.8e-261) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 7e-112) {
		tmp = t_1;
	} else if (x <= 3.6e+18) {
		tmp = t_3;
	} else if (x <= 9.5e+52) {
		tmp = t_2;
	} else if (x <= 7.8e+81) {
		tmp = t_3;
	} else if (x <= 7.4e+175) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if x <= -8300000000000.0:
		tmp = t_2
	elif x <= -4.5e-151:
		tmp = t_1
	elif x <= 6.8e-261:
		tmp = i * ((a * b) - (y * j))
	elif x <= 7e-112:
		tmp = t_1
	elif x <= 3.6e+18:
		tmp = t_3
	elif x <= 9.5e+52:
		tmp = t_2
	elif x <= 7.8e+81:
		tmp = t_3
	elif x <= 7.4e+175:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (x <= -8300000000000.0)
		tmp = t_2;
	elseif (x <= -4.5e-151)
		tmp = t_1;
	elseif (x <= 6.8e-261)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 7e-112)
		tmp = t_1;
	elseif (x <= 3.6e+18)
		tmp = t_3;
	elseif (x <= 9.5e+52)
		tmp = t_2;
	elseif (x <= 7.8e+81)
		tmp = t_3;
	elseif (x <= 7.4e+175)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (x <= -8300000000000.0)
		tmp = t_2;
	elseif (x <= -4.5e-151)
		tmp = t_1;
	elseif (x <= 6.8e-261)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 7e-112)
		tmp = t_1;
	elseif (x <= 3.6e+18)
		tmp = t_3;
	elseif (x <= 9.5e+52)
		tmp = t_2;
	elseif (x <= 7.8e+81)
		tmp = t_3;
	elseif (x <= 7.4e+175)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8300000000000.0], t$95$2, If[LessEqual[x, -4.5e-151], t$95$1, If[LessEqual[x, 6.8e-261], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-112], t$95$1, If[LessEqual[x, 3.6e+18], t$95$3, If[LessEqual[x, 9.5e+52], t$95$2, If[LessEqual[x, 7.8e+81], t$95$3, If[LessEqual[x, 7.4e+175], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.3e12 or 3.6e18 < x < 9.49999999999999994e52 or 7.39999999999999932e175 < x

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 69.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 71.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 71.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 71.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 71.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 71.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 71.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 71.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 69.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -8.3e12 < x < -4.5000000000000002e-151 or 6.8e-261 < x < 6.99999999999999988e-112

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 81.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 84.6%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 61.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   if -4.5000000000000002e-151 < x < 6.8e-261

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 76.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 76.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in i around inf 59.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 59.2%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      3. *-commutative 59.2%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   9. Simplified 59.2%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if 6.99999999999999988e-112 < x < 3.6e18 or 9.49999999999999994e52 < x < 7.8000000000000002e81

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 68.8%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 7.8000000000000002e81 < x < 7.39999999999999932e175

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 77.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 68.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 68.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 64.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 64.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 64.6%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 64.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 64.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8300000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+175}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 8: 56.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ t_2 := x \cdot \left(t \cdot \left(-a\right)\right) - z \cdot \left(b \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (* x z)) (* a (- (* x t) (* b i)))))
        (t_2 (- (* x (* t (- a))) (* z (* b c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -2.9e+111)
     t_3
     (if (<= j -8.2e-21)
       t_2
       (if (<= j 4.6e-274)
         t_1
         (if (<= j 1.85e-175) t_2 (if (<= j 6.8e+75) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)));
	double t_2 = (x * (t * -a)) - (z * (b * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.9e+111) {
		tmp = t_3;
	} else if (j <= -8.2e-21) {
		tmp = t_2;
	} else if (j <= 4.6e-274) {
		tmp = t_1;
	} else if (j <= 1.85e-175) {
		tmp = t_2;
	} else if (j <= 6.8e+75) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)))
    t_2 = (x * (t * -a)) - (z * (b * c))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-2.9d+111)) then
        tmp = t_3
    else if (j <= (-8.2d-21)) then
        tmp = t_2
    else if (j <= 4.6d-274) then
        tmp = t_1
    else if (j <= 1.85d-175) then
        tmp = t_2
    else if (j <= 6.8d+75) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)));
	double t_2 = (x * (t * -a)) - (z * (b * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.9e+111) {
		tmp = t_3;
	} else if (j <= -8.2e-21) {
		tmp = t_2;
	} else if (j <= 4.6e-274) {
		tmp = t_1;
	} else if (j <= 1.85e-175) {
		tmp = t_2;
	} else if (j <= 6.8e+75) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)))
	t_2 = (x * (t * -a)) - (z * (b * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.9e+111:
		tmp = t_3
	elif j <= -8.2e-21:
		tmp = t_2
	elif j <= 4.6e-274:
		tmp = t_1
	elif j <= 1.85e-175:
		tmp = t_2
	elif j <= 6.8e+75:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(x * z)) - Float64(a * Float64(Float64(x * t) - Float64(b * i))))
	t_2 = Float64(Float64(x * Float64(t * Float64(-a))) - Float64(z * Float64(b * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.9e+111)
		tmp = t_3;
	elseif (j <= -8.2e-21)
		tmp = t_2;
	elseif (j <= 4.6e-274)
		tmp = t_1;
	elseif (j <= 1.85e-175)
		tmp = t_2;
	elseif (j <= 6.8e+75)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)));
	t_2 = (x * (t * -a)) - (z * (b * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.9e+111)
		tmp = t_3;
	elseif (j <= -8.2e-21)
		tmp = t_2;
	elseif (j <= 4.6e-274)
		tmp = t_1;
	elseif (j <= 1.85e-175)
		tmp = t_2;
	elseif (j <= 6.8e+75)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e+111], t$95$3, If[LessEqual[j, -8.2e-21], t$95$2, If[LessEqual[j, 4.6e-274], t$95$1, If[LessEqual[j, 1.85e-175], t$95$2, If[LessEqual[j, 6.8e+75], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.9e111 or 6.80000000000000022e75 < j

   1. Initial program 65.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 65.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 65.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 65.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 65.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 65.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 65.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 65.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 65.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 71.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 76.2%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 65.7%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   if -2.9e111 < j < -8.19999999999999988e-21 or 4.59999999999999992e-274 < j < 1.84999999999999999e-175

   1. Initial program 68.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 67.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in j around 0 66.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(z \cdot b\right)} \]

   6. Taylor expanded in y around 0 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - c \cdot \left(b \cdot z\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.7%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} - c \cdot \left(b \cdot z\right) \]

      2. associate-*r* 68.4%

         \[\leadsto \left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) - c \cdot \left(b \cdot z\right) \]

      3. distribute-lft-neg-in 68.4%

         \[\leadsto \color{blue}{\left(-a \cdot t\right) \cdot x} - c \cdot \left(b \cdot z\right) \]

      4. distribute-rgt-neg-in 68.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x - c \cdot \left(b \cdot z\right) \]

      5. associate-*r* 70.8%

         \[\leadsto \left(a \cdot \left(-t\right)\right) \cdot x - \color{blue}{\left(c \cdot b\right) \cdot z} \]

      6. *-commutative 70.8%

         \[\leadsto \left(a \cdot \left(-t\right)\right) \cdot x - \color{blue}{z \cdot \left(c \cdot b\right)} \]

   8. Simplified 70.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right) \cdot x - z \cdot \left(c \cdot b\right)} \]

   if -8.19999999999999988e-21 < j < 4.59999999999999992e-274 or 1.84999999999999999e-175 < j < 6.80000000000000022e75

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 77.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 77.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 77.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 77.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 77.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 73.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 75.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 67.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in c around 0 65.6%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + y \cdot \left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 9: 57.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_3 := x \cdot \left(t \cdot \left(-a\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (* x z)) (* a (- (* x t) (* b i)))))
        (t_2 (+ (* j (- (* t c) (* y i))) (* x (* y z))))
        (t_3 (- (* x (* t (- a))) (* z (* b c)))))
   (if (<= j -2.9e+111)
     t_2
     (if (<= j -7.2e-21)
       t_3
       (if (<= j 6.8e-274)
         t_1
         (if (<= j 6.3e-176) t_3 (if (<= j 7e-91) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)));
	double t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_3 = (x * (t * -a)) - (z * (b * c));
	double tmp;
	if (j <= -2.9e+111) {
		tmp = t_2;
	} else if (j <= -7.2e-21) {
		tmp = t_3;
	} else if (j <= 6.8e-274) {
		tmp = t_1;
	} else if (j <= 6.3e-176) {
		tmp = t_3;
	} else if (j <= 7e-91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)))
    t_2 = (j * ((t * c) - (y * i))) + (x * (y * z))
    t_3 = (x * (t * -a)) - (z * (b * c))
    if (j <= (-2.9d+111)) then
        tmp = t_2
    else if (j <= (-7.2d-21)) then
        tmp = t_3
    else if (j <= 6.8d-274) then
        tmp = t_1
    else if (j <= 6.3d-176) then
        tmp = t_3
    else if (j <= 7d-91) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)));
	double t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_3 = (x * (t * -a)) - (z * (b * c));
	double tmp;
	if (j <= -2.9e+111) {
		tmp = t_2;
	} else if (j <= -7.2e-21) {
		tmp = t_3;
	} else if (j <= 6.8e-274) {
		tmp = t_1;
	} else if (j <= 6.3e-176) {
		tmp = t_3;
	} else if (j <= 7e-91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)))
	t_2 = (j * ((t * c) - (y * i))) + (x * (y * z))
	t_3 = (x * (t * -a)) - (z * (b * c))
	tmp = 0
	if j <= -2.9e+111:
		tmp = t_2
	elif j <= -7.2e-21:
		tmp = t_3
	elif j <= 6.8e-274:
		tmp = t_1
	elif j <= 6.3e-176:
		tmp = t_3
	elif j <= 7e-91:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(x * z)) - Float64(a * Float64(Float64(x * t) - Float64(b * i))))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_3 = Float64(Float64(x * Float64(t * Float64(-a))) - Float64(z * Float64(b * c)))
	tmp = 0.0
	if (j <= -2.9e+111)
		tmp = t_2;
	elseif (j <= -7.2e-21)
		tmp = t_3;
	elseif (j <= 6.8e-274)
		tmp = t_1;
	elseif (j <= 6.3e-176)
		tmp = t_3;
	elseif (j <= 7e-91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * (x * z)) - (a * ((x * t) - (b * i)));
	t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	t_3 = (x * (t * -a)) - (z * (b * c));
	tmp = 0.0;
	if (j <= -2.9e+111)
		tmp = t_2;
	elseif (j <= -7.2e-21)
		tmp = t_3;
	elseif (j <= 6.8e-274)
		tmp = t_1;
	elseif (j <= 6.3e-176)
		tmp = t_3;
	elseif (j <= 7e-91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e+111], t$95$2, If[LessEqual[j, -7.2e-21], t$95$3, If[LessEqual[j, 6.8e-274], t$95$1, If[LessEqual[j, 6.3e-176], t$95$3, If[LessEqual[j, 7e-91], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.9e111 or 6.9999999999999997e-91 < j

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 72.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 71.6%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 65.7%

      \[\leadsto \left(c \cdot t - y \cdot i\right) \cdot j + \color{blue}{\left(y \cdot z\right)} \cdot x \]

   if -2.9e111 < j < -7.19999999999999979e-21 or 6.79999999999999962e-274 < j < 6.30000000000000011e-176

   1. Initial program 68.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 67.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in j around 0 66.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(z \cdot b\right)} \]

   6. Taylor expanded in y around 0 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - c \cdot \left(b \cdot z\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.7%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} - c \cdot \left(b \cdot z\right) \]

      2. associate-*r* 68.4%

         \[\leadsto \left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) - c \cdot \left(b \cdot z\right) \]

      3. distribute-lft-neg-in 68.4%

         \[\leadsto \color{blue}{\left(-a \cdot t\right) \cdot x} - c \cdot \left(b \cdot z\right) \]

      4. distribute-rgt-neg-in 68.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x - c \cdot \left(b \cdot z\right) \]

      5. associate-*r* 70.8%

         \[\leadsto \left(a \cdot \left(-t\right)\right) \cdot x - \color{blue}{\left(c \cdot b\right) \cdot z} \]

      6. *-commutative 70.8%

         \[\leadsto \left(a \cdot \left(-t\right)\right) \cdot x - \color{blue}{z \cdot \left(c \cdot b\right)} \]

   8. Simplified 70.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right) \cdot x - z \cdot \left(c \cdot b\right)} \]

   if -7.19999999999999979e-21 < j < 6.79999999999999962e-274 or 6.30000000000000011e-176 < j < 6.9999999999999997e-91

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 70.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 72.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 67.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in c around 0 70.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + y \cdot \left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 10: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -10500000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-113}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= x -10500000000000.0)
     (- (* x (- (* y z) (* t a))) (* c (* z b)))
     (if (<= x -4.8e-152)
       t_1
       (if (<= x 4.6e-262)
         (* i (- (* a b) (* y j)))
         (if (<= x 6.4e-113)
           (+ t_1 (* x (* y z)))
           (if (<= x 2.5e-49)
             (* b (- (* a i) (* z c)))
             (- (* y (* x z)) (* a (- (* x t) (* b i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (x <= -10500000000000.0) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else if (x <= -4.8e-152) {
		tmp = t_1;
	} else if (x <= 4.6e-262) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 6.4e-113) {
		tmp = t_1 + (x * (y * z));
	} else if (x <= 2.5e-49) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (y * (x * z)) - (a * ((x * t) - (b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (x <= (-10500000000000.0d0)) then
        tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
    else if (x <= (-4.8d-152)) then
        tmp = t_1
    else if (x <= 4.6d-262) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 6.4d-113) then
        tmp = t_1 + (x * (y * z))
    else if (x <= 2.5d-49) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (y * (x * z)) - (a * ((x * t) - (b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (x <= -10500000000000.0) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else if (x <= -4.8e-152) {
		tmp = t_1;
	} else if (x <= 4.6e-262) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 6.4e-113) {
		tmp = t_1 + (x * (y * z));
	} else if (x <= 2.5e-49) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (y * (x * z)) - (a * ((x * t) - (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if x <= -10500000000000.0:
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
	elif x <= -4.8e-152:
		tmp = t_1
	elif x <= 4.6e-262:
		tmp = i * ((a * b) - (y * j))
	elif x <= 6.4e-113:
		tmp = t_1 + (x * (y * z))
	elif x <= 2.5e-49:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (y * (x * z)) - (a * ((x * t) - (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (x <= -10500000000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)));
	elseif (x <= -4.8e-152)
		tmp = t_1;
	elseif (x <= 4.6e-262)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 6.4e-113)
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	elseif (x <= 2.5e-49)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(y * Float64(x * z)) - Float64(a * Float64(Float64(x * t) - Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (x <= -10500000000000.0)
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	elseif (x <= -4.8e-152)
		tmp = t_1;
	elseif (x <= 4.6e-262)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 6.4e-113)
		tmp = t_1 + (x * (y * z));
	elseif (x <= 2.5e-49)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (y * (x * z)) - (a * ((x * t) - (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -10500000000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-152], t$95$1, If[LessEqual[x, 4.6e-262], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e-113], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-49], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.05e13

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 66.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 66.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 66.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 66.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 66.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around 0 71.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(t \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in j around 0 73.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(z \cdot b\right)} \]

   if -1.05e13 < x < -4.8e-152

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 78.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 82.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 60.9%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   if -4.8e-152 < x < 4.6000000000000002e-262

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 81.0%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 81.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in i around inf 62.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 62.2%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 62.2%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      3. *-commutative 62.2%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   9. Simplified 62.2%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if 4.6000000000000002e-262 < x < 6.4000000000000003e-113

   1. Initial program 69.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 69.2%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 63.2%

      \[\leadsto \left(c \cdot t - y \cdot i\right) \cdot j + \color{blue}{\left(y \cdot z\right)} \cdot x \]

   if 6.4000000000000003e-113 < x < 2.4999999999999999e-49

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 100.0%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 2.4999999999999999e-49 < x

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 71.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 73.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 72.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in c around 0 72.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + y \cdot \left(z \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10500000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-152}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - b \cdot i\right)\\ \end{array} \]

Alternative 11: 59.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-284}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))))
   (if (<= y -1.1e-135)
     t_1
     (if (<= y 7e-284)
       (+ (* z (- (* x y) (* b c))) (* i (* a b)))
       (if (<= y 1.4e-126)
         t_1
         (+ (* y (- (* x z) (* i j))) (* t (- (* c j) (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (y <= -1.1e-135) {
		tmp = t_1;
	} else if (y <= 7e-284) {
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	} else if (y <= 1.4e-126) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    if (y <= (-1.1d-135)) then
        tmp = t_1
    else if (y <= 7d-284) then
        tmp = (z * ((x * y) - (b * c))) + (i * (a * b))
    else if (y <= 1.4d-126) then
        tmp = t_1
    else
        tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (y <= -1.1e-135) {
		tmp = t_1;
	} else if (y <= 7e-284) {
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	} else if (y <= 1.4e-126) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if y <= -1.1e-135:
		tmp = t_1
	elif y <= 7e-284:
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b))
	elif y <= 1.4e-126:
		tmp = t_1
	else:
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (y <= -1.1e-135)
		tmp = t_1;
	elseif (y <= 7e-284)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(i * Float64(a * b)));
	elseif (y <= 1.4e-126)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (y <= -1.1e-135)
		tmp = t_1;
	elseif (y <= 7e-284)
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	elseif (y <= 1.4e-126)
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (i * j))) + (t * ((c * j) - (x * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e-135], t$95$1, If[LessEqual[y, 7e-284], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-126], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e-135 or 6.99999999999999951e-284 < y < 1.39999999999999996e-126

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 74.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -1.1e-135 < y < 6.99999999999999951e-284

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 76.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 81.1%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 78.6%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in t around 0 71.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   if 1.39999999999999996e-126 < y

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 63.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 63.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 56.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 68.2%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.2%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 68.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 68.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 68.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 68.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 68.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 68.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 69.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 69.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 69.3%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 69.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 69.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 69.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 69.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-135}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-284}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 12: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -16500000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+90}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -16500000000000.0)
     t_2
     (if (<= x -1.1e-147)
       t_1
       (if (<= x 6.6e-261)
         (* i (- (* a b) (* y j)))
         (if (<= x 5e-112)
           t_1
           (if (<= x 1.82e+19)
             (* b (- (* a i) (* z c)))
             (if (<= x 1.4e+47)
               (+ (* x (* y z)) (* j (* t c)))
               (if (<= x 1.35e+90) (* a (- (* b i) (* x t))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -16500000000000.0) {
		tmp = t_2;
	} else if (x <= -1.1e-147) {
		tmp = t_1;
	} else if (x <= 6.6e-261) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 5e-112) {
		tmp = t_1;
	} else if (x <= 1.82e+19) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.4e+47) {
		tmp = (x * (y * z)) + (j * (t * c));
	} else if (x <= 1.35e+90) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-16500000000000.0d0)) then
        tmp = t_2
    else if (x <= (-1.1d-147)) then
        tmp = t_1
    else if (x <= 6.6d-261) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 5d-112) then
        tmp = t_1
    else if (x <= 1.82d+19) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 1.4d+47) then
        tmp = (x * (y * z)) + (j * (t * c))
    else if (x <= 1.35d+90) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -16500000000000.0) {
		tmp = t_2;
	} else if (x <= -1.1e-147) {
		tmp = t_1;
	} else if (x <= 6.6e-261) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 5e-112) {
		tmp = t_1;
	} else if (x <= 1.82e+19) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.4e+47) {
		tmp = (x * (y * z)) + (j * (t * c));
	} else if (x <= 1.35e+90) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -16500000000000.0:
		tmp = t_2
	elif x <= -1.1e-147:
		tmp = t_1
	elif x <= 6.6e-261:
		tmp = i * ((a * b) - (y * j))
	elif x <= 5e-112:
		tmp = t_1
	elif x <= 1.82e+19:
		tmp = b * ((a * i) - (z * c))
	elif x <= 1.4e+47:
		tmp = (x * (y * z)) + (j * (t * c))
	elif x <= 1.35e+90:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -16500000000000.0)
		tmp = t_2;
	elseif (x <= -1.1e-147)
		tmp = t_1;
	elseif (x <= 6.6e-261)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 5e-112)
		tmp = t_1;
	elseif (x <= 1.82e+19)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 1.4e+47)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(j * Float64(t * c)));
	elseif (x <= 1.35e+90)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -16500000000000.0)
		tmp = t_2;
	elseif (x <= -1.1e-147)
		tmp = t_1;
	elseif (x <= 6.6e-261)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 5e-112)
		tmp = t_1;
	elseif (x <= 1.82e+19)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 1.4e+47)
		tmp = (x * (y * z)) + (j * (t * c));
	elseif (x <= 1.35e+90)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -16500000000000.0], t$95$2, If[LessEqual[x, -1.1e-147], t$95$1, If[LessEqual[x, 6.6e-261], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-112], t$95$1, If[LessEqual[x, 1.82e+19], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+47], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+90], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.65e13 or 1.35e90 < x

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 70.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 70.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 72.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 72.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 72.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 72.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 72.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 72.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 72.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 72.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 72.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 66.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -1.65e13 < x < -1.1000000000000001e-147 or 6.5999999999999996e-261 < x < 5.00000000000000044e-112

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 81.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 84.6%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 61.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   if -1.1000000000000001e-147 < x < 6.5999999999999996e-261

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 76.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 76.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in i around inf 59.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 59.2%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      3. *-commutative 59.2%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   9. Simplified 59.2%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if 5.00000000000000044e-112 < x < 1.82e19

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 70.5%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 1.82e19 < x < 1.39999999999999994e47

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 100.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 86.5%

      \[\leadsto \left(c \cdot t - y \cdot i\right) \cdot j + \color{blue}{\left(y \cdot z\right)} \cdot x \]

   6. Taylor expanded in c around inf 86.5%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j + \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   8. Simplified 86.5%

      \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j + \left(y \cdot z\right) \cdot x \]

   if 1.39999999999999994e47 < x < 1.35e90

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 78.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 78.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 78.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 78.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 78.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 67.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 67.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 67.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 67.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16500000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+90}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 13: 57.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-209}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -1.5e+214)
     t_1
     (if (<= t -4.3e-67)
       (- (* y (- (* x z) (* i j))) (* t (* x a)))
       (if (<= t 1.85e-209)
         (+ (* z (- (* x y) (* b c))) (* i (* a b)))
         (if (<= t 1.35e+23)
           (- (* x (- (* y z) (* t a))) (* y (* i j)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.5e+214) {
		tmp = t_1;
	} else if (t <= -4.3e-67) {
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	} else if (t <= 1.85e-209) {
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	} else if (t <= 1.35e+23) {
		tmp = (x * ((y * z) - (t * a))) - (y * (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-1.5d+214)) then
        tmp = t_1
    else if (t <= (-4.3d-67)) then
        tmp = (y * ((x * z) - (i * j))) - (t * (x * a))
    else if (t <= 1.85d-209) then
        tmp = (z * ((x * y) - (b * c))) + (i * (a * b))
    else if (t <= 1.35d+23) then
        tmp = (x * ((y * z) - (t * a))) - (y * (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.5e+214) {
		tmp = t_1;
	} else if (t <= -4.3e-67) {
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	} else if (t <= 1.85e-209) {
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	} else if (t <= 1.35e+23) {
		tmp = (x * ((y * z) - (t * a))) - (y * (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.5e+214:
		tmp = t_1
	elif t <= -4.3e-67:
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a))
	elif t <= 1.85e-209:
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b))
	elif t <= 1.35e+23:
		tmp = (x * ((y * z) - (t * a))) - (y * (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.5e+214)
		tmp = t_1;
	elseif (t <= -4.3e-67)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(t * Float64(x * a)));
	elseif (t <= 1.85e-209)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(i * Float64(a * b)));
	elseif (t <= 1.35e+23)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(y * Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.5e+214)
		tmp = t_1;
	elseif (t <= -4.3e-67)
		tmp = (y * ((x * z) - (i * j))) - (t * (x * a));
	elseif (t <= 1.85e-209)
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	elseif (t <= 1.35e+23)
		tmp = (x * ((y * z) - (t * a))) - (y * (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+214], t$95$1, If[LessEqual[t, -4.3e-67], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-209], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+23], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5000000000000001e214 or 1.3499999999999999e23 < t

   1. Initial program 58.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 58.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 58.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 60.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 60.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 60.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 60.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 60.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 60.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 60.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 60.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 60.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 60.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 60.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 60.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 60.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 69.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 69.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 69.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 69.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 69.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -1.5000000000000001e214 < t < -4.30000000000000027e-67

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 76.2%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 70.1%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 70.1%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 70.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 70.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 70.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 70.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 70.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 70.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 70.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 70.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 70.1%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 70.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 70.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 70.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 70.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 70.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in x around inf 60.5%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{a \cdot \left(t \cdot x\right)} \]
   9. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(t \cdot x\right) \cdot a} \]

      2. associate-*l* 70.2%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(x \cdot a\right)} \]

      3. *-commutative 70.2%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x\right)} \]

   10. Simplified 70.2%

       \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x\right)} \]

   if -4.30000000000000027e-67 < t < 1.8499999999999999e-209

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 80.0%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 80.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 69.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in t around 0 69.5%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   if 1.8499999999999999e-209 < t < 1.3499999999999999e23

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 70.6%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in c around 0 68.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]
   6. Step-by-step derivation

      1. associate-*r* 65.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y\right) \cdot j\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]

      2. *-commutative 65.0%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(y \cdot i\right)} \cdot j\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]

      3. associate-*r* 68.7%

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(i \cdot j\right)\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]

      4. mul-1-neg 68.7%

         \[\leadsto \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]

      5. distribute-rgt-neg-in 68.7%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]

      6. *-commutative 68.7%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) + \left(y \cdot z - a \cdot t\right) \cdot x \]

      7. distribute-rgt-neg-in 68.7%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]

   7. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-67}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-209}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 14: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{-154} \lor \neg \left(t \leq 4.7 \cdot 10^{-212}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -6.4e-154) (not (<= t 4.7e-212)))
   (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
   (+ (* z (- (* x y) (* b c))) (* i (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -6.4e-154) || !(t <= 4.7e-212)) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-6.4d-154)) .or. (.not. (t <= 4.7d-212))) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else
        tmp = (z * ((x * y) - (b * c))) + (i * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -6.4e-154) || !(t <= 4.7e-212)) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -6.4e-154) or not (t <= 4.7e-212):
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	else:
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -6.4e-154) || !(t <= 4.7e-212))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(i * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -6.4e-154) || ~((t <= 4.7e-212)))
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	else
		tmp = (z * ((x * y) - (b * c))) + (i * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -6.4e-154], N[Not[LessEqual[t, 4.7e-212]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.40000000000000009e-154 or 4.69999999999999998e-212 < t

   1. Initial program 69.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 68.4%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -6.40000000000000009e-154 < t < 4.69999999999999998e-212

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 81.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 81.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 71.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in t around 0 73.7%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{-154} \lor \neg \left(t \leq 4.7 \cdot 10^{-212}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 15: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{-55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j))))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -1e-55)
     t_3
     (if (<= c -6.5e-198)
       t_2
       (if (<= c -3.6e-287)
         t_1
         (if (<= c 5e-23)
           t_2
           (if (<= c 3e+91) t_1 (if (<= c 2.7e+104) (* y (* x z)) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1e-55) {
		tmp = t_3;
	} else if (c <= -6.5e-198) {
		tmp = t_2;
	} else if (c <= -3.6e-287) {
		tmp = t_1;
	} else if (c <= 5e-23) {
		tmp = t_2;
	} else if (c <= 3e+91) {
		tmp = t_1;
	} else if (c <= 2.7e+104) {
		tmp = y * (x * z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = a * ((b * i) - (x * t))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-1d-55)) then
        tmp = t_3
    else if (c <= (-6.5d-198)) then
        tmp = t_2
    else if (c <= (-3.6d-287)) then
        tmp = t_1
    else if (c <= 5d-23) then
        tmp = t_2
    else if (c <= 3d+91) then
        tmp = t_1
    else if (c <= 2.7d+104) then
        tmp = y * (x * z)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1e-55) {
		tmp = t_3;
	} else if (c <= -6.5e-198) {
		tmp = t_2;
	} else if (c <= -3.6e-287) {
		tmp = t_1;
	} else if (c <= 5e-23) {
		tmp = t_2;
	} else if (c <= 3e+91) {
		tmp = t_1;
	} else if (c <= 2.7e+104) {
		tmp = y * (x * z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = a * ((b * i) - (x * t))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1e-55:
		tmp = t_3
	elif c <= -6.5e-198:
		tmp = t_2
	elif c <= -3.6e-287:
		tmp = t_1
	elif c <= 5e-23:
		tmp = t_2
	elif c <= 3e+91:
		tmp = t_1
	elif c <= 2.7e+104:
		tmp = y * (x * z)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1e-55)
		tmp = t_3;
	elseif (c <= -6.5e-198)
		tmp = t_2;
	elseif (c <= -3.6e-287)
		tmp = t_1;
	elseif (c <= 5e-23)
		tmp = t_2;
	elseif (c <= 3e+91)
		tmp = t_1;
	elseif (c <= 2.7e+104)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = a * ((b * i) - (x * t));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1e-55)
		tmp = t_3;
	elseif (c <= -6.5e-198)
		tmp = t_2;
	elseif (c <= -3.6e-287)
		tmp = t_1;
	elseif (c <= 5e-23)
		tmp = t_2;
	elseif (c <= 3e+91)
		tmp = t_1;
	elseif (c <= 2.7e+104)
		tmp = y * (x * z);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e-55], t$95$3, If[LessEqual[c, -6.5e-198], t$95$2, If[LessEqual[c, -3.6e-287], t$95$1, If[LessEqual[c, 5e-23], t$95$2, If[LessEqual[c, 3e+91], t$95$1, If[LessEqual[c, 2.7e+104], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.99999999999999995e-56 or 2.69999999999999985e104 < c

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 58.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   if -9.99999999999999995e-56 < c < -6.5000000000000004e-198 or -3.6000000000000001e-287 < c < 5.0000000000000002e-23

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 78.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 78.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 78.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 55.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 55.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.9%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 55.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -6.5000000000000004e-198 < c < -3.6000000000000001e-287 or 5.0000000000000002e-23 < c < 3.00000000000000006e91

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 72.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 72.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in i around inf 60.9%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 60.9%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 60.9%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      3. *-commutative 60.9%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   9. Simplified 60.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if 3.00000000000000006e91 < c < 2.69999999999999985e104

   1. Initial program 50.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 50.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 50.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 50.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 50.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 50.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 50.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 50.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 26.3%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 26.3%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 51.3%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf 75.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-287}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+91}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 16: 51.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-11}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 11.2:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.16e+35)
     t_2
     (if (<= y -1.95e-11)
       (* i (- (* a b) (* y j)))
       (if (<= y -4.6e-50)
         (* c (- (* t j) (* z b)))
         (if (<= y -8.5e-141)
           t_1
           (if (<= y 7.2e-284)
             (* b (- (* a i) (* z c)))
             (if (<= y 11.2) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.16e+35) {
		tmp = t_2;
	} else if (y <= -1.95e-11) {
		tmp = i * ((a * b) - (y * j));
	} else if (y <= -4.6e-50) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= -8.5e-141) {
		tmp = t_1;
	} else if (y <= 7.2e-284) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 11.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.16d+35)) then
        tmp = t_2
    else if (y <= (-1.95d-11)) then
        tmp = i * ((a * b) - (y * j))
    else if (y <= (-4.6d-50)) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= (-8.5d-141)) then
        tmp = t_1
    else if (y <= 7.2d-284) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 11.2d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.16e+35) {
		tmp = t_2;
	} else if (y <= -1.95e-11) {
		tmp = i * ((a * b) - (y * j));
	} else if (y <= -4.6e-50) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= -8.5e-141) {
		tmp = t_1;
	} else if (y <= 7.2e-284) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 11.2) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.16e+35:
		tmp = t_2
	elif y <= -1.95e-11:
		tmp = i * ((a * b) - (y * j))
	elif y <= -4.6e-50:
		tmp = c * ((t * j) - (z * b))
	elif y <= -8.5e-141:
		tmp = t_1
	elif y <= 7.2e-284:
		tmp = b * ((a * i) - (z * c))
	elif y <= 11.2:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.16e+35)
		tmp = t_2;
	elseif (y <= -1.95e-11)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (y <= -4.6e-50)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= -8.5e-141)
		tmp = t_1;
	elseif (y <= 7.2e-284)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 11.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.16e+35)
		tmp = t_2;
	elseif (y <= -1.95e-11)
		tmp = i * ((a * b) - (y * j));
	elseif (y <= -4.6e-50)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= -8.5e-141)
		tmp = t_1;
	elseif (y <= 7.2e-284)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 11.2)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.16e+35], t$95$2, If[LessEqual[y, -1.95e-11], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-50], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-141], t$95$1, If[LessEqual[y, 7.2e-284], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 11.2], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.1600000000000001e35 or 11.199999999999999 < y

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 62.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 62.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 62.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 62.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 62.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 62.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 62.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 64.0%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 65.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 61.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 61.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 61.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.1600000000000001e35 < y < -1.95000000000000005e-11

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 88.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 88.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in i around inf 88.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 88.8%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 88.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      3. *-commutative 88.8%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   9. Simplified 88.8%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if -1.95000000000000005e-11 < y < -4.60000000000000039e-50

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 86.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.6%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 86.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 86.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 54.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   if -4.60000000000000039e-50 < y < -8.50000000000000021e-141 or 7.2000000000000004e-284 < y < 11.199999999999999

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 77.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 78.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 78.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 59.3%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 59.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 59.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 59.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 59.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -8.50000000000000021e-141 < y < 7.2000000000000004e-284

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 70.9%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-11}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 11.2:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 17: 51.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -85000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -85000000.0)
     t_2
     (if (<= y -1.9e-143)
       t_1
       (if (<= y 2.8e-284)
         (* b (- (* a i) (* z c)))
         (if (<= y 1e-95)
           t_1
           (if (<= y 1.05e+57)
             (* a (- (* b i) (* x t)))
             (if (<= y 8e+68) (* j (- (* t c) (* y i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -85000000.0) {
		tmp = t_2;
	} else if (y <= -1.9e-143) {
		tmp = t_1;
	} else if (y <= 2.8e-284) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 1e-95) {
		tmp = t_1;
	} else if (y <= 1.05e+57) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 8e+68) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-85000000.0d0)) then
        tmp = t_2
    else if (y <= (-1.9d-143)) then
        tmp = t_1
    else if (y <= 2.8d-284) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 1d-95) then
        tmp = t_1
    else if (y <= 1.05d+57) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 8d+68) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -85000000.0) {
		tmp = t_2;
	} else if (y <= -1.9e-143) {
		tmp = t_1;
	} else if (y <= 2.8e-284) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 1e-95) {
		tmp = t_1;
	} else if (y <= 1.05e+57) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 8e+68) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -85000000.0:
		tmp = t_2
	elif y <= -1.9e-143:
		tmp = t_1
	elif y <= 2.8e-284:
		tmp = b * ((a * i) - (z * c))
	elif y <= 1e-95:
		tmp = t_1
	elif y <= 1.05e+57:
		tmp = a * ((b * i) - (x * t))
	elif y <= 8e+68:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -85000000.0)
		tmp = t_2;
	elseif (y <= -1.9e-143)
		tmp = t_1;
	elseif (y <= 2.8e-284)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 1e-95)
		tmp = t_1;
	elseif (y <= 1.05e+57)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 8e+68)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -85000000.0)
		tmp = t_2;
	elseif (y <= -1.9e-143)
		tmp = t_1;
	elseif (y <= 2.8e-284)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 1e-95)
		tmp = t_1;
	elseif (y <= 1.05e+57)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 8e+68)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -85000000.0], t$95$2, If[LessEqual[y, -1.9e-143], t$95$1, If[LessEqual[y, 2.8e-284], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-95], t$95$1, If[LessEqual[y, 1.05e+57], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+68], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.5e7 or 7.99999999999999962e68 < y

   1. Initial program 61.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 61.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 61.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 61.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 61.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 61.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 61.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 61.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 61.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 63.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 63.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 63.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 63.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 63.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 63.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -8.5e7 < y < -1.89999999999999991e-143 or 2.8000000000000003e-284 < y < 9.99999999999999989e-96

   1. Initial program 80.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 80.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 80.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 80.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 80.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 80.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 80.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 80.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 80.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 80.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 80.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 80.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 80.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 57.7%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 57.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 57.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 57.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -1.89999999999999991e-143 < y < 2.8000000000000003e-284

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 70.9%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 9.99999999999999989e-96 < y < 1.04999999999999995e57

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 78.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 78.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 78.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 78.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 78.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 78.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 58.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 58.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.9%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 58.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if 1.04999999999999995e57 < y < 7.99999999999999962e68

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 66.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 100.0%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 100.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -85000000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 10^{-95}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 18: 28.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c\right) \cdot \left(-z\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+227}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* b c) (- z))) (t_2 (* t (* c j))))
   (if (<= c -1.65e+165)
     t_2
     (if (<= c -5.3e+113)
       t_1
       (if (<= c -1.5e-55)
         t_2
         (if (<= c 4.9e-64)
           (* x (* t (- a)))
           (if (<= c 9.2e+114)
             (* y (* x z))
             (if (<= c 7.6e+171)
               (* t (* x (- a)))
               (if (<= c 2.1e+227) t_1 (* j (* t c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * c) * -z;
	double t_2 = t * (c * j);
	double tmp;
	if (c <= -1.65e+165) {
		tmp = t_2;
	} else if (c <= -5.3e+113) {
		tmp = t_1;
	} else if (c <= -1.5e-55) {
		tmp = t_2;
	} else if (c <= 4.9e-64) {
		tmp = x * (t * -a);
	} else if (c <= 9.2e+114) {
		tmp = y * (x * z);
	} else if (c <= 7.6e+171) {
		tmp = t * (x * -a);
	} else if (c <= 2.1e+227) {
		tmp = t_1;
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) * -z
    t_2 = t * (c * j)
    if (c <= (-1.65d+165)) then
        tmp = t_2
    else if (c <= (-5.3d+113)) then
        tmp = t_1
    else if (c <= (-1.5d-55)) then
        tmp = t_2
    else if (c <= 4.9d-64) then
        tmp = x * (t * -a)
    else if (c <= 9.2d+114) then
        tmp = y * (x * z)
    else if (c <= 7.6d+171) then
        tmp = t * (x * -a)
    else if (c <= 2.1d+227) then
        tmp = t_1
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * c) * -z;
	double t_2 = t * (c * j);
	double tmp;
	if (c <= -1.65e+165) {
		tmp = t_2;
	} else if (c <= -5.3e+113) {
		tmp = t_1;
	} else if (c <= -1.5e-55) {
		tmp = t_2;
	} else if (c <= 4.9e-64) {
		tmp = x * (t * -a);
	} else if (c <= 9.2e+114) {
		tmp = y * (x * z);
	} else if (c <= 7.6e+171) {
		tmp = t * (x * -a);
	} else if (c <= 2.1e+227) {
		tmp = t_1;
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * c) * -z
	t_2 = t * (c * j)
	tmp = 0
	if c <= -1.65e+165:
		tmp = t_2
	elif c <= -5.3e+113:
		tmp = t_1
	elif c <= -1.5e-55:
		tmp = t_2
	elif c <= 4.9e-64:
		tmp = x * (t * -a)
	elif c <= 9.2e+114:
		tmp = y * (x * z)
	elif c <= 7.6e+171:
		tmp = t * (x * -a)
	elif c <= 2.1e+227:
		tmp = t_1
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * c) * Float64(-z))
	t_2 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -1.65e+165)
		tmp = t_2;
	elseif (c <= -5.3e+113)
		tmp = t_1;
	elseif (c <= -1.5e-55)
		tmp = t_2;
	elseif (c <= 4.9e-64)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (c <= 9.2e+114)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 7.6e+171)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 2.1e+227)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * c) * -z;
	t_2 = t * (c * j);
	tmp = 0.0;
	if (c <= -1.65e+165)
		tmp = t_2;
	elseif (c <= -5.3e+113)
		tmp = t_1;
	elseif (c <= -1.5e-55)
		tmp = t_2;
	elseif (c <= 4.9e-64)
		tmp = x * (t * -a);
	elseif (c <= 9.2e+114)
		tmp = y * (x * z);
	elseif (c <= 7.6e+171)
		tmp = t * (x * -a);
	elseif (c <= 2.1e+227)
		tmp = t_1;
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e+165], t$95$2, If[LessEqual[c, -5.3e+113], t$95$1, If[LessEqual[c, -1.5e-55], t$95$2, If[LessEqual[c, 4.9e-64], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e+114], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e+171], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e+227], t$95$1, N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.6499999999999999e165 or -5.29999999999999967e113 < c < -1.50000000000000008e-55

   1. Initial program 69.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 64.3%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 75.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 75.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 75.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 75.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 75.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 75.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 75.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 77.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 77.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 77.3%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 77.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 77.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 77.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 77.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 77.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in c around inf 47.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      2. associate-*l* 53.2%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

      3. *-commutative 53.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   10. Simplified 53.2%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if -1.6499999999999999e165 < c < -5.29999999999999967e113 or 7.6000000000000004e171 < c < 2.10000000000000019e227

   1. Initial program 65.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 65.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 65.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 65.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 65.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 65.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 65.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 65.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 65.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 69.1%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around 0 51.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot b\right)\right)} \cdot z \]
   6. Step-by-step derivation

      1. neg-mul-1 51.4%

         \[\leadsto \color{blue}{\left(-c \cdot b\right)} \cdot z \]

      2. distribute-rgt-neg-in 51.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(-b\right)\right)} \cdot z \]

   7. Simplified 51.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(-b\right)\right)} \cdot z \]

   if -1.50000000000000008e-55 < c < 4.9000000000000002e-64

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 61.9%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 61.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 61.4%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 61.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 61.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 61.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 61.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 61.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 61.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 62.4%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 62.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 62.4%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 62.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 62.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 62.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 62.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 62.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in a around inf 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 34.5%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 37.4%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-lft-neg-in 37.4%

         \[\leadsto \color{blue}{\left(-a \cdot t\right) \cdot x} \]

      4. distribute-rgt-neg-in 37.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x \]

   10. Simplified 37.4%

       \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right) \cdot x} \]

   if 4.9000000000000002e-64 < c < 9.2000000000000001e114

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 72.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 64.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 66.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 58.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf 38.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 9.2000000000000001e114 < c < 7.6000000000000004e171

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 77.0%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 77.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 54.4%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   8. Step-by-step derivation

      1. *-commutative 54.4%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 54.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 54.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 54.4%

         \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) \]

   9. Simplified 54.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right)} \]

   10. Taylor expanded in c around 0 48.2%

       \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 48.2%

          \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

       2. *-commutative 48.2%

          \[\leadsto t \cdot \left(-\color{blue}{x \cdot a}\right) \]

       3. distribute-rgt-neg-in 48.2%

          \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   12. Simplified 48.2%

       \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   if 2.10000000000000019e227 < c

   1. Initial program 48.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 48.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 48.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 48.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 48.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 48.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 48.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 48.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 48.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 66.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 71.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 64.1%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   8. Taylor expanded in c around inf 64.2%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j \]
   9. Step-by-step derivation

      1. *-commutative 64.2%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   10. Simplified 64.2%

       \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{+113}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+227}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 19: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -2.8e+165)
     t_1
     (if (<= c -6.8e+120)
       (* z (* x y))
       (if (<= c -2.6e-56)
         t_1
         (if (<= c 1.6e-57)
           (* t (* x (- a)))
           (if (<= c 4.7e+110) (* y (* x z)) (* j (* t c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -2.8e+165) {
		tmp = t_1;
	} else if (c <= -6.8e+120) {
		tmp = z * (x * y);
	} else if (c <= -2.6e-56) {
		tmp = t_1;
	} else if (c <= 1.6e-57) {
		tmp = t * (x * -a);
	} else if (c <= 4.7e+110) {
		tmp = y * (x * z);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (c <= (-2.8d+165)) then
        tmp = t_1
    else if (c <= (-6.8d+120)) then
        tmp = z * (x * y)
    else if (c <= (-2.6d-56)) then
        tmp = t_1
    else if (c <= 1.6d-57) then
        tmp = t * (x * -a)
    else if (c <= 4.7d+110) then
        tmp = y * (x * z)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -2.8e+165) {
		tmp = t_1;
	} else if (c <= -6.8e+120) {
		tmp = z * (x * y);
	} else if (c <= -2.6e-56) {
		tmp = t_1;
	} else if (c <= 1.6e-57) {
		tmp = t * (x * -a);
	} else if (c <= 4.7e+110) {
		tmp = y * (x * z);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -2.8e+165:
		tmp = t_1
	elif c <= -6.8e+120:
		tmp = z * (x * y)
	elif c <= -2.6e-56:
		tmp = t_1
	elif c <= 1.6e-57:
		tmp = t * (x * -a)
	elif c <= 4.7e+110:
		tmp = y * (x * z)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -2.8e+165)
		tmp = t_1;
	elseif (c <= -6.8e+120)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= -2.6e-56)
		tmp = t_1;
	elseif (c <= 1.6e-57)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 4.7e+110)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (c <= -2.8e+165)
		tmp = t_1;
	elseif (c <= -6.8e+120)
		tmp = z * (x * y);
	elseif (c <= -2.6e-56)
		tmp = t_1;
	elseif (c <= 1.6e-57)
		tmp = t * (x * -a);
	elseif (c <= 4.7e+110)
		tmp = y * (x * z);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e+165], t$95$1, If[LessEqual[c, -6.8e+120], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.6e-56], t$95$1, If[LessEqual[c, 1.6e-57], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.7e+110], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.7999999999999998e165 or -6.79999999999999998e120 < c < -2.59999999999999997e-56

   1. Initial program 70.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 62.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 72.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 72.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 72.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 74.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 74.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 74.5%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 74.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 74.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 74.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 74.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 74.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      2. associate-*l* 51.4%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

      3. *-commutative 51.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   10. Simplified 51.4%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if -2.7999999999999998e165 < c < -6.79999999999999998e120

   1. Initial program 59.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 59.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 59.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 67.9%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 44.4%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -2.59999999999999997e-56 < c < 1.6e-57

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 71.2%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 76.2%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 39.9%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   8. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 39.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 39.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 39.9%

         \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) \]

   9. Simplified 39.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right)} \]

   10. Taylor expanded in c around 0 37.4%

       \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 37.4%

          \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

       2. *-commutative 37.4%

          \[\leadsto t \cdot \left(-\color{blue}{x \cdot a}\right) \]

       3. distribute-rgt-neg-in 37.4%

          \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   12. Simplified 37.4%

       \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   if 1.6e-57 < c < 4.6999999999999998e110

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 66.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 68.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 59.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf 39.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 4.6999999999999998e110 < c

   1. Initial program 60.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 60.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 60.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 60.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 73.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 75.2%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 53.8%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   8. Taylor expanded in c around inf 43.7%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j \]
   9. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 20: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -1.55e+165)
     t_1
     (if (<= c -2.55e+119)
       (* z (* x y))
       (if (<= c -8.2e-56)
         t_1
         (if (<= c 8.5e-60)
           (* x (* t (- a)))
           (if (<= c 8.6e+111) (* y (* x z)) (* j (* t c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -1.55e+165) {
		tmp = t_1;
	} else if (c <= -2.55e+119) {
		tmp = z * (x * y);
	} else if (c <= -8.2e-56) {
		tmp = t_1;
	} else if (c <= 8.5e-60) {
		tmp = x * (t * -a);
	} else if (c <= 8.6e+111) {
		tmp = y * (x * z);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (c <= (-1.55d+165)) then
        tmp = t_1
    else if (c <= (-2.55d+119)) then
        tmp = z * (x * y)
    else if (c <= (-8.2d-56)) then
        tmp = t_1
    else if (c <= 8.5d-60) then
        tmp = x * (t * -a)
    else if (c <= 8.6d+111) then
        tmp = y * (x * z)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -1.55e+165) {
		tmp = t_1;
	} else if (c <= -2.55e+119) {
		tmp = z * (x * y);
	} else if (c <= -8.2e-56) {
		tmp = t_1;
	} else if (c <= 8.5e-60) {
		tmp = x * (t * -a);
	} else if (c <= 8.6e+111) {
		tmp = y * (x * z);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -1.55e+165:
		tmp = t_1
	elif c <= -2.55e+119:
		tmp = z * (x * y)
	elif c <= -8.2e-56:
		tmp = t_1
	elif c <= 8.5e-60:
		tmp = x * (t * -a)
	elif c <= 8.6e+111:
		tmp = y * (x * z)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -1.55e+165)
		tmp = t_1;
	elseif (c <= -2.55e+119)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= -8.2e-56)
		tmp = t_1;
	elseif (c <= 8.5e-60)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (c <= 8.6e+111)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (c <= -1.55e+165)
		tmp = t_1;
	elseif (c <= -2.55e+119)
		tmp = z * (x * y);
	elseif (c <= -8.2e-56)
		tmp = t_1;
	elseif (c <= 8.5e-60)
		tmp = x * (t * -a);
	elseif (c <= 8.6e+111)
		tmp = y * (x * z);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+165], t$95$1, If[LessEqual[c, -2.55e+119], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.2e-56], t$95$1, If[LessEqual[c, 8.5e-60], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.6e+111], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.5500000000000001e165 or -2.54999999999999992e119 < c < -8.2000000000000003e-56

   1. Initial program 70.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 62.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 72.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 72.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 72.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 74.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 74.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 74.5%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 74.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 74.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 74.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 74.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 74.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   9. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      2. associate-*l* 51.4%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

      3. *-commutative 51.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   10. Simplified 51.4%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if -1.5500000000000001e165 < c < -2.54999999999999992e119

   1. Initial program 59.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 59.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 59.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 59.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 67.9%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 44.4%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -8.2000000000000003e-56 < c < 8.50000000000000044e-60

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 61.9%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 61.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 61.4%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 61.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 61.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 61.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 61.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 61.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 61.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 62.4%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 62.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 62.4%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 62.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 62.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 62.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 62.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 62.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in a around inf 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 34.5%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 37.4%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-lft-neg-in 37.4%

         \[\leadsto \color{blue}{\left(-a \cdot t\right) \cdot x} \]

      4. distribute-rgt-neg-in 37.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x \]

   10. Simplified 37.4%

       \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right) \cdot x} \]

   if 8.50000000000000044e-60 < c < 8.59999999999999987e111

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 66.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 68.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 59.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf 39.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 8.59999999999999987e111 < c

   1. Initial program 60.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 60.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 60.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 60.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 60.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 73.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 75.2%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 53.8%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   8. Taylor expanded in c around inf 43.7%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j \]
   9. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 21: 52.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{-56} \lor \neg \left(c \leq 1.05 \cdot 10^{+93}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -4.6e-56) (not (<= c 1.05e+93)))
   (* c (- (* t j) (* z b)))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -4.6e-56) || !(c <= 1.05e+93)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-4.6d-56)) .or. (.not. (c <= 1.05d+93))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -4.6e-56) || !(c <= 1.05e+93)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -4.6e-56) or not (c <= 1.05e+93):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -4.6e-56) || !(c <= 1.05e+93))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -4.6e-56) || ~((c <= 1.05e+93)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -4.6e-56], N[Not[LessEqual[c, 1.05e+93]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.60000000000000005e-56 or 1.0499999999999999e93 < c

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 66.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 66.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 66.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 66.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 66.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 66.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 58.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   if -4.60000000000000005e-56 < c < 1.0499999999999999e93

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 77.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 77.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 77.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 77.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 77.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 77.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 77.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 77.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 50.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 50.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{-56} \lor \neg \left(c \leq 1.05 \cdot 10^{+93}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 22: 52.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+21} \lor \neg \left(t \leq 4.1 \cdot 10^{-32}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -7.4e+21) (not (<= t 4.1e-32)))
   (* t (- (* c j) (* x a)))
   (* i (- (* a b) (* y j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -7.4e+21) || !(t <= 4.1e-32)) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-7.4d+21)) .or. (.not. (t <= 4.1d-32))) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = i * ((a * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -7.4e+21) || !(t <= 4.1e-32)) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -7.4e+21) or not (t <= 4.1e-32):
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = i * ((a * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -7.4e+21) || !(t <= 4.1e-32))
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -7.4e+21) || ~((t <= 4.1e-32)))
		tmp = t * ((c * j) - (x * a));
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -7.4e+21], N[Not[LessEqual[t, 4.1e-32]], $MachinePrecision]], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4e21 or 4.09999999999999975e-32 < t

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 64.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 64.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 65.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 65.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 65.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 65.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 65.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 65.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 64.0%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 64.0%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 64.0%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 64.0%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 64.0%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -7.4e21 < t < 4.09999999999999975e-32

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 81.8%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 81.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in i around inf 53.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 53.0%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 53.0%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      3. *-commutative 53.0%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   9. Simplified 53.0%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+21} \lor \neg \left(t \leq 4.1 \cdot 10^{-32}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 23: 42.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.75e+186)
   (* z (* x y))
   (if (<= y 1.4e+101) (* a (- (* b i) (* x t))) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.75e+186) {
		tmp = z * (x * y);
	} else if (y <= 1.4e+101) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.75d+186)) then
        tmp = z * (x * y)
    else if (y <= 1.4d+101) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.75e+186) {
		tmp = z * (x * y);
	} else if (y <= 1.4e+101) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.75e+186:
		tmp = z * (x * y)
	elif y <= 1.4e+101:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.75e+186)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 1.4e+101)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.75e+186)
		tmp = z * (x * y);
	elseif (y <= 1.4e+101)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.75e+186], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+101], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999993e186

   1. Initial program 58.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 52.9%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 49.6%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -1.74999999999999993e186 < y < 1.39999999999999991e101

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 77.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 78.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 78.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 78.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 78.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 78.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 78.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 47.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 47.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 47.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if 1.39999999999999991e101 < y

   1. Initial program 54.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 54.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 54.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 54.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 54.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 54.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 54.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 54.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 54.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 52.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 52.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 55.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf 48.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 24: 30.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-222}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -1.75e+25)
     t_1
     (if (<= t -1.1e-222)
       (* a (* b i))
       (if (<= t 9.6e+21) (* y (* x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.75e+25) {
		tmp = t_1;
	} else if (t <= -1.1e-222) {
		tmp = a * (b * i);
	} else if (t <= 9.6e+21) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-1.75d+25)) then
        tmp = t_1
    else if (t <= (-1.1d-222)) then
        tmp = a * (b * i)
    else if (t <= 9.6d+21) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.75e+25) {
		tmp = t_1;
	} else if (t <= -1.1e-222) {
		tmp = a * (b * i);
	} else if (t <= 9.6e+21) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -1.75e+25:
		tmp = t_1
	elif t <= -1.1e-222:
		tmp = a * (b * i)
	elif t <= 9.6e+21:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -1.75e+25)
		tmp = t_1;
	elseif (t <= -1.1e-222)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= 9.6e+21)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -1.75e+25)
		tmp = t_1;
	elseif (t <= -1.1e-222)
		tmp = a * (b * i);
	elseif (t <= 9.6e+21)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+25], t$95$1, If[LessEqual[t, -1.1e-222], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+21], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e25 or 9.6e21 < t

   1. Initial program 61.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 61.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 61.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 70.2%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 68.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.4%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 68.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 68.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 68.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 68.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 68.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 68.4%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 70.2%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 70.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 70.2%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 70.2%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 70.2%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 70.2%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 70.2%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 70.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in c around inf 40.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.75e25 < t < -1.1e-222

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 79.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 50.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -1.1e-222 < t < 9.6e21

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 82.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 82.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 66.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf 30.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-222}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 25: 30.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -6.6e+26)
   (* c (* t j))
   (if (<= t -2.7e-223)
     (* a (* b i))
     (if (<= t 3.45e+22) (* y (* x z)) (* j (* t c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -6.6e+26) {
		tmp = c * (t * j);
	} else if (t <= -2.7e-223) {
		tmp = a * (b * i);
	} else if (t <= 3.45e+22) {
		tmp = y * (x * z);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-6.6d+26)) then
        tmp = c * (t * j)
    else if (t <= (-2.7d-223)) then
        tmp = a * (b * i)
    else if (t <= 3.45d+22) then
        tmp = y * (x * z)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -6.6e+26) {
		tmp = c * (t * j);
	} else if (t <= -2.7e-223) {
		tmp = a * (b * i);
	} else if (t <= 3.45e+22) {
		tmp = y * (x * z);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -6.6e+26:
		tmp = c * (t * j)
	elif t <= -2.7e-223:
		tmp = a * (b * i)
	elif t <= 3.45e+22:
		tmp = y * (x * z)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -6.6e+26)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -2.7e-223)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= 3.45e+22)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -6.6e+26)
		tmp = c * (t * j);
	elseif (t <= -2.7e-223)
		tmp = a * (b * i);
	elseif (t <= 3.45e+22)
		tmp = y * (x * z);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -6.6e+26], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-223], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.45e+22], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.59999999999999987e26

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 63.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 63.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 78.9%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 76.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 76.9%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 76.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 76.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 76.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 76.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 76.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 76.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 76.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 76.9%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 76.9%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 76.9%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 76.9%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 76.9%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 76.9%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in c around inf 43.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -6.59999999999999987e26 < t < -2.69999999999999988e-223

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 79.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 79.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 79.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 50.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -2.69999999999999988e-223 < t < 3.4499999999999999e22

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 82.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 82.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around 0 66.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right) + -1 \cdot \left(\left(c \cdot b - y \cdot x\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf 30.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 3.4499999999999999e22 < t

   1. Initial program 60.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 60.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 60.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 60.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 60.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 60.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 60.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 60.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 60.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 60.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 66.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 42.3%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   8. Taylor expanded in c around inf 37.4%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j \]
   9. Step-by-step derivation

      1. *-commutative 37.4%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   10. Simplified 37.4%

       \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 26: 31.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+26} \lor \neg \left(t \leq 1.55 \cdot 10^{-37}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -8.5e+26) (not (<= t 1.55e-37))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -8.5e+26) || !(t <= 1.55e-37)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-8.5d+26)) .or. (.not. (t <= 1.55d-37))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -8.5e+26) || !(t <= 1.55e-37)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -8.5e+26) or not (t <= 1.55e-37):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -8.5e+26) || !(t <= 1.55e-37))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -8.5e+26) || ~((t <= 1.55e-37)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -8.5e+26], N[Not[LessEqual[t, 1.55e-37]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5e26 or 1.54999999999999997e-37 < t

   1. Initial program 64.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 71.8%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in t around -inf 69.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right) + \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right)} \]

      2. +-commutative 69.5%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + -1 \cdot \left(\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      3. mul-1-neg 69.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \color{blue}{\left(-\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t\right)} \]

      4. unsub-neg 69.5%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t} \]

      5. mul-1-neg 69.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      6. distribute-rgt-neg-in 69.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + \color{blue}{y \cdot \left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      7. mul-1-neg 69.5%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      8. distribute-lft-in 71.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      9. mul-1-neg 71.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      10. unsub-neg 71.1%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right) \cdot t \]

      11. *-commutative 71.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{t \cdot \left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \]

      12. mul-1-neg 71.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \]

      13. unsub-neg 71.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \color{blue}{\left(a \cdot x - c \cdot j\right)} \]

      14. *-commutative 71.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(\color{blue}{x \cdot a} - c \cdot j\right) \]

   7. Simplified 71.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - t \cdot \left(x \cdot a - c \cdot j\right)} \]

   8. Taylor expanded in c around inf 37.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -8.5e26 < t < 1.54999999999999997e-37

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 79.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 79.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 79.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 79.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 79.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 79.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 79.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 79.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 79.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 39.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 39.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 39.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 39.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 39.3%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 35.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+26} \lor \neg \left(t \leq 1.55 \cdot 10^{-37}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 27: 23.0% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x 2.2e-32) (* b (* a i)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= 2.2e-32) {
		tmp = b * (a * i);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= 2.2d-32) then
        tmp = b * (a * i)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= 2.2e-32) {
		tmp = b * (a * i);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= 2.2e-32:
		tmp = b * (a * i)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= 2.2e-32)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= 2.2e-32)
		tmp = b * (a * i);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, 2.2e-32], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.2e-32

   1. Initial program 69.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 69.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 69.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 70.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 70.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 70.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 70.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 70.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 70.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 70.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 70.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 70.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 70.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 70.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 70.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 70.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 37.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 37.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 37.6%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 37.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 37.6%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 19.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 23.2%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

      2. *-commutative 23.2%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   9. Simplified 23.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   if 2.2e-32 < x

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 76.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 49.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 49.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 49.2%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 49.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 49.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 36.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 28: 23.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. sub-neg 71.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. associate-+l+ 71.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   3. fma-def 72.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   4. +-commutative 72.6%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   5. fma-def 72.6%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   6. sub-neg 72.6%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   7. +-commutative 72.6%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   8. *-commutative 72.6%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   9. distribute-rgt-neg-in 72.6%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   10. fma-def 72.6%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   11. *-commutative 72.6%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   12. distribute-rgt-neg-in 72.6%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

   13. sub-neg 72.6%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

   14. distribute-neg-in 72.6%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

   15. unsub-neg 72.6%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

3. Simplified 73.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

4. Taylor expanded in a around inf 41.3%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
5. Step-by-step derivation

   1. +-commutative 41.3%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 41.3%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 41.3%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

6. Simplified 41.3%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

7. Taylor expanded in i around inf 24.7%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

8. Final simplification 24.7%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))