Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.7% → 81.7%

Time: 27.8s

Alternatives: 25

Speedup: 0.5×

• 57.7% 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: 73.7% 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: 81.7% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (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))
     (* 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 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 = a * ((b * i) - (x * t));
	}
	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(a * Float64(Float64(b * i) - Float64(x * t)));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $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 92.1%

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

      1. sub-neg 92.1%

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

      2. associate-+l+ 92.1%

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

      3. fma-def 92.1%

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

      4. +-commutative 92.1%

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

      5. fma-def 92.1%

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

      6. *-commutative 92.1%

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

      7. *-commutative 92.1%

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

      8. distribute-rgt-neg-in 92.1%

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

      9. sub-neg 92.1%

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

      10. +-commutative 92.1%

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

      11. distribute-neg-in 92.1%

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

      12. unsub-neg 92.1%

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

      13. remove-double-neg 92.1%

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

      14. *-commutative 92.1%

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

      15. *-commutative 92.1%

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

   3. Simplified 92.1%

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

   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. sub-neg 0.0%

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

      2. associate-+l+ 0.0%

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

      3. fma-def 13.6%

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

      4. +-commutative 13.6%

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

      5. fma-def 15.9%

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

      6. *-commutative 15.9%

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

      7. *-commutative 15.9%

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

      8. distribute-rgt-neg-in 15.9%

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

      9. sub-neg 15.9%

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

      10. +-commutative 15.9%

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

      11. distribute-neg-in 15.9%

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

      12. unsub-neg 15.9%

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

      13. remove-double-neg 15.9%

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

      14. *-commutative 15.9%

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

      15. *-commutative 15.9%

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

   3. Simplified 15.9%

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

   4. Taylor expanded in a around inf 51.0%

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

   5. Taylor expanded in a around 0 51.0%

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

      1. *-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. *-commutative 51.0%

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

      4. unsub-neg 51.0%

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

   7. Simplified 51.0%

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

4. Final simplification 85.0%

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

Alternative 2: 81.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* j (- (* t c) (* y i)))
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c)))))))
   (if (<= t_1 INFINITY) t_1 (* 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 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 = a * ((b * i) - (x * t));
	}
	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 = a * ((b * i) - (x * t));
	}
	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 = a * ((b * i) - (x * t))
	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(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)
	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 = a * ((b * i) - (x * t));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $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 92.1%

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

   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. sub-neg 0.0%

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

      2. associate-+l+ 0.0%

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

      3. fma-def 13.6%

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

      4. +-commutative 13.6%

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

      5. fma-def 15.9%

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

      6. *-commutative 15.9%

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

      7. *-commutative 15.9%

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

      8. distribute-rgt-neg-in 15.9%

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

      9. sub-neg 15.9%

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

      10. +-commutative 15.9%

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

      11. distribute-neg-in 15.9%

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

      12. unsub-neg 15.9%

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

      13. remove-double-neg 15.9%

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

      14. *-commutative 15.9%

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

      15. *-commutative 15.9%

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

   3. Simplified 15.9%

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

   4. Taylor expanded in a around inf 51.0%

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

   5. Taylor expanded in a around 0 51.0%

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

      1. *-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. *-commutative 51.0%

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

      4. unsub-neg 51.0%

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

   7. Simplified 51.0%

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

4. Final simplification 85.0%

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

Alternative 3: 58.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.55 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 195:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* y (* x z)) (* b (- (* a i) (* z c)))))
        (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -2.8e+255)
     t_2
     (if (<= t -7.2e+233)
       t_1
       (if (<= t -2.4e+51)
         t_2
         (if (<= t -4.55e-35)
           (+ (* j (- (* t c) (* y i))) (* x (* y z)))
           (if (<= t 195.0) 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)) + (b * ((a * i) - (z * c)));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.8e+255) {
		tmp = t_2;
	} else if (t <= -7.2e+233) {
		tmp = t_1;
	} else if (t <= -2.4e+51) {
		tmp = t_2;
	} else if (t <= -4.55e-35) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (t <= 195.0) {
		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 = (y * (x * z)) + (b * ((a * i) - (z * c)))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-2.8d+255)) then
        tmp = t_2
    else if (t <= (-7.2d+233)) then
        tmp = t_1
    else if (t <= (-2.4d+51)) then
        tmp = t_2
    else if (t <= (-4.55d-35)) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (t <= 195.0d0) 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)) + (b * ((a * i) - (z * c)));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.8e+255) {
		tmp = t_2;
	} else if (t <= -7.2e+233) {
		tmp = t_1;
	} else if (t <= -2.4e+51) {
		tmp = t_2;
	} else if (t <= -4.55e-35) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (t <= 195.0) {
		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)) + (b * ((a * i) - (z * c)))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.8e+255:
		tmp = t_2
	elif t <= -7.2e+233:
		tmp = t_1
	elif t <= -2.4e+51:
		tmp = t_2
	elif t <= -4.55e-35:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif t <= 195.0:
		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(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.8e+255)
		tmp = t_2;
	elseif (t <= -7.2e+233)
		tmp = t_1;
	elseif (t <= -2.4e+51)
		tmp = t_2;
	elseif (t <= -4.55e-35)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (t <= 195.0)
		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)) + (b * ((a * i) - (z * c)));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.8e+255)
		tmp = t_2;
	elseif (t <= -7.2e+233)
		tmp = t_1;
	elseif (t <= -2.4e+51)
		tmp = t_2;
	elseif (t <= -4.55e-35)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (t <= 195.0)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+255], t$95$2, If[LessEqual[t, -7.2e+233], t$95$1, If[LessEqual[t, -2.4e+51], t$95$2, If[LessEqual[t, -4.55e-35], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 195.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.80000000000000013e255 or -7.1999999999999996e233 < t < -2.3999999999999999e51 or 195 < t

   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. sub-neg 66.4%

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

      2. associate-+l+ 66.4%

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

      3. fma-def 68.3%

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

      4. +-commutative 68.3%

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

      5. fma-def 69.3%

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

      6. *-commutative 69.3%

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

      7. *-commutative 69.3%

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

      8. distribute-rgt-neg-in 69.3%

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

      9. sub-neg 69.3%

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

      10. +-commutative 69.3%

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

      11. distribute-neg-in 69.3%

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

      12. unsub-neg 69.3%

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

      13. remove-double-neg 69.3%

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

      14. *-commutative 69.3%

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

      15. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in z around 0 62.7%

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

   5. Taylor expanded in t around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. mul-1-neg 68.5%

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

      3. unsub-neg 68.5%

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

   7. Simplified 68.5%

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

   if -2.80000000000000013e255 < t < -7.1999999999999996e233 or -4.55000000000000022e-35 < t < 195

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. fma-def 86.5%

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

      3. *-commutative 86.5%

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

      4. *-commutative 86.5%

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

      5. *-commutative 86.5%

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

      6. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in j around 0 78.3%

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

   5. Taylor expanded in y around inf 72.9%

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

   if -2.3999999999999999e51 < t < -4.55000000000000022e-35

   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 t around 0 61.4%

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

      1. fma-neg 61.4%

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

      2. *-commutative 61.4%

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

      3. *-commutative 61.4%

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

      4. *-commutative 61.4%

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

      5. fma-neg 61.4%

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

      6. distribute-rgt-neg-out 61.4%

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

      7. distribute-rgt-neg-in 61.4%

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

      8. neg-sub0 61.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 61.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 61.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 61.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 61.4%

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

      13. +-commutative 61.4%

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

      14. *-commutative 61.4%

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

      15. sub-neg 61.4%

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

   6. Simplified 61.4%

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

   7. Taylor expanded in y around inf 73.8%

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

      1. associate-*r* 69.9%

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

   9. Simplified 69.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+255}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.55 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 195:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 4: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+255}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+233}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i (* a b)) (* t (- (* x a) (* c j)))))
        (t_2 (+ (* y (* x z)) (* b (- (* a i) (* z c))))))
   (if (<= t -2.8e+255)
     (* t (- (* c j) (* x a)))
     (if (<= t -7.2e+233)
       t_2
       (if (<= t -9.5e+49)
         t_1
         (if (<= t -3.3e-35)
           (+ (* j (- (* t c) (* y i))) (* x (* y z)))
           (if (<= t 9e+14) t_2 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 = (i * (a * b)) - (t * ((x * a) - (c * j)));
	double t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (t <= -2.8e+255) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -7.2e+233) {
		tmp = t_2;
	} else if (t <= -9.5e+49) {
		tmp = t_1;
	} else if (t <= -3.3e-35) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (t <= 9e+14) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (i * (a * b)) - (t * ((x * a) - (c * j)))
    t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)))
    if (t <= (-2.8d+255)) then
        tmp = t * ((c * j) - (x * a))
    else if (t <= (-7.2d+233)) then
        tmp = t_2
    else if (t <= (-9.5d+49)) then
        tmp = t_1
    else if (t <= (-3.3d-35)) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (t <= 9d+14) then
        tmp = t_2
    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 = (i * (a * b)) - (t * ((x * a) - (c * j)));
	double t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (t <= -2.8e+255) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -7.2e+233) {
		tmp = t_2;
	} else if (t <= -9.5e+49) {
		tmp = t_1;
	} else if (t <= -3.3e-35) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (t <= 9e+14) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * (a * b)) - (t * ((x * a) - (c * j)))
	t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)))
	tmp = 0
	if t <= -2.8e+255:
		tmp = t * ((c * j) - (x * a))
	elif t <= -7.2e+233:
		tmp = t_2
	elif t <= -9.5e+49:
		tmp = t_1
	elif t <= -3.3e-35:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif t <= 9e+14:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(a * b)) - Float64(t * Float64(Float64(x * a) - Float64(c * j))))
	t_2 = Float64(Float64(y * Float64(x * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (t <= -2.8e+255)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (t <= -7.2e+233)
		tmp = t_2;
	elseif (t <= -9.5e+49)
		tmp = t_1;
	elseif (t <= -3.3e-35)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (t <= 9e+14)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * (a * b)) - (t * ((x * a) - (c * j)));
	t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (t <= -2.8e+255)
		tmp = t * ((c * j) - (x * a));
	elseif (t <= -7.2e+233)
		tmp = t_2;
	elseif (t <= -9.5e+49)
		tmp = t_1;
	elseif (t <= -3.3e-35)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (t <= 9e+14)
		tmp = t_2;
	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[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+255], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e+233], t$95$2, If[LessEqual[t, -9.5e+49], t$95$1, If[LessEqual[t, -3.3e-35], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+14], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.80000000000000013e255

   1. Initial program 45.5%

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

      1. sub-neg 45.5%

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

      2. associate-+l+ 45.5%

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

      3. fma-def 56.6%

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

      4. +-commutative 56.6%

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

      5. fma-def 56.6%

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

      6. *-commutative 56.6%

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

      7. *-commutative 56.6%

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

      8. distribute-rgt-neg-in 56.6%

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

      9. sub-neg 56.6%

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

      10. +-commutative 56.6%

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

      11. distribute-neg-in 56.6%

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

      12. unsub-neg 56.6%

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

      13. remove-double-neg 56.6%

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

      14. *-commutative 56.6%

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

      15. *-commutative 56.6%

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

   3. Simplified 56.6%

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

   4. Taylor expanded in z around 0 45.2%

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

   5. Taylor expanded in t around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. mul-1-neg 88.7%

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

      3. unsub-neg 88.7%

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

   7. Simplified 88.7%

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

   if -2.80000000000000013e255 < t < -7.1999999999999996e233 or -3.3e-35 < t < 9e14

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. fma-def 86.5%

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

      3. *-commutative 86.5%

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

      4. *-commutative 86.5%

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

      5. *-commutative 86.5%

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

      6. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in j around 0 78.3%

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

   5. Taylor expanded in y around inf 72.9%

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

   if -7.1999999999999996e233 < t < -9.49999999999999969e49 or 9e14 < t

   1. Initial program 68.4%

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

      1. sub-neg 68.4%

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

      2. associate-+l+ 68.4%

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

      3. fma-def 69.5%

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

      4. +-commutative 69.5%

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

      5. fma-def 70.5%

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

      6. *-commutative 70.5%

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

      7. *-commutative 70.5%

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

      8. distribute-rgt-neg-in 70.5%

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

      9. sub-neg 70.5%

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

      10. +-commutative 70.5%

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

      11. distribute-neg-in 70.5%

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

      12. unsub-neg 70.5%

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

      13. remove-double-neg 70.5%

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

      14. *-commutative 70.5%

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

      15. *-commutative 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in z around 0 64.4%

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

   5. Taylor expanded in i around -inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

      4. *-commutative 62.1%

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

      5. associate-*r* 65.4%

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

      6. *-commutative 65.4%

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

      7. associate-*r* 70.6%

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

      8. associate-*r* 70.6%

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

      9. distribute-rgt-in 72.8%

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

      10. mul-1-neg 72.8%

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

      11. unsub-neg 72.8%

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

      12. mul-1-neg 72.8%

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

      13. unsub-neg 72.8%

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

      14. *-commutative 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in y around 0 73.0%

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

      1. fma-neg 73.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, c \cdot j - a \cdot x, --1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} \]

      2. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{j \cdot c} - a \cdot x, --1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right) \]

      3. fma-def 73.0%

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

      4. mul-1-neg 73.0%

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

      5. *-commutative 73.0%

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

      6. *-commutative 73.0%

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

      7. associate-*r* 71.0%

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

      8. remove-double-neg 71.0%

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

      9. *-commutative 71.0%

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

      10. associate-*r* 72.0%

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

      11. cancel-sign-sub 72.0%

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

   10. Simplified 72.0%

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

   if -9.49999999999999969e49 < t < -3.3e-35

   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 t around 0 61.4%

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

      1. fma-neg 61.4%

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

      2. *-commutative 61.4%

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

      3. *-commutative 61.4%

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

      4. *-commutative 61.4%

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

      5. fma-neg 61.4%

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

      6. distribute-rgt-neg-out 61.4%

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

      7. distribute-rgt-neg-in 61.4%

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

      8. neg-sub0 61.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 61.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 61.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 61.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 61.4%

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

      13. +-commutative 61.4%

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

      14. *-commutative 61.4%

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

      15. sub-neg 61.4%

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

   6. Simplified 61.4%

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

   7. Taylor expanded in y around inf 73.8%

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

      1. associate-*r* 69.9%

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

   9. Simplified 69.9%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} + j \cdot \left(t \cdot c - y \cdot i\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+255}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+49}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \end{array} \]

Alternative 5: 61.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+255}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 480:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* y (* x z)) (* b (- (* a i) (* z c))))))
   (if (<= t -2.8e+255)
     (* t (- (* c j) (* x a)))
     (if (<= t -7.2e+233)
       t_1
       (if (<= t -4.8e-44)
         (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
         (if (<= t 480.0) t_1 (- (* i (* a b)) (* t (- (* x a) (* c 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 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (t <= -2.8e+255) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -7.2e+233) {
		tmp = t_1;
	} else if (t <= -4.8e-44) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (t <= 480.0) {
		tmp = t_1;
	} else {
		tmp = (i * (a * b)) - (t * ((x * a) - (c * 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) :: tmp
    t_1 = (y * (x * z)) + (b * ((a * i) - (z * c)))
    if (t <= (-2.8d+255)) then
        tmp = t * ((c * j) - (x * a))
    else if (t <= (-7.2d+233)) then
        tmp = t_1
    else if (t <= (-4.8d-44)) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else if (t <= 480.0d0) then
        tmp = t_1
    else
        tmp = (i * (a * b)) - (t * ((x * a) - (c * 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 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (t <= -2.8e+255) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -7.2e+233) {
		tmp = t_1;
	} else if (t <= -4.8e-44) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (t <= 480.0) {
		tmp = t_1;
	} else {
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * (x * z)) + (b * ((a * i) - (z * c)))
	tmp = 0
	if t <= -2.8e+255:
		tmp = t * ((c * j) - (x * a))
	elif t <= -7.2e+233:
		tmp = t_1
	elif t <= -4.8e-44:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	elif t <= 480.0:
		tmp = t_1
	else:
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(x * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (t <= -2.8e+255)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (t <= -7.2e+233)
		tmp = t_1;
	elseif (t <= -4.8e-44)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	elseif (t <= 480.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(i * Float64(a * b)) - Float64(t * Float64(Float64(x * a) - Float64(c * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (t <= -2.8e+255)
		tmp = t * ((c * j) - (x * a));
	elseif (t <= -7.2e+233)
		tmp = t_1;
	elseif (t <= -4.8e-44)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	elseif (t <= 480.0)
		tmp = t_1;
	else
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+255], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e+233], t$95$1, If[LessEqual[t, -4.8e-44], 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[t, 480.0], t$95$1, N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.80000000000000013e255

   1. Initial program 45.5%

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

      1. sub-neg 45.5%

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

      2. associate-+l+ 45.5%

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

      3. fma-def 56.6%

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

      4. +-commutative 56.6%

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

      5. fma-def 56.6%

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

      6. *-commutative 56.6%

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

      7. *-commutative 56.6%

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

      8. distribute-rgt-neg-in 56.6%

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

      9. sub-neg 56.6%

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

      10. +-commutative 56.6%

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

      11. distribute-neg-in 56.6%

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

      12. unsub-neg 56.6%

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

      13. remove-double-neg 56.6%

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

      14. *-commutative 56.6%

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

      15. *-commutative 56.6%

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

   3. Simplified 56.6%

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

   4. Taylor expanded in z around 0 45.2%

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

   5. Taylor expanded in t around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. mul-1-neg 88.7%

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

      3. unsub-neg 88.7%

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

   7. Simplified 88.7%

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

   if -2.80000000000000013e255 < t < -7.1999999999999996e233 or -4.80000000000000017e-44 < t < 480

   1. Initial program 86.3%

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

      1. +-commutative 86.3%

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

      2. fma-def 86.3%

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

      3. *-commutative 86.3%

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

      4. *-commutative 86.3%

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

      5. *-commutative 86.3%

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

      6. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in j around 0 77.9%

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

   5. Taylor expanded in y around inf 73.2%

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

   if -7.1999999999999996e233 < t < -4.80000000000000017e-44

   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. +-commutative 75.8%

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

      2. associate-+r- 75.8%

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

      3. fma-def 77.6%

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

      4. *-commutative 77.6%

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

      5. *-commutative 77.6%

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

      6. *-commutative 77.6%

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

      7. fma-neg 77.6%

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

      8. *-commutative 77.6%

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

      9. distribute-rgt-neg-in 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in b around 0 78.5%

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

   if 480 < t

   1. Initial program 60.7%

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

      1. sub-neg 60.7%

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

      2. associate-+l+ 60.7%

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

      3. fma-def 62.3%

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

      4. +-commutative 62.3%

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

      5. fma-def 62.3%

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

      6. *-commutative 62.3%

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

      7. *-commutative 62.3%

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

      8. distribute-rgt-neg-in 62.3%

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

      9. sub-neg 62.3%

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

      10. +-commutative 62.3%

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

      11. distribute-neg-in 62.3%

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

      12. unsub-neg 62.3%

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

      13. remove-double-neg 62.3%

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

      14. *-commutative 62.3%

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

      15. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in z around 0 63.9%

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

   5. Taylor expanded in i around -inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-*r* 63.9%

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

      6. *-commutative 63.9%

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

      7. associate-*r* 68.5%

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

      8. associate-*r* 68.5%

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

      9. distribute-rgt-in 71.7%

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

      10. mul-1-neg 71.7%

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

      11. unsub-neg 71.7%

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

      12. mul-1-neg 71.7%

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

      13. unsub-neg 71.7%

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

      14. *-commutative 71.7%

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

   7. Simplified 71.7%

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

   8. Taylor expanded in y around 0 70.5%

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

      1. fma-neg 70.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, c \cdot j - a \cdot x, --1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} \]

      2. *-commutative 70.5%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{j \cdot c} - a \cdot x, --1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right) \]

      3. fma-def 70.5%

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

      4. mul-1-neg 70.5%

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

      5. *-commutative 70.5%

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

      6. *-commutative 70.5%

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

      7. associate-*r* 69.0%

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

      8. remove-double-neg 69.0%

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

      9. *-commutative 69.0%

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

      10. associate-*r* 70.4%

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

      11. cancel-sign-sub 70.4%

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

   10. Simplified 70.4%

       \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right) - \left(-i\right) \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+255}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 480:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \end{array} \]

Alternative 6: 63.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;\left(t_1 + c \cdot \left(t \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-97}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 5500000:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= t -9.2e+111)
     (- (+ t_1 (* c (* t j))) (* c (* z b)))
     (if (<= t -1.7e-97)
       (+ (* j (- (* t c) (* y i))) (- (* a (* b i)) (* a (* x t))))
       (if (<= t 5500000.0)
         (+ t_1 (* b (- (* a i) (* z c))))
         (+ (* 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 t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (t <= -9.2e+111) {
		tmp = (t_1 + (c * (t * j))) - (c * (z * b));
	} else if (t <= -1.7e-97) {
		tmp = (j * ((t * c) - (y * i))) + ((a * (b * i)) - (a * (x * t)));
	} else if (t <= 5500000.0) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (t <= (-9.2d+111)) then
        tmp = (t_1 + (c * (t * j))) - (c * (z * b))
    else if (t <= (-1.7d-97)) then
        tmp = (j * ((t * c) - (y * i))) + ((a * (b * i)) - (a * (x * t)))
    else if (t <= 5500000.0d0) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = (t * ((c * j) - (x * a))) + (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 t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (t <= -9.2e+111) {
		tmp = (t_1 + (c * (t * j))) - (c * (z * b));
	} else if (t <= -1.7e-97) {
		tmp = (j * ((t * c) - (y * i))) + ((a * (b * i)) - (a * (x * t)));
	} else if (t <= 5500000.0) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if t <= -9.2e+111:
		tmp = (t_1 + (c * (t * j))) - (c * (z * b))
	elif t <= -1.7e-97:
		tmp = (j * ((t * c) - (y * i))) + ((a * (b * i)) - (a * (x * t)))
	elif t <= 5500000.0:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (t <= -9.2e+111)
		tmp = Float64(Float64(t_1 + Float64(c * Float64(t * j))) - Float64(c * Float64(z * b)));
	elseif (t <= -1.7e-97)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(Float64(a * Float64(b * i)) - Float64(a * Float64(x * t))));
	elseif (t <= 5500000.0)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + 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)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (t <= -9.2e+111)
		tmp = (t_1 + (c * (t * j))) - (c * (z * b));
	elseif (t <= -1.7e-97)
		tmp = (j * ((t * c) - (y * i))) + ((a * (b * i)) - (a * (x * t)));
	elseif (t <= 5500000.0)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+111], N[(N[(t$95$1 + N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-97], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5500000.0], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(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]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.20000000000000008e111

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-+r- 69.0%

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

      3. fma-def 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

      6. *-commutative 71.9%

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

      7. fma-neg 71.9%

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

      8. *-commutative 71.9%

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

      9. distribute-rgt-neg-in 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in i around 0 77.2%

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

   if -9.20000000000000008e111 < t < -1.6999999999999999e-97

   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. sub-neg 73.5%

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

      2. associate-+l+ 73.5%

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

      3. fma-def 79.3%

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

      4. +-commutative 79.3%

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

      5. fma-def 79.3%

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

      6. *-commutative 79.3%

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

      7. *-commutative 79.3%

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

      8. distribute-rgt-neg-in 79.3%

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

      9. sub-neg 79.3%

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

      10. +-commutative 79.3%

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

      11. distribute-neg-in 79.3%

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

      12. unsub-neg 79.3%

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

      13. remove-double-neg 79.3%

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

      14. *-commutative 79.3%

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

      15. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in z around 0 77.1%

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

   if -1.6999999999999999e-97 < t < 5.5e6

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. fma-def 89.2%

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

      3. *-commutative 89.2%

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

      4. *-commutative 89.2%

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

      5. *-commutative 89.2%

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

      6. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in j around 0 81.9%

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

   if 5.5e6 < t

   1. Initial program 60.7%

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

      1. sub-neg 60.7%

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

      2. associate-+l+ 60.7%

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

      3. fma-def 62.3%

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

      4. +-commutative 62.3%

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

      5. fma-def 62.3%

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

      6. *-commutative 62.3%

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

      7. *-commutative 62.3%

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

      8. distribute-rgt-neg-in 62.3%

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

      9. sub-neg 62.3%

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

      10. +-commutative 62.3%

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

      11. distribute-neg-in 62.3%

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

      12. unsub-neg 62.3%

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

      13. remove-double-neg 62.3%

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

      14. *-commutative 62.3%

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

      15. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in z around 0 63.9%

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

   5. Taylor expanded in i around -inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-*r* 63.9%

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

      6. *-commutative 63.9%

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

      7. associate-*r* 68.5%

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

      8. associate-*r* 68.5%

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

      9. distribute-rgt-in 71.7%

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

      10. mul-1-neg 71.7%

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

      11. unsub-neg 71.7%

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

      12. mul-1-neg 71.7%

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

      13. unsub-neg 71.7%

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

      14. *-commutative 71.7%

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

   7. Simplified 71.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \left(y \cdot j - b \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-97}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(a \cdot \left(b \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 5500000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 7: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -2.5e+48)
     t_2
     (if (<= t -1.05e+17)
       (* j (- (* t c) (* y i)))
       (if (<= t -4.8e-28)
         t_2
         (if (<= t -1.1e-88)
           (* i (- (* a b) (* y j)))
           (if (<= t 4.9e-247)
             t_1
             (if (<= t 3.2e-179)
               (* x (- (* y z) (* t a)))
               (if (<= t 235000000000.0) 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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.5e+48) {
		tmp = t_2;
	} else if (t <= -1.05e+17) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= -4.8e-28) {
		tmp = t_2;
	} else if (t <= -1.1e-88) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 4.9e-247) {
		tmp = t_1;
	} else if (t <= 3.2e-179) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 235000000000.0) {
		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 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-2.5d+48)) then
        tmp = t_2
    else if (t <= (-1.05d+17)) then
        tmp = j * ((t * c) - (y * i))
    else if (t <= (-4.8d-28)) then
        tmp = t_2
    else if (t <= (-1.1d-88)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 4.9d-247) then
        tmp = t_1
    else if (t <= 3.2d-179) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 235000000000.0d0) 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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.5e+48) {
		tmp = t_2;
	} else if (t <= -1.05e+17) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= -4.8e-28) {
		tmp = t_2;
	} else if (t <= -1.1e-88) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 4.9e-247) {
		tmp = t_1;
	} else if (t <= 3.2e-179) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 235000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.5e+48:
		tmp = t_2
	elif t <= -1.05e+17:
		tmp = j * ((t * c) - (y * i))
	elif t <= -4.8e-28:
		tmp = t_2
	elif t <= -1.1e-88:
		tmp = i * ((a * b) - (y * j))
	elif t <= 4.9e-247:
		tmp = t_1
	elif t <= 3.2e-179:
		tmp = x * ((y * z) - (t * a))
	elif t <= 235000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.5e+48)
		tmp = t_2;
	elseif (t <= -1.05e+17)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (t <= -4.8e-28)
		tmp = t_2;
	elseif (t <= -1.1e-88)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 4.9e-247)
		tmp = t_1;
	elseif (t <= 3.2e-179)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 235000000000.0)
		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 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.5e+48)
		tmp = t_2;
	elseif (t <= -1.05e+17)
		tmp = j * ((t * c) - (y * i));
	elseif (t <= -4.8e-28)
		tmp = t_2;
	elseif (t <= -1.1e-88)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 4.9e-247)
		tmp = t_1;
	elseif (t <= 3.2e-179)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 235000000000.0)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+48], t$95$2, If[LessEqual[t, -1.05e+17], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.8e-28], t$95$2, If[LessEqual[t, -1.1e-88], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e-247], t$95$1, If[LessEqual[t, 3.2e-179], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 235000000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.49999999999999987e48 or -1.05e17 < t < -4.8000000000000004e-28 or 2.35e11 < t

   1. Initial program 65.9%

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

      1. sub-neg 65.9%

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

      2. associate-+l+ 65.9%

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

      3. fma-def 67.6%

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

      4. +-commutative 67.6%

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

      5. fma-def 68.5%

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

      6. *-commutative 68.5%

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

      7. *-commutative 68.5%

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

      8. distribute-rgt-neg-in 68.5%

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

      9. sub-neg 68.5%

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

      10. +-commutative 68.5%

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

      11. distribute-neg-in 68.5%

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

      12. unsub-neg 68.5%

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

      13. remove-double-neg 68.5%

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

      14. *-commutative 68.5%

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

      15. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in z around 0 62.7%

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

   5. Taylor expanded in t around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

   7. Simplified 65.4%

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

   if -2.49999999999999987e48 < t < -1.05e17

   1. Initial program 64.0%

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

      1. cancel-sign-sub 64.0%

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

      2. cancel-sign-sub-inv 64.0%

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

      3. *-commutative 64.0%

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

      4. *-commutative 64.0%

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

      5. remove-double-neg 64.0%

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

      6. *-commutative 64.0%

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

      7. *-commutative 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in t around 0 81.7%

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

      1. fma-neg 81.7%

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

      2. *-commutative 81.7%

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

      3. *-commutative 81.7%

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

      4. *-commutative 81.7%

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

      5. fma-neg 81.7%

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

      6. distribute-rgt-neg-out 81.7%

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

      7. distribute-rgt-neg-in 81.7%

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

      8. neg-sub0 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 81.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 81.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 81.7%

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

      13. +-commutative 81.7%

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

      14. *-commutative 81.7%

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

      15. sub-neg 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in j around inf 81.8%

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

   if -4.8000000000000004e-28 < t < -1.10000000000000002e-88

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-+r- 72.9%

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

      3. fma-def 72.9%

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

      4. *-commutative 72.9%

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

      5. *-commutative 72.9%

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

      6. *-commutative 72.9%

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

      7. fma-neg 78.5%

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

      8. *-commutative 78.5%

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

      9. distribute-rgt-neg-in 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in i around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. sub-neg 67.3%

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

      3. mul-1-neg 67.3%

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

      4. remove-double-neg 67.3%

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

      5. +-commutative 67.3%

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

      6. mul-1-neg 67.3%

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

      7. unsub-neg 67.3%

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

      8. *-commutative 67.3%

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

   6. Simplified 67.3%

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

   if -1.10000000000000002e-88 < t < 4.9e-247 or 3.2000000000000001e-179 < t < 2.35e11

   1. Initial program 88.6%

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

      1. +-commutative 88.6%

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

      2. fma-def 88.6%

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

      3. *-commutative 88.6%

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

      4. *-commutative 88.6%

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

      5. *-commutative 88.6%

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

      6. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in b around inf 61.5%

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

   if 4.9e-247 < t < 3.2000000000000001e-179

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. fma-def 93.0%

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

      3. *-commutative 93.0%

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

      4. *-commutative 93.0%

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

      5. *-commutative 93.0%

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

      6. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in j around 0 87.4%

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

   5. Taylor expanded in x around inf 66.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-247}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 8: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-304}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 10^{+14}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* a i)) (* j (- (* y i) (* t c)))))
        (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -7.5e+49)
     t_2
     (if (<= t -1.75e-101)
       t_1
       (if (<= t 5.5e-304)
         (* z (- (* x y) (* b c)))
         (if (<= t 6.5e-250)
           t_1
           (if (<= t 4.8e-181)
             (* x (- (* y z) (* t a)))
             (if (<= t 1e+14) (* b (- (* a i) (* z c))) 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 = (b * (a * i)) - (j * ((y * i) - (t * c)));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -7.5e+49) {
		tmp = t_2;
	} else if (t <= -1.75e-101) {
		tmp = t_1;
	} else if (t <= 5.5e-304) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 6.5e-250) {
		tmp = t_1;
	} else if (t <= 4.8e-181) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 1e+14) {
		tmp = b * ((a * i) - (z * c));
	} 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 = (b * (a * i)) - (j * ((y * i) - (t * c)))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-7.5d+49)) then
        tmp = t_2
    else if (t <= (-1.75d-101)) then
        tmp = t_1
    else if (t <= 5.5d-304) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 6.5d-250) then
        tmp = t_1
    else if (t <= 4.8d-181) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 1d+14) then
        tmp = b * ((a * i) - (z * c))
    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 = (b * (a * i)) - (j * ((y * i) - (t * c)));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -7.5e+49) {
		tmp = t_2;
	} else if (t <= -1.75e-101) {
		tmp = t_1;
	} else if (t <= 5.5e-304) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 6.5e-250) {
		tmp = t_1;
	} else if (t <= 4.8e-181) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 1e+14) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * (a * i)) - (j * ((y * i) - (t * c)))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -7.5e+49:
		tmp = t_2
	elif t <= -1.75e-101:
		tmp = t_1
	elif t <= 5.5e-304:
		tmp = z * ((x * y) - (b * c))
	elif t <= 6.5e-250:
		tmp = t_1
	elif t <= 4.8e-181:
		tmp = x * ((y * z) - (t * a))
	elif t <= 1e+14:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(a * i)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -7.5e+49)
		tmp = t_2;
	elseif (t <= -1.75e-101)
		tmp = t_1;
	elseif (t <= 5.5e-304)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 6.5e-250)
		tmp = t_1;
	elseif (t <= 4.8e-181)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 1e+14)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * (a * i)) - (j * ((y * i) - (t * c)));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -7.5e+49)
		tmp = t_2;
	elseif (t <= -1.75e-101)
		tmp = t_1;
	elseif (t <= 5.5e-304)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 6.5e-250)
		tmp = t_1;
	elseif (t <= 4.8e-181)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 1e+14)
		tmp = b * ((a * i) - (z * c));
	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[(b * N[(a * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+49], t$95$2, If[LessEqual[t, -1.75e-101], t$95$1, If[LessEqual[t, 5.5e-304], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-250], t$95$1, If[LessEqual[t, 4.8e-181], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+14], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.4999999999999995e49 or 1e14 < t

   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. sub-neg 66.4%

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

      2. associate-+l+ 66.4%

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

      3. fma-def 68.2%

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

      4. +-commutative 68.2%

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

      5. fma-def 69.2%

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

      6. *-commutative 69.2%

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

      7. *-commutative 69.2%

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

      8. distribute-rgt-neg-in 69.2%

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

      9. sub-neg 69.2%

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

      10. +-commutative 69.2%

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

      11. distribute-neg-in 69.2%

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

      12. unsub-neg 69.2%

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

      13. remove-double-neg 69.2%

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

      14. *-commutative 69.2%

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

      15. *-commutative 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in z around 0 61.2%

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

   5. Taylor expanded in t around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

   7. Simplified 65.8%

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

   if -7.4999999999999995e49 < t < -1.74999999999999997e-101 or 5.50000000000000035e-304 < t < 6.49999999999999942e-250

   1. Initial program 75.5%

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

      1. cancel-sign-sub 75.5%

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

      2. cancel-sign-sub-inv 75.5%

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

      3. *-commutative 75.5%

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

      4. *-commutative 75.5%

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

      5. remove-double-neg 75.5%

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

      6. *-commutative 75.5%

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

      7. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in i around inf 75.0%

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

      1. associate-*r* 71.3%

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

      2. *-commutative 71.3%

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

   6. Simplified 71.3%

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

   if -1.74999999999999997e-101 < t < 5.50000000000000035e-304

   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. +-commutative 81.5%

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

      2. fma-def 81.5%

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

      3. *-commutative 81.5%

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

      4. *-commutative 81.5%

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

      5. *-commutative 81.5%

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

      6. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in j around 0 77.6%

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

   5. Taylor expanded in z around inf 62.5%

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

   if 6.49999999999999942e-250 < t < 4.8000000000000002e-181

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. fma-def 92.9%

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

      3. *-commutative 92.9%

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

      4. *-commutative 92.9%

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

      5. *-commutative 92.9%

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

      6. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in j around 0 87.4%

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

   5. Taylor expanded in x around inf 66.6%

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

   if 4.8000000000000002e-181 < t < 1e14

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. fma-def 96.2%

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

      3. *-commutative 96.2%

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

      4. *-commutative 96.2%

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

      5. *-commutative 96.2%

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

      6. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in b around inf 67.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-304}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 10^{+14}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 9: 57.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -6.5e+48)
     t_1
     (if (<= a 2.15e-172)
       (+ (* j (- (* t c) (* y i))) (* x (* y z)))
       (if (<= a 1.8e-100)
         (- (* z (* c (- b))) (* j (* y i)))
         (if (<= a 1.06e-48)
           (- (* b (* a i)) (* j (- (* y i) (* t c))))
           (if (<= a 1.6e+64) (- (* c (* t j)) (* z (* b c))) 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.5e+48) {
		tmp = t_1;
	} else if (a <= 2.15e-172) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (a <= 1.8e-100) {
		tmp = (z * (c * -b)) - (j * (y * i));
	} else if (a <= 1.06e-48) {
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	} else if (a <= 1.6e+64) {
		tmp = (c * (t * j)) - (z * (b * c));
	} 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 = a * ((b * i) - (x * t))
    if (a <= (-6.5d+48)) then
        tmp = t_1
    else if (a <= 2.15d-172) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (a <= 1.8d-100) then
        tmp = (z * (c * -b)) - (j * (y * i))
    else if (a <= 1.06d-48) then
        tmp = (b * (a * i)) - (j * ((y * i) - (t * c)))
    else if (a <= 1.6d+64) then
        tmp = (c * (t * j)) - (z * (b * c))
    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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.5e+48) {
		tmp = t_1;
	} else if (a <= 2.15e-172) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (a <= 1.8e-100) {
		tmp = (z * (c * -b)) - (j * (y * i));
	} else if (a <= 1.06e-48) {
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	} else if (a <= 1.6e+64) {
		tmp = (c * (t * j)) - (z * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -6.5e+48:
		tmp = t_1
	elif a <= 2.15e-172:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif a <= 1.8e-100:
		tmp = (z * (c * -b)) - (j * (y * i))
	elif a <= 1.06e-48:
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)))
	elif a <= 1.6e+64:
		tmp = (c * (t * j)) - (z * (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.5e+48)
		tmp = t_1;
	elseif (a <= 2.15e-172)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (a <= 1.8e-100)
		tmp = Float64(Float64(z * Float64(c * Float64(-b))) - Float64(j * Float64(y * i)));
	elseif (a <= 1.06e-48)
		tmp = Float64(Float64(b * Float64(a * i)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	elseif (a <= 1.6e+64)
		tmp = Float64(Float64(c * Float64(t * j)) - Float64(z * Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -6.5e+48)
		tmp = t_1;
	elseif (a <= 2.15e-172)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (a <= 1.8e-100)
		tmp = (z * (c * -b)) - (j * (y * i));
	elseif (a <= 1.06e-48)
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	elseif (a <= 1.6e+64)
		tmp = (c * (t * j)) - (z * (b * c));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+48], t$95$1, If[LessEqual[a, 2.15e-172], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-100], N[(N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e-48], N[(N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+64], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.49999999999999972e48 or 1.60000000000000009e64 < a

   1. Initial program 66.8%

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

      1. sub-neg 66.8%

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

      2. associate-+l+ 66.8%

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

      3. fma-def 69.5%

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

      4. +-commutative 69.5%

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

      5. fma-def 70.4%

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

      6. *-commutative 70.4%

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

      7. *-commutative 70.4%

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

      8. distribute-rgt-neg-in 70.4%

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

      9. sub-neg 70.4%

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

      10. +-commutative 70.4%

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

      11. distribute-neg-in 70.4%

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

      12. unsub-neg 70.4%

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

      13. remove-double-neg 70.4%

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

      14. *-commutative 70.4%

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

      15. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in a around inf 69.8%

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

   5. Taylor expanded in a around 0 69.8%

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

      1. *-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. *-commutative 69.8%

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

      4. unsub-neg 69.8%

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

   7. Simplified 69.8%

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

   if -6.49999999999999972e48 < a < 2.1499999999999999e-172

   1. Initial program 84.9%

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

      1. cancel-sign-sub 84.9%

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

      2. cancel-sign-sub-inv 84.9%

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

      3. *-commutative 84.9%

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

      4. *-commutative 84.9%

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

      5. remove-double-neg 84.9%

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

      6. *-commutative 84.9%

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

      7. *-commutative 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in t around 0 79.0%

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

      1. fma-neg 79.9%

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

      2. *-commutative 79.9%

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

      3. *-commutative 79.9%

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

      4. *-commutative 79.9%

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

      5. fma-neg 79.9%

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

      6. distribute-rgt-neg-out 79.9%

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

      7. distribute-rgt-neg-in 79.9%

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

      8. neg-sub0 79.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.9%

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

      13. +-commutative 79.9%

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

      14. *-commutative 79.9%

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

      15. sub-neg 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in y around inf 61.1%

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

      1. associate-*r* 63.9%

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

   9. Simplified 63.9%

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

   if 2.1499999999999999e-172 < a < 1.7999999999999999e-100

   1. Initial program 79.2%

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

      1. cancel-sign-sub 79.2%

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

      2. cancel-sign-sub-inv 79.2%

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

      3. *-commutative 79.2%

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

      4. *-commutative 79.2%

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

      5. remove-double-neg 79.2%

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

      6. *-commutative 79.2%

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

      7. *-commutative 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in c around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. associate-*r* 82.2%

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

      3. distribute-rgt-neg-in 82.2%

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

      4. *-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in t around 0 82.3%

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

      1. neg-mul-1 82.3%

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

      2. distribute-rgt-neg-in 82.3%

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

   9. Simplified 82.3%

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

   if 1.7999999999999999e-100 < a < 1.0600000000000001e-48

   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 i around inf 83.3%

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

      1. associate-*r* 83.3%

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

      2. *-commutative 83.3%

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

   6. Simplified 83.3%

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

   if 1.0600000000000001e-48 < a < 1.60000000000000009e64

   1. Initial program 84.6%

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

      1. cancel-sign-sub 84.6%

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

      2. cancel-sign-sub-inv 84.6%

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

      3. *-commutative 84.6%

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

      4. *-commutative 84.6%

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

      5. remove-double-neg 84.6%

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

      6. *-commutative 84.6%

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

      7. *-commutative 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in c around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-*r* 75.2%

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

      3. distribute-rgt-neg-in 75.2%

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

      4. *-commutative 75.2%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in t around inf 75.3%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 10: 65.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-29} \lor \neg \left(t \leq 230000000\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -2.6e-29) (not (<= t 230000000.0)))
   (+ (* t (- (* c j) (* x a))) (* i (- (* a b) (* y j))))
   (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z 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 <= -2.6e-29) || !(t <= 230000000.0)) {
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * 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 <= (-2.6d-29)) .or. (.not. (t <= 230000000.0d0))) then
        tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)))
    else
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * 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 <= -2.6e-29) || !(t <= 230000000.0)) {
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -2.6e-29) or not (t <= 230000000.0):
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -2.6e-29) || !(t <= 230000000.0))
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(i * Float64(Float64(a * b) - Float64(y * j))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -2.6e-29) || ~((t <= 230000000.0)))
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	else
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -2.6e-29], N[Not[LessEqual[t, 230000000.0]], $MachinePrecision]], N[(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]), $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]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6000000000000002e-29 or 2.3e8 < t

   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. sub-neg 65.6%

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

      2. associate-+l+ 65.6%

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

      3. fma-def 67.9%

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

      4. +-commutative 67.9%

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

      5. fma-def 68.6%

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

      6. *-commutative 68.6%

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

      7. *-commutative 68.6%

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

      8. distribute-rgt-neg-in 68.6%

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

      9. sub-neg 68.6%

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

      10. +-commutative 68.6%

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

      11. distribute-neg-in 68.6%

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

      12. unsub-neg 68.6%

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

      13. remove-double-neg 68.6%

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

      14. *-commutative 68.6%

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

      15. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in z around 0 64.9%

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

   5. Taylor expanded in i around -inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

      5. associate-*r* 64.7%

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

      6. *-commutative 64.7%

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

      7. associate-*r* 70.5%

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

      8. associate-*r* 70.5%

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

      9. distribute-rgt-in 72.8%

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

      10. mul-1-neg 72.8%

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

      11. unsub-neg 72.8%

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

      12. mul-1-neg 72.8%

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

      13. unsub-neg 72.8%

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

      14. *-commutative 72.8%

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

   7. Simplified 72.8%

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

   if -2.6000000000000002e-29 < t < 2.3e8

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. fma-def 87.6%

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

      3. *-commutative 87.6%

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

      4. *-commutative 87.6%

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

      5. *-commutative 87.6%

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

      6. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in j around 0 78.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-29} \lor \neg \left(t \leq 230000000\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 11: 62.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 420:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.15e-43)
   (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
   (if (<= t 420.0)
     (+ (* y (* x z)) (* b (- (* a i) (* z c))))
     (+ (* 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 <= -1.15e-43) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (t <= 420.0) {
		tmp = (y * (x * z)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (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 <= (-1.15d-43)) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else if (t <= 420.0d0) then
        tmp = (y * (x * z)) + (b * ((a * i) - (z * c)))
    else
        tmp = (t * ((c * j) - (x * a))) + (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 <= -1.15e-43) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (t <= 420.0) {
		tmp = (y * (x * z)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.15e-43:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	elif t <= 420.0:
		tmp = (y * (x * z)) + (b * ((a * i) - (z * c)))
	else:
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.15e-43)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	elseif (t <= 420.0)
		tmp = Float64(Float64(y * Float64(x * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + 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 <= -1.15e-43)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	elseif (t <= 420.0)
		tmp = (y * (x * z)) + (b * ((a * i) - (z * c)));
	else
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.15e-43], 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[t, 420.0], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(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]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1499999999999999e-43

   1. Initial program 71.3%

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

      1. +-commutative 71.3%

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

      2. associate-+r- 71.3%

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

      3. fma-def 72.7%

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

      4. *-commutative 72.7%

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

      5. *-commutative 72.7%

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

      6. *-commutative 72.7%

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

      7. fma-neg 72.7%

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

      8. *-commutative 72.7%

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

      9. distribute-rgt-neg-in 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in b around 0 73.4%

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

   if -1.1499999999999999e-43 < t < 420

   1. Initial program 87.3%

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

      1. +-commutative 87.3%

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

      2. fma-def 87.3%

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

      3. *-commutative 87.3%

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

      4. *-commutative 87.3%

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

      5. *-commutative 87.3%

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

      6. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in j around 0 78.5%

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

   5. Taylor expanded in y around inf 71.9%

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

   if 420 < t

   1. Initial program 60.7%

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

      1. sub-neg 60.7%

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

      2. associate-+l+ 60.7%

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

      3. fma-def 62.3%

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

      4. +-commutative 62.3%

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

      5. fma-def 62.3%

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

      6. *-commutative 62.3%

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

      7. *-commutative 62.3%

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

      8. distribute-rgt-neg-in 62.3%

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

      9. sub-neg 62.3%

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

      10. +-commutative 62.3%

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

      11. distribute-neg-in 62.3%

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

      12. unsub-neg 62.3%

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

      13. remove-double-neg 62.3%

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

      14. *-commutative 62.3%

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

      15. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in z around 0 63.9%

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

   5. Taylor expanded in i around -inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-*r* 63.9%

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

      6. *-commutative 63.9%

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

      7. associate-*r* 68.5%

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

      8. associate-*r* 68.5%

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

      9. distribute-rgt-in 71.7%

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

      10. mul-1-neg 71.7%

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

      11. unsub-neg 71.7%

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

      12. mul-1-neg 71.7%

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

      13. unsub-neg 71.7%

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

      14. *-commutative 71.7%

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

   7. Simplified 71.7%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 420:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 12: 41.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 1.82 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -4.1e+46)
     t_1
     (if (<= a -6e-160)
       (* y (* x z))
       (if (<= a 3e-227)
         (* b (* c (- z)))
         (if (<= a 1.82e-178)
           (* x (* y z))
           (if (<= a 1.8e+40) (* c (* b (- 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.1e+46) {
		tmp = t_1;
	} else if (a <= -6e-160) {
		tmp = y * (x * z);
	} else if (a <= 3e-227) {
		tmp = b * (c * -z);
	} else if (a <= 1.82e-178) {
		tmp = x * (y * z);
	} else if (a <= 1.8e+40) {
		tmp = c * (b * -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 = a * ((b * i) - (x * t))
    if (a <= (-4.1d+46)) then
        tmp = t_1
    else if (a <= (-6d-160)) then
        tmp = y * (x * z)
    else if (a <= 3d-227) then
        tmp = b * (c * -z)
    else if (a <= 1.82d-178) then
        tmp = x * (y * z)
    else if (a <= 1.8d+40) then
        tmp = c * (b * -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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.1e+46) {
		tmp = t_1;
	} else if (a <= -6e-160) {
		tmp = y * (x * z);
	} else if (a <= 3e-227) {
		tmp = b * (c * -z);
	} else if (a <= 1.82e-178) {
		tmp = x * (y * z);
	} else if (a <= 1.8e+40) {
		tmp = c * (b * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.1e+46:
		tmp = t_1
	elif a <= -6e-160:
		tmp = y * (x * z)
	elif a <= 3e-227:
		tmp = b * (c * -z)
	elif a <= 1.82e-178:
		tmp = x * (y * z)
	elif a <= 1.8e+40:
		tmp = c * (b * -z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.1e+46)
		tmp = t_1;
	elseif (a <= -6e-160)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 3e-227)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (a <= 1.82e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1.8e+40)
		tmp = Float64(c * Float64(b * Float64(-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 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.1e+46)
		tmp = t_1;
	elseif (a <= -6e-160)
		tmp = y * (x * z);
	elseif (a <= 3e-227)
		tmp = b * (c * -z);
	elseif (a <= 1.82e-178)
		tmp = x * (y * z);
	elseif (a <= 1.8e+40)
		tmp = c * (b * -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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+46], t$95$1, If[LessEqual[a, -6e-160], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-227], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.82e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+40], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.1e46 or 1.79999999999999998e40 < a

   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. sub-neg 68.9%

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

      2. associate-+l+ 68.9%

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

      3. fma-def 71.5%

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

      4. +-commutative 71.5%

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

      5. fma-def 72.3%

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

      6. *-commutative 72.3%

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

      7. *-commutative 72.3%

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

      8. distribute-rgt-neg-in 72.3%

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

      9. sub-neg 72.3%

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

      10. +-commutative 72.3%

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

      11. distribute-neg-in 72.3%

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

      12. unsub-neg 72.3%

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

      13. remove-double-neg 72.3%

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

      14. *-commutative 72.3%

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

      15. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in a around inf 67.5%

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

   5. Taylor expanded in a around 0 67.5%

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

      1. *-commutative 67.5%

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

      2. mul-1-neg 67.5%

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

      3. *-commutative 67.5%

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

      4. unsub-neg 67.5%

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

   7. Simplified 67.5%

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

   if -4.1e46 < a < -5.99999999999999993e-160

   1. Initial program 86.2%

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

      1. cancel-sign-sub 86.2%

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

      2. cancel-sign-sub-inv 86.2%

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

      3. *-commutative 86.2%

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

      4. *-commutative 86.2%

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

      5. remove-double-neg 86.2%

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

      6. *-commutative 86.2%

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

      7. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in t around 0 79.2%

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

      1. fma-neg 79.2%

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

      2. *-commutative 79.2%

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

      3. *-commutative 79.2%

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

      4. *-commutative 79.2%

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

      5. fma-neg 79.2%

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

      6. distribute-rgt-neg-out 79.2%

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

      7. distribute-rgt-neg-in 79.2%

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

      8. neg-sub0 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.2%

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

      13. +-commutative 79.2%

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

      14. *-commutative 79.2%

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

      15. sub-neg 79.2%

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

   6. Simplified 79.2%

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

   7. Taylor expanded in y around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. mul-1-neg 61.7%

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

      3. unsub-neg 61.7%

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

   9. Simplified 61.7%

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

   10. Taylor expanded in z around inf 50.0%

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

   if -5.99999999999999993e-160 < a < 3e-227

   1. Initial program 85.7%

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

      1. +-commutative 85.7%

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

      2. fma-def 85.7%

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

      3. *-commutative 85.7%

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

      4. *-commutative 85.7%

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

      5. *-commutative 85.7%

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

      6. *-commutative 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in b around inf 45.5%

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

   5. Taylor expanded in i around 0 37.7%

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

      1. neg-mul-1 37.7%

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

      2. distribute-rgt-neg-in 37.7%

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

   7. Simplified 37.7%

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

   if 3e-227 < a < 1.8199999999999999e-178

   1. Initial program 80.0%

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

      1. cancel-sign-sub 80.0%

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

      2. cancel-sign-sub-inv 80.0%

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

      3. *-commutative 80.0%

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

      4. *-commutative 80.0%

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

      5. remove-double-neg 80.0%

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

      6. *-commutative 80.0%

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

      7. *-commutative 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in t around 0 79.8%

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

      1. fma-neg 79.8%

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

      2. *-commutative 79.8%

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

      3. *-commutative 79.8%

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

      4. *-commutative 79.8%

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

      5. fma-neg 79.8%

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

      6. distribute-rgt-neg-out 79.8%

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

      7. distribute-rgt-neg-in 79.8%

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

      8. neg-sub0 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.8%

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

      13. +-commutative 79.8%

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

      14. *-commutative 79.8%

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

      15. sub-neg 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in y around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

   9. Simplified 70.5%

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

   10. Taylor expanded in z around inf 60.5%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 60.7%

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

       2. *-commutative 60.7%

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

   12. Simplified 60.7%

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

   if 1.8199999999999999e-178 < a < 1.79999999999999998e40

   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. +-commutative 74.8%

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

      2. fma-def 74.8%

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

      3. *-commutative 74.8%

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

      4. *-commutative 74.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 74.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 74.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 57.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in c around inf 49.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 49.7%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      2. mul-1-neg 49.7%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   7. Simplified 49.7%

      \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 1.82 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 13: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -4e-28)
     t_2
     (if (<= t -5.5e-86)
       (* i (- (* a b) (* y j)))
       (if (<= t 6.5e-245)
         t_1
         (if (<= t 2.9e-181) (* x (* y z)) (if (<= t 1.85e+15) 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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4e-28) {
		tmp = t_2;
	} else if (t <= -5.5e-86) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 6.5e-245) {
		tmp = t_1;
	} else if (t <= 2.9e-181) {
		tmp = x * (y * z);
	} else if (t <= 1.85e+15) {
		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 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-4d-28)) then
        tmp = t_2
    else if (t <= (-5.5d-86)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 6.5d-245) then
        tmp = t_1
    else if (t <= 2.9d-181) then
        tmp = x * (y * z)
    else if (t <= 1.85d+15) 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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4e-28) {
		tmp = t_2;
	} else if (t <= -5.5e-86) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 6.5e-245) {
		tmp = t_1;
	} else if (t <= 2.9e-181) {
		tmp = x * (y * z);
	} else if (t <= 1.85e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -4e-28:
		tmp = t_2
	elif t <= -5.5e-86:
		tmp = i * ((a * b) - (y * j))
	elif t <= 6.5e-245:
		tmp = t_1
	elif t <= 2.9e-181:
		tmp = x * (y * z)
	elif t <= 1.85e+15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4e-28)
		tmp = t_2;
	elseif (t <= -5.5e-86)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 6.5e-245)
		tmp = t_1;
	elseif (t <= 2.9e-181)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 1.85e+15)
		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 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -4e-28)
		tmp = t_2;
	elseif (t <= -5.5e-86)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 6.5e-245)
		tmp = t_1;
	elseif (t <= 2.9e-181)
		tmp = x * (y * z);
	elseif (t <= 1.85e+15)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e-28], t$95$2, If[LessEqual[t, -5.5e-86], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-245], t$95$1, If[LessEqual[t, 2.9e-181], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+15], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.99999999999999988e-28 or 1.85e15 < t

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 65.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 68.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 68.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in z around 0 64.3%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(i \cdot b\right)\right)} \]

   5. Taylor expanded in t around inf 63.4%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   6. Step-by-step derivation

      1. *-commutative 63.4%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 63.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 63.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   7. Simplified 63.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -3.99999999999999988e-28 < t < -5.5e-86

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. associate-+r- 72.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

      3. fma-def 72.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - i \cdot a\right) \]

      4. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right) \]

      5. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right) \]

      6. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right) \]

      7. fma-neg 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -i \cdot a\right)} \]

      8. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, -\color{blue}{a \cdot i}\right) \]

      9. distribute-rgt-neg-in 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in i around inf 67.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   5. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. sub-neg 67.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(a \cdot b\right)\right)\right)} \]

      3. mul-1-neg 67.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-a \cdot b\right)}\right)\right) \]

      4. remove-double-neg 67.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{a \cdot b}\right) \]

      5. +-commutative 67.3%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 67.3%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 67.3%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      8. *-commutative 67.3%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   6. Simplified 67.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if -5.5e-86 < t < 6.5000000000000004e-245 or 2.8999999999999998e-181 < t < 1.85e15

   1. Initial program 88.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 88.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 88.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 88.8%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 88.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 88.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 88.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 62.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   if 6.5000000000000004e-245 < t < 2.8999999999999998e-181

   1. Initial program 92.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 92.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 92.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 92.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 92.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 92.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 92.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 92.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 78.8%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 78.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 78.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 78.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 78.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 78.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 78.9%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 78.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 78.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 78.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 78.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 78.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 78.9%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 56.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 56.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 56.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 56.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 56.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 40.9%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 61.5%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. *-commutative 61.5%

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   12. Simplified 61.5%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-245}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 14: 52.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 320000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -5.5e-28)
     t_2
     (if (<= t -2e-86)
       (* i (- (* a b) (* y j)))
       (if (<= t 5.4e-243)
         t_1
         (if (<= t 3.1e-181)
           (* y (- (* x z) (* i j)))
           (if (<= t 320000.0) 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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.5e-28) {
		tmp = t_2;
	} else if (t <= -2e-86) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 5.4e-243) {
		tmp = t_1;
	} else if (t <= 3.1e-181) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 320000.0) {
		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 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-5.5d-28)) then
        tmp = t_2
    else if (t <= (-2d-86)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 5.4d-243) then
        tmp = t_1
    else if (t <= 3.1d-181) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 320000.0d0) 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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.5e-28) {
		tmp = t_2;
	} else if (t <= -2e-86) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 5.4e-243) {
		tmp = t_1;
	} else if (t <= 3.1e-181) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 320000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -5.5e-28:
		tmp = t_2
	elif t <= -2e-86:
		tmp = i * ((a * b) - (y * j))
	elif t <= 5.4e-243:
		tmp = t_1
	elif t <= 3.1e-181:
		tmp = y * ((x * z) - (i * j))
	elif t <= 320000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.5e-28)
		tmp = t_2;
	elseif (t <= -2e-86)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 5.4e-243)
		tmp = t_1;
	elseif (t <= 3.1e-181)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 320000.0)
		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 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -5.5e-28)
		tmp = t_2;
	elseif (t <= -2e-86)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 5.4e-243)
		tmp = t_1;
	elseif (t <= 3.1e-181)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 320000.0)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-28], t$95$2, If[LessEqual[t, -2e-86], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-243], t$95$1, If[LessEqual[t, 3.1e-181], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 320000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.49999999999999967e-28 or 3.2e5 < t

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 65.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 68.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 68.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 68.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 68.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in z around 0 64.3%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(i \cdot b\right)\right)} \]

   5. Taylor expanded in t around inf 63.4%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   6. Step-by-step derivation

      1. *-commutative 63.4%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 63.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 63.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   7. Simplified 63.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -5.49999999999999967e-28 < t < -2.00000000000000017e-86

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. associate-+r- 72.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

      3. fma-def 72.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - i \cdot a\right) \]

      4. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right) \]

      5. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right) \]

      6. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right) \]

      7. fma-neg 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -i \cdot a\right)} \]

      8. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, -\color{blue}{a \cdot i}\right) \]

      9. distribute-rgt-neg-in 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in i around inf 67.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   5. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. sub-neg 67.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(a \cdot b\right)\right)\right)} \]

      3. mul-1-neg 67.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-a \cdot b\right)}\right)\right) \]

      4. remove-double-neg 67.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{a \cdot b}\right) \]

      5. +-commutative 67.3%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 67.3%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 67.3%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      8. *-commutative 67.3%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   6. Simplified 67.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if -2.00000000000000017e-86 < t < 5.40000000000000021e-243 or 3.10000000000000021e-181 < t < 3.2e5

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 88.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 88.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 62.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   if 5.40000000000000021e-243 < t < 3.10000000000000021e-181

   1. Initial program 92.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 92.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 92.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 92.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 92.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 92.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 92.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 92.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 77.5%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 77.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 77.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 77.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 77.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 77.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 77.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 77.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 77.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 77.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 77.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 77.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 77.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 59.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 59.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 59.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-243}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 320000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 15: 52.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 3100000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -2.6e+48)
     t_1
     (if (<= t -1.35e+17)
       (* j (- (* t c) (* y i)))
       (if (<= t -4.5e-28)
         t_1
         (if (<= t -2.8e-86)
           (* i (- (* a b) (* y j)))
           (if (<= t 3100000000000.0) (* b (- (* a i) (* z c))) 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 <= -2.6e+48) {
		tmp = t_1;
	} else if (t <= -1.35e+17) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= -4.5e-28) {
		tmp = t_1;
	} else if (t <= -2.8e-86) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 3100000000000.0) {
		tmp = b * ((a * i) - (z * c));
	} 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 <= (-2.6d+48)) then
        tmp = t_1
    else if (t <= (-1.35d+17)) then
        tmp = j * ((t * c) - (y * i))
    else if (t <= (-4.5d-28)) then
        tmp = t_1
    else if (t <= (-2.8d-86)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 3100000000000.0d0) then
        tmp = b * ((a * i) - (z * c))
    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 <= -2.6e+48) {
		tmp = t_1;
	} else if (t <= -1.35e+17) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= -4.5e-28) {
		tmp = t_1;
	} else if (t <= -2.8e-86) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 3100000000000.0) {
		tmp = b * ((a * i) - (z * c));
	} 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 <= -2.6e+48:
		tmp = t_1
	elif t <= -1.35e+17:
		tmp = j * ((t * c) - (y * i))
	elif t <= -4.5e-28:
		tmp = t_1
	elif t <= -2.8e-86:
		tmp = i * ((a * b) - (y * j))
	elif t <= 3100000000000.0:
		tmp = b * ((a * i) - (z * c))
	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 <= -2.6e+48)
		tmp = t_1;
	elseif (t <= -1.35e+17)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (t <= -4.5e-28)
		tmp = t_1;
	elseif (t <= -2.8e-86)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 3100000000000.0)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	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 <= -2.6e+48)
		tmp = t_1;
	elseif (t <= -1.35e+17)
		tmp = j * ((t * c) - (y * i));
	elseif (t <= -4.5e-28)
		tmp = t_1;
	elseif (t <= -2.8e-86)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 3100000000000.0)
		tmp = b * ((a * i) - (z * c));
	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, -2.6e+48], t$95$1, If[LessEqual[t, -1.35e+17], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.5e-28], t$95$1, If[LessEqual[t, -2.8e-86], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3100000000000.0], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.59999999999999995e48 or -1.35e17 < t < -4.4999999999999998e-28 or 3.1e12 < t

   1. Initial program 65.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 65.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 67.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 67.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 68.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 68.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 68.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 68.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 68.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 68.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 68.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 68.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 68.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 68.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 68.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 68.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in z around 0 62.7%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(i \cdot b\right)\right)} \]

   5. Taylor expanded in t around inf 65.4%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   6. Step-by-step derivation

      1. *-commutative 65.4%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 65.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 65.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -2.59999999999999995e48 < t < -1.35e17

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 81.7%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 81.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 81.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 81.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 81.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 81.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 81.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 81.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 81.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 81.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 81.8%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   if -4.4999999999999998e-28 < t < -2.80000000000000009e-86

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. associate-+r- 72.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

      3. fma-def 72.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - i \cdot a\right) \]

      4. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right) \]

      5. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right) \]

      6. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right) \]

      7. fma-neg 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -i \cdot a\right)} \]

      8. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, -\color{blue}{a \cdot i}\right) \]

      9. distribute-rgt-neg-in 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in i around inf 67.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   5. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. sub-neg 67.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(a \cdot b\right)\right)\right)} \]

      3. mul-1-neg 67.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-a \cdot b\right)}\right)\right) \]

      4. remove-double-neg 67.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{a \cdot b}\right) \]

      5. +-commutative 67.3%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 67.3%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 67.3%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      8. *-commutative 67.3%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   6. Simplified 67.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if -2.80000000000000009e-86 < t < 3.1e12

   1. Initial program 89.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 89.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 89.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 57.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 3100000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 16: 29.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+103}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* b (- z)))))
   (if (<= a -1.7e+103)
     (* i (* a b))
     (if (<= a -1.65e-159)
       (* y (* x z))
       (if (<= a -5.5e-289)
         t_1
         (if (<= a 3e-178)
           (* x (* y z))
           (if (<= a 1.7e+62) t_1 (* b (* a 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 = c * (b * -z);
	double tmp;
	if (a <= -1.7e+103) {
		tmp = i * (a * b);
	} else if (a <= -1.65e-159) {
		tmp = y * (x * z);
	} else if (a <= -5.5e-289) {
		tmp = t_1;
	} else if (a <= 3e-178) {
		tmp = x * (y * z);
	} else if (a <= 1.7e+62) {
		tmp = t_1;
	} else {
		tmp = b * (a * 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 = c * (b * -z)
    if (a <= (-1.7d+103)) then
        tmp = i * (a * b)
    else if (a <= (-1.65d-159)) then
        tmp = y * (x * z)
    else if (a <= (-5.5d-289)) then
        tmp = t_1
    else if (a <= 3d-178) then
        tmp = x * (y * z)
    else if (a <= 1.7d+62) then
        tmp = t_1
    else
        tmp = b * (a * 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 = c * (b * -z);
	double tmp;
	if (a <= -1.7e+103) {
		tmp = i * (a * b);
	} else if (a <= -1.65e-159) {
		tmp = y * (x * z);
	} else if (a <= -5.5e-289) {
		tmp = t_1;
	} else if (a <= 3e-178) {
		tmp = x * (y * z);
	} else if (a <= 1.7e+62) {
		tmp = t_1;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (b * -z)
	tmp = 0
	if a <= -1.7e+103:
		tmp = i * (a * b)
	elif a <= -1.65e-159:
		tmp = y * (x * z)
	elif a <= -5.5e-289:
		tmp = t_1
	elif a <= 3e-178:
		tmp = x * (y * z)
	elif a <= 1.7e+62:
		tmp = t_1
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(b * Float64(-z)))
	tmp = 0.0
	if (a <= -1.7e+103)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= -1.65e-159)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -5.5e-289)
		tmp = t_1;
	elseif (a <= 3e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1.7e+62)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (b * -z);
	tmp = 0.0;
	if (a <= -1.7e+103)
		tmp = i * (a * b);
	elseif (a <= -1.65e-159)
		tmp = y * (x * z);
	elseif (a <= -5.5e-289)
		tmp = t_1;
	elseif (a <= 3e-178)
		tmp = x * (y * z);
	elseif (a <= 1.7e+62)
		tmp = t_1;
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+103], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e-159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-289], t$95$1, If[LessEqual[a, 3e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+62], t$95$1, N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.6999999999999999e103

   1. Initial program 64.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 64.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 64.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 67.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 67.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in z around 0 67.8%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(i \cdot b\right)\right)} \]

   5. Taylor expanded in i around -inf 67.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right) + \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)} \]

      2. mul-1-neg 67.5%

         \[\leadsto \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \color{blue}{\left(-i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)} \]

      3. unsub-neg 67.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)} \]

      4. *-commutative 67.5%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot t\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      5. associate-*r* 67.5%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot t} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      6. *-commutative 67.5%

         \[\leadsto \left(\left(c \cdot j\right) \cdot t + -1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)}\right)\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      7. associate-*r* 62.3%

         \[\leadsto \left(\left(c \cdot j\right) \cdot t + -1 \cdot \color{blue}{\left(\left(a \cdot x\right) \cdot t\right)}\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      8. associate-*r* 62.3%

         \[\leadsto \left(\left(c \cdot j\right) \cdot t + \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t}\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      9. distribute-rgt-in 65.0%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      10. mul-1-neg 65.0%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      11. unsub-neg 65.0%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      12. mul-1-neg 65.0%

          \[\leadsto t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \left(y \cdot j + \color{blue}{\left(-a \cdot b\right)}\right) \]

      13. unsub-neg 65.0%

          \[\leadsto t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \color{blue}{\left(y \cdot j - a \cdot b\right)} \]

      14. *-commutative 65.0%

          \[\leadsto t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \left(y \cdot j - \color{blue}{b \cdot a}\right) \]

   7. Simplified 65.0%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \left(y \cdot j - b \cdot a\right)} \]

   8. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -1.6999999999999999e103 < a < -1.6500000000000001e-159

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 88.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 88.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 73.4%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 73.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 73.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 73.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 73.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 73.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 73.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 73.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 73.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 73.4%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 73.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 73.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 73.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 73.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 73.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 73.4%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 73.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 52.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 52.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 52.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 52.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 52.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 42.7%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.6500000000000001e-159 < a < -5.5000000000000004e-289 or 2.9999999999999999e-178 < a < 1.70000000000000007e62

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 80.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 62.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in c around inf 43.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      2. mul-1-neg 43.1%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   7. Simplified 43.1%

      \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   if -5.5000000000000004e-289 < a < 2.9999999999999999e-178

   1. Initial program 85.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 85.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 87.5%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 87.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 51.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 51.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 39.5%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 44.1%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. *-commutative 44.1%

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   12. Simplified 44.1%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 1.70000000000000007e62 < a

   1. Initial program 58.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 60.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 44.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 44.0%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+103}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 17: 30.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{if}\;a \leq -8 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* b (- z)))))
   (if (<= a -8e+60)
     (* a (* x (- t)))
     (if (<= a -3.9e-159)
       (* y (* x z))
       (if (<= a -3.6e-286)
         t_1
         (if (<= a 1.7e-178)
           (* x (* y z))
           (if (<= a 2.8e+62) t_1 (* b (* a 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 = c * (b * -z);
	double tmp;
	if (a <= -8e+60) {
		tmp = a * (x * -t);
	} else if (a <= -3.9e-159) {
		tmp = y * (x * z);
	} else if (a <= -3.6e-286) {
		tmp = t_1;
	} else if (a <= 1.7e-178) {
		tmp = x * (y * z);
	} else if (a <= 2.8e+62) {
		tmp = t_1;
	} else {
		tmp = b * (a * 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 = c * (b * -z)
    if (a <= (-8d+60)) then
        tmp = a * (x * -t)
    else if (a <= (-3.9d-159)) then
        tmp = y * (x * z)
    else if (a <= (-3.6d-286)) then
        tmp = t_1
    else if (a <= 1.7d-178) then
        tmp = x * (y * z)
    else if (a <= 2.8d+62) then
        tmp = t_1
    else
        tmp = b * (a * 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 = c * (b * -z);
	double tmp;
	if (a <= -8e+60) {
		tmp = a * (x * -t);
	} else if (a <= -3.9e-159) {
		tmp = y * (x * z);
	} else if (a <= -3.6e-286) {
		tmp = t_1;
	} else if (a <= 1.7e-178) {
		tmp = x * (y * z);
	} else if (a <= 2.8e+62) {
		tmp = t_1;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (b * -z)
	tmp = 0
	if a <= -8e+60:
		tmp = a * (x * -t)
	elif a <= -3.9e-159:
		tmp = y * (x * z)
	elif a <= -3.6e-286:
		tmp = t_1
	elif a <= 1.7e-178:
		tmp = x * (y * z)
	elif a <= 2.8e+62:
		tmp = t_1
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(b * Float64(-z)))
	tmp = 0.0
	if (a <= -8e+60)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (a <= -3.9e-159)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -3.6e-286)
		tmp = t_1;
	elseif (a <= 1.7e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 2.8e+62)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (b * -z);
	tmp = 0.0;
	if (a <= -8e+60)
		tmp = a * (x * -t);
	elseif (a <= -3.9e-159)
		tmp = y * (x * z);
	elseif (a <= -3.6e-286)
		tmp = t_1;
	elseif (a <= 1.7e-178)
		tmp = x * (y * z);
	elseif (a <= 2.8e+62)
		tmp = t_1;
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+60], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.9e-159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.6e-286], t$95$1, If[LessEqual[a, 1.7e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+62], t$95$1, N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.9999999999999996e60

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 76.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 76.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 62.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   5. Taylor expanded in t around inf 41.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. *-commutative 41.8%

         \[\leadsto a \cdot \left(-\color{blue}{x \cdot t}\right) \]

      3. distribute-rgt-neg-in 41.8%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   7. Simplified 41.8%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -7.9999999999999996e60 < a < -3.89999999999999977e-159

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 86.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 79.7%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 79.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 60.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 60.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 60.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 60.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 48.9%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.89999999999999977e-159 < a < -3.60000000000000013e-286 or 1.69999999999999986e-178 < a < 2.80000000000000014e62

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 80.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 62.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in c around inf 43.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      2. mul-1-neg 43.1%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   7. Simplified 43.1%

      \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   if -3.60000000000000013e-286 < a < 1.69999999999999986e-178

   1. Initial program 85.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 85.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 87.5%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 87.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 87.5%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 87.5%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 51.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 51.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 39.5%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 44.1%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. *-commutative 44.1%

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   12. Simplified 44.1%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 2.80000000000000014e62 < a

   1. Initial program 58.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 60.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 44.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 44.0%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-286}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 18: 30.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{-224}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -4e+58)
   (* a (* x (- t)))
   (if (<= a -1.65e-159)
     (* y (* x z))
     (if (<= a 1e-224)
       (* b (* c (- z)))
       (if (<= a 4e-178)
         (* x (* y z))
         (if (<= a 8e+58) (* c (* b (- z))) (* b (* a 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 (a <= -4e+58) {
		tmp = a * (x * -t);
	} else if (a <= -1.65e-159) {
		tmp = y * (x * z);
	} else if (a <= 1e-224) {
		tmp = b * (c * -z);
	} else if (a <= 4e-178) {
		tmp = x * (y * z);
	} else if (a <= 8e+58) {
		tmp = c * (b * -z);
	} else {
		tmp = b * (a * 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 (a <= (-4d+58)) then
        tmp = a * (x * -t)
    else if (a <= (-1.65d-159)) then
        tmp = y * (x * z)
    else if (a <= 1d-224) then
        tmp = b * (c * -z)
    else if (a <= 4d-178) then
        tmp = x * (y * z)
    else if (a <= 8d+58) then
        tmp = c * (b * -z)
    else
        tmp = b * (a * 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 (a <= -4e+58) {
		tmp = a * (x * -t);
	} else if (a <= -1.65e-159) {
		tmp = y * (x * z);
	} else if (a <= 1e-224) {
		tmp = b * (c * -z);
	} else if (a <= 4e-178) {
		tmp = x * (y * z);
	} else if (a <= 8e+58) {
		tmp = c * (b * -z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -4e+58:
		tmp = a * (x * -t)
	elif a <= -1.65e-159:
		tmp = y * (x * z)
	elif a <= 1e-224:
		tmp = b * (c * -z)
	elif a <= 4e-178:
		tmp = x * (y * z)
	elif a <= 8e+58:
		tmp = c * (b * -z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -4e+58)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (a <= -1.65e-159)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1e-224)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (a <= 4e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 8e+58)
		tmp = Float64(c * Float64(b * Float64(-z)));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -4e+58)
		tmp = a * (x * -t);
	elseif (a <= -1.65e-159)
		tmp = y * (x * z);
	elseif (a <= 1e-224)
		tmp = b * (c * -z);
	elseif (a <= 4e-178)
		tmp = x * (y * z);
	elseif (a <= 8e+58)
		tmp = c * (b * -z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -4e+58], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e-159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-224], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+58], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.99999999999999978e58

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 76.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 76.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 62.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   5. Taylor expanded in t around inf 41.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. *-commutative 41.8%

         \[\leadsto a \cdot \left(-\color{blue}{x \cdot t}\right) \]

      3. distribute-rgt-neg-in 41.8%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   7. Simplified 41.8%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -3.99999999999999978e58 < a < -1.6500000000000001e-159

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 86.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 79.7%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 79.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 60.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 60.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 60.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 60.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 48.9%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.6500000000000001e-159 < a < 1e-224

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 85.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 85.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around 0 37.7%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 37.7%

         \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

      2. distribute-rgt-neg-in 37.7%

         \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   7. Simplified 37.7%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   if 1e-224 < a < 3.9999999999999998e-178

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 79.8%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 79.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 70.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 70.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 70.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 70.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 70.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 60.5%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 60.7%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. *-commutative 60.7%

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   12. Simplified 60.7%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 3.9999999999999998e-178 < a < 7.99999999999999955e58

   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. +-commutative 79.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 64.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in c around inf 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      2. mul-1-neg 46.4%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   7. Simplified 46.4%

      \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   if 7.99999999999999955e58 < a

   1. Initial program 58.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 60.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 44.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 44.0%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{-224}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+58}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 19: 30.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(-t \cdot a\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.35e+59)
   (* x (- (* t a)))
   (if (<= a -5.5e-160)
     (* y (* x z))
     (if (<= a 1.16e-225)
       (* b (* c (- z)))
       (if (<= a 2.4e-178)
         (* x (* y z))
         (if (<= a 6.2e+61) (* c (* b (- z))) (* b (* a 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 (a <= -1.35e+59) {
		tmp = x * -(t * a);
	} else if (a <= -5.5e-160) {
		tmp = y * (x * z);
	} else if (a <= 1.16e-225) {
		tmp = b * (c * -z);
	} else if (a <= 2.4e-178) {
		tmp = x * (y * z);
	} else if (a <= 6.2e+61) {
		tmp = c * (b * -z);
	} else {
		tmp = b * (a * 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 (a <= (-1.35d+59)) then
        tmp = x * -(t * a)
    else if (a <= (-5.5d-160)) then
        tmp = y * (x * z)
    else if (a <= 1.16d-225) then
        tmp = b * (c * -z)
    else if (a <= 2.4d-178) then
        tmp = x * (y * z)
    else if (a <= 6.2d+61) then
        tmp = c * (b * -z)
    else
        tmp = b * (a * 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 (a <= -1.35e+59) {
		tmp = x * -(t * a);
	} else if (a <= -5.5e-160) {
		tmp = y * (x * z);
	} else if (a <= 1.16e-225) {
		tmp = b * (c * -z);
	} else if (a <= 2.4e-178) {
		tmp = x * (y * z);
	} else if (a <= 6.2e+61) {
		tmp = c * (b * -z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.35e+59:
		tmp = x * -(t * a)
	elif a <= -5.5e-160:
		tmp = y * (x * z)
	elif a <= 1.16e-225:
		tmp = b * (c * -z)
	elif a <= 2.4e-178:
		tmp = x * (y * z)
	elif a <= 6.2e+61:
		tmp = c * (b * -z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.35e+59)
		tmp = Float64(x * Float64(-Float64(t * a)));
	elseif (a <= -5.5e-160)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1.16e-225)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (a <= 2.4e-178)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 6.2e+61)
		tmp = Float64(c * Float64(b * Float64(-z)));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.35e+59)
		tmp = x * -(t * a);
	elseif (a <= -5.5e-160)
		tmp = y * (x * z);
	elseif (a <= 1.16e-225)
		tmp = b * (c * -z);
	elseif (a <= 2.4e-178)
		tmp = x * (y * z);
	elseif (a <= 6.2e+61)
		tmp = c * (b * -z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.35e+59], N[(x * (-N[(t * a), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, -5.5e-160], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e-225], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-178], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+61], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.3500000000000001e59

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 76.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 76.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 62.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   5. Taylor expanded in t around inf 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 41.8%

         \[\leadsto -a \cdot \color{blue}{\left(x \cdot t\right)} \]

      3. *-commutative 41.8%

         \[\leadsto -\color{blue}{\left(x \cdot t\right) \cdot a} \]

      4. distribute-lft-neg-out 41.8%

         \[\leadsto \color{blue}{\left(-x \cdot t\right) \cdot a} \]

      5. *-commutative 41.8%

         \[\leadsto \left(-\color{blue}{t \cdot x}\right) \cdot a \]

      6. mul-1-neg 41.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \cdot a \]

      7. associate-*r* 41.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \cdot a \]

      8. *-commutative 41.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot t\right)\right)} \cdot a \]

      9. associate-*l* 45.1%

         \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot t\right) \cdot a\right)} \]

      10. neg-mul-1 45.1%

          \[\leadsto x \cdot \left(\color{blue}{\left(-t\right)} \cdot a\right) \]

   7. Simplified 45.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(-t\right) \cdot a\right)} \]

   if -1.3500000000000001e59 < a < -5.5e-160

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 86.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 86.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 79.7%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 79.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.7%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 79.7%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 60.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 60.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 60.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 60.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 48.9%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -5.5e-160 < a < 1.16000000000000001e-225

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 85.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 85.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around 0 37.7%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 37.7%

         \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

      2. distribute-rgt-neg-in 37.7%

         \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   7. Simplified 37.7%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   if 1.16000000000000001e-225 < a < 2.40000000000000005e-178

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 79.8%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 79.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.8%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 79.8%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 70.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 70.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 70.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 70.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 70.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 60.5%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 60.7%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. *-commutative 60.7%

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   12. Simplified 60.7%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 2.40000000000000005e-178 < a < 6.1999999999999998e61

   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. +-commutative 79.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 79.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 64.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in c around inf 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      2. mul-1-neg 46.4%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   7. Simplified 46.4%

      \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   if 6.1999999999999998e61 < a

   1. Initial program 58.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 60.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 44.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 44.0%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(-t \cdot a\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 20: 43.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.4 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{+47}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -7.4e+46)
     t_1
     (if (<= a -6e-160)
       (* y (* x z))
       (if (<= a 1e+47) (* b (- (* a i) (* z c))) 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.4e+46) {
		tmp = t_1;
	} else if (a <= -6e-160) {
		tmp = y * (x * z);
	} else if (a <= 1e+47) {
		tmp = b * ((a * i) - (z * c));
	} 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 = a * ((b * i) - (x * t))
    if (a <= (-7.4d+46)) then
        tmp = t_1
    else if (a <= (-6d-160)) then
        tmp = y * (x * z)
    else if (a <= 1d+47) then
        tmp = b * ((a * i) - (z * c))
    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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.4e+46) {
		tmp = t_1;
	} else if (a <= -6e-160) {
		tmp = y * (x * z);
	} else if (a <= 1e+47) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -7.4e+46:
		tmp = t_1
	elif a <= -6e-160:
		tmp = y * (x * z)
	elif a <= 1e+47:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7.4e+46)
		tmp = t_1;
	elseif (a <= -6e-160)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1e+47)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -7.4e+46)
		tmp = t_1;
	elseif (a <= -6e-160)
		tmp = y * (x * z);
	elseif (a <= 1e+47)
		tmp = b * ((a * i) - (z * c));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.4e+46], t$95$1, If[LessEqual[a, -6e-160], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+47], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.3999999999999998e46 or 1e47 < a

   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. sub-neg 68.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 68.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 71.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 71.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 72.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 72.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 72.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 72.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 72.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 72.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 72.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 72.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 72.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 72.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 72.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 67.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   5. Taylor expanded in a around 0 67.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} + -1 \cdot \left(t \cdot x\right)\right) \]

      2. mul-1-neg 67.5%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. *-commutative 67.5%

         \[\leadsto a \cdot \left(b \cdot i + \left(-\color{blue}{x \cdot t}\right)\right) \]

      4. unsub-neg 67.5%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - x \cdot t\right)} \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - x \cdot t\right)} \]

   if -7.3999999999999998e46 < a < -5.99999999999999993e-160

   1. Initial program 86.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 86.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 79.2%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 79.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 61.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 61.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 61.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 50.0%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -5.99999999999999993e-160 < a < 1e47

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 81.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 45.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{+47}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 21: 48.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+66}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -4.8e+46)
     t_1
     (if (<= a -3.7e-158)
       (* y (* x z))
       (if (<= a 1.9e+66) (* c (- (* t j) (* z b))) 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.8e+46) {
		tmp = t_1;
	} else if (a <= -3.7e-158) {
		tmp = y * (x * z);
	} else if (a <= 1.9e+66) {
		tmp = c * ((t * j) - (z * b));
	} 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 = a * ((b * i) - (x * t))
    if (a <= (-4.8d+46)) then
        tmp = t_1
    else if (a <= (-3.7d-158)) then
        tmp = y * (x * z)
    else if (a <= 1.9d+66) then
        tmp = c * ((t * j) - (z * b))
    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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.8e+46) {
		tmp = t_1;
	} else if (a <= -3.7e-158) {
		tmp = y * (x * z);
	} else if (a <= 1.9e+66) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.8e+46:
		tmp = t_1
	elif a <= -3.7e-158:
		tmp = y * (x * z)
	elif a <= 1.9e+66:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.8e+46)
		tmp = t_1;
	elseif (a <= -3.7e-158)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1.9e+66)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.8e+46)
		tmp = t_1;
	elseif (a <= -3.7e-158)
		tmp = y * (x * z);
	elseif (a <= 1.9e+66)
		tmp = c * ((t * j) - (z * b));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+46], t$95$1, If[LessEqual[a, -3.7e-158], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+66], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.80000000000000017e46 or 1.9000000000000001e66 < a

   1. Initial program 66.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 66.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 66.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 69.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 69.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 70.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 70.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 70.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 70.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 70.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 70.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 70.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 70.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 70.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 70.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 70.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around inf 69.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   5. Taylor expanded in a around 0 69.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 69.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} + -1 \cdot \left(t \cdot x\right)\right) \]

      2. mul-1-neg 69.8%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. *-commutative 69.8%

         \[\leadsto a \cdot \left(b \cdot i + \left(-\color{blue}{x \cdot t}\right)\right) \]

      4. unsub-neg 69.8%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - x \cdot t\right)} \]

   7. Simplified 69.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - x \cdot t\right)} \]

   if -4.80000000000000017e46 < a < -3.7000000000000001e-158

   1. Initial program 86.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 86.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 86.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 79.2%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 79.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 79.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 79.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 61.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 61.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 61.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 50.0%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.7000000000000001e-158 < a < 1.9000000000000001e66

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. associate-+r- 82.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

      3. fma-def 82.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - i \cdot a\right) \]

      4. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right) \]

      5. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right) \]

      6. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right) \]

      7. fma-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -i \cdot a\right)} \]

      8. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, -\color{blue}{a \cdot i}\right) \]

      9. distribute-rgt-neg-in 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 57.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+66}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 22: 28.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+93}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -8.4e+102)
   (* i (* a b))
   (if (<= a 2.4e-191)
     (* x (* y z))
     (if (<= a 2.7e+93) (* c (* t j)) (* b (* a 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 (a <= -8.4e+102) {
		tmp = i * (a * b);
	} else if (a <= 2.4e-191) {
		tmp = x * (y * z);
	} else if (a <= 2.7e+93) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * 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 (a <= (-8.4d+102)) then
        tmp = i * (a * b)
    else if (a <= 2.4d-191) then
        tmp = x * (y * z)
    else if (a <= 2.7d+93) then
        tmp = c * (t * j)
    else
        tmp = b * (a * 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 (a <= -8.4e+102) {
		tmp = i * (a * b);
	} else if (a <= 2.4e-191) {
		tmp = x * (y * z);
	} else if (a <= 2.7e+93) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -8.4e+102:
		tmp = i * (a * b)
	elif a <= 2.4e-191:
		tmp = x * (y * z)
	elif a <= 2.7e+93:
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -8.4e+102)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= 2.4e-191)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 2.7e+93)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -8.4e+102)
		tmp = i * (a * b);
	elseif (a <= 2.4e-191)
		tmp = x * (y * z);
	elseif (a <= 2.7e+93)
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -8.4e+102], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-191], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+93], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.40000000000000006e102

   1. Initial program 64.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 64.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 64.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 67.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 67.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 70.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 70.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in z around 0 67.8%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(i \cdot b\right)\right)} \]

   5. Taylor expanded in i around -inf 67.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right) + \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + -1 \cdot \left(i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)} \]

      2. mul-1-neg 67.5%

         \[\leadsto \left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) + \color{blue}{\left(-i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)\right)} \]

      3. unsub-neg 67.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(t \cdot j\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right)} \]

      4. *-commutative 67.5%

         \[\leadsto \left(c \cdot \color{blue}{\left(j \cdot t\right)} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      5. associate-*r* 67.5%

         \[\leadsto \left(\color{blue}{\left(c \cdot j\right) \cdot t} + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      6. *-commutative 67.5%

         \[\leadsto \left(\left(c \cdot j\right) \cdot t + -1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)}\right)\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      7. associate-*r* 62.3%

         \[\leadsto \left(\left(c \cdot j\right) \cdot t + -1 \cdot \color{blue}{\left(\left(a \cdot x\right) \cdot t\right)}\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      8. associate-*r* 62.3%

         \[\leadsto \left(\left(c \cdot j\right) \cdot t + \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t}\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      9. distribute-rgt-in 65.0%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      10. mul-1-neg 65.0%

          \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      11. unsub-neg 65.0%

          \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - i \cdot \left(y \cdot j + -1 \cdot \left(a \cdot b\right)\right) \]

      12. mul-1-neg 65.0%

          \[\leadsto t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \left(y \cdot j + \color{blue}{\left(-a \cdot b\right)}\right) \]

      13. unsub-neg 65.0%

          \[\leadsto t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \color{blue}{\left(y \cdot j - a \cdot b\right)} \]

      14. *-commutative 65.0%

          \[\leadsto t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \left(y \cdot j - \color{blue}{b \cdot a}\right) \]

   7. Simplified 65.0%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) - i \cdot \left(y \cdot j - b \cdot a\right)} \]

   8. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -8.40000000000000006e102 < a < 2.3999999999999999e-191

   1. Initial program 87.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 87.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 87.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 87.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 87.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 87.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 87.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 87.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 76.4%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 77.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 77.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 77.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 77.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 77.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 77.2%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 77.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 77.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 77.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 77.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 77.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 77.2%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 47.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   8. Step-by-step derivation

      1. +-commutative 47.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 47.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 47.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 47.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   10. Taylor expanded in z around inf 36.1%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 36.7%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. *-commutative 36.7%

          \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   12. Simplified 36.7%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 2.3999999999999999e-191 < a < 2.6999999999999999e93

   1. Initial program 75.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 68.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 68.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 68.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 68.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 68.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 68.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 68.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 68.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 68.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 68.6%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 68.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 68.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 68.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 68.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 68.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 68.6%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 68.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 33.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 2.6999999999999999e93 < a

   1. Initial program 58.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 60.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.3%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 60.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 60.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 52.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 48.4%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 48.4%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+93}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 23: 28.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-14} \lor \neg \left(a \leq 1.4 \cdot 10^{+92}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -4.2e-14) (not (<= a 1.4e+92))) (* b (* a i)) (* c (* t 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 ((a <= -4.2e-14) || !(a <= 1.4e+92)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * 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 ((a <= (-4.2d-14)) .or. (.not. (a <= 1.4d+92))) then
        tmp = b * (a * i)
    else
        tmp = c * (t * 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 ((a <= -4.2e-14) || !(a <= 1.4e+92)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -4.2e-14) or not (a <= 1.4e+92):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -4.2e-14) || !(a <= 1.4e+92))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -4.2e-14) || ~((a <= 1.4e+92)))
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -4.2e-14], N[Not[LessEqual[a, 1.4e+92]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1999999999999998e-14 or 1.4e92 < a

   1. Initial program 69.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 70.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 70.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 44.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 38.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 38.3%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if -4.1999999999999998e-14 < a < 1.4e92

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around 0 74.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. fma-neg 75.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. fma-neg 75.3%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \color{blue}{\mathsf{fma}\left(z, c, -a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. distribute-rgt-neg-out 75.3%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, -b \cdot \mathsf{fma}\left(z, c, \color{blue}{a \cdot \left(-i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. distribute-rgt-neg-in 75.3%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, \color{blue}{b \cdot \left(-\mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      8. neg-sub0 75.3%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(0 - \mathsf{fma}\left(z, c, a \cdot \left(-i\right)\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      9. distribute-rgt-neg-out 75.3%

         \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \mathsf{fma}\left(z, c, \color{blue}{-a \cdot i}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      10. fma-neg 75.3%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(0 - \color{blue}{\left(z \cdot c - a \cdot i\right)}\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      11. associate-+l- 75.3%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(\left(0 - z \cdot c\right) + a \cdot i\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      12. neg-sub0 75.3%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(\color{blue}{\left(-z \cdot c\right)} + a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      13. +-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i + \left(-z \cdot c\right)\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      14. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i + \left(-\color{blue}{c \cdot z}\right)\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      15. sub-neg 75.3%

          \[\leadsto \mathsf{fma}\left(y, z \cdot x, b \cdot \color{blue}{\left(a \cdot i - c \cdot z\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot x, b \cdot \left(a \cdot i - c \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 26.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-14} \lor \neg \left(a \leq 1.4 \cdot 10^{+92}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 24: 21.8% 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 76.2%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. sub-neg 76.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. associate-+l+ 76.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   3. fma-def 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   4. +-commutative 78.6%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   5. fma-def 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. *-commutative 79.0%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   7. *-commutative 79.0%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   8. distribute-rgt-neg-in 79.0%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

   9. sub-neg 79.0%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

   10. +-commutative 79.0%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

   11. distribute-neg-in 79.0%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

   12. unsub-neg 79.0%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

   13. remove-double-neg 79.0%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

   14. *-commutative 79.0%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

   15. *-commutative 79.0%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

3. Simplified 79.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

4. Taylor expanded in a around inf 40.3%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

5. Taylor expanded in t around 0 21.9%

   \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

6. Final simplification 21.9%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Alternative 25: 21.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* b (* a i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * 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 = b * (a * 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 b * (a * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return b * (a * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(b * Float64(a * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = b * (a * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.2%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 76.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-def 77.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   3. *-commutative 77.0%

      \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   4. *-commutative 77.0%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   5. *-commutative 77.0%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

   6. *-commutative 77.0%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

3. Simplified 77.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

4. Taylor expanded in b around inf 42.0%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

5. Taylor expanded in i around inf 23.0%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
6. Step-by-step derivation

   1. *-commutative 23.0%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

7. Simplified 23.0%

   \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

8. Final simplification 23.0%

   \[\leadsto b \cdot \left(a \cdot i\right) \]

Developer target: 68.7% 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 2023238 
(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)))))