Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.2% → 81.7%

Time: 28.3s

Alternatives: 26

Speedup: 0.5×

• 59.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (y * z) - (t * a);
	double t_3 = (t * c) - (y * i);
	double tmp;
	if ((((x * t_2) + t_1) + (j * t_3)) <= ((double) INFINITY)) {
		tmp = fma(x, t_2, fma(j, t_3, t_1));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	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(Float64(y * z) - Float64(t * a))
	t_3 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(Float64(x * t_2) + t_1) + Float64(j * t_3)) <= Inf)
		tmp = fma(x, t_2, fma(j, t_3, t_1));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return 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[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision], Infinity], N[(x * t$95$2 + N[(j * t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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 90.7%

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

      1. sub-neg 90.7%

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

      2. associate-+l+ 90.7%

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

      3. fma-def 90.7%

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

      4. +-commutative 90.7%

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

      5. fma-def 90.7%

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

      6. *-commutative 90.7%

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

      7. *-commutative 90.7%

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

      8. distribute-rgt-neg-in 90.7%

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

      9. sub-neg 90.7%

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

      10. +-commutative 90.7%

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

      11. distribute-neg-in 90.7%

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

      12. unsub-neg 90.7%

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

      13. remove-double-neg 90.7%

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

      14. *-commutative 90.7%

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

      15. *-commutative 90.7%

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

   3. Simplified 90.7%

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

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

   1. Initial program 0.0%

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

      1. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. remove-double-neg 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

   6. Simplified 57.0%

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

4. Final simplification 84.6%

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

Alternative 2: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * ((x * z) - (i * j))
	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(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * 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))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * ((x * z) - (i * j));
	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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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 90.7%

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

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

   1. Initial program 0.0%

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

      1. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. remove-double-neg 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

   6. Simplified 57.0%

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

4. Final simplification 84.6%

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

Alternative 3: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + t_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2e+101)
     (+ (* j (* t c)) t_1)
     (if (<= x 3.4e+19)
       (+
        (* j (- (* t c) (* y i)))
        (- (* z (* x y)) (* b (- (* z c) (* a i)))))
       (+ t_1 (* 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 t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2e+101) {
		tmp = (j * (t * c)) + t_1;
	} else if (x <= 3.4e+19) {
		tmp = (j * ((t * c) - (y * i))) + ((z * (x * y)) - (b * ((z * c) - (a * i))));
	} else {
		tmp = t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2d+101)) then
        tmp = (j * (t * c)) + t_1
    else if (x <= 3.4d+19) then
        tmp = (j * ((t * c) - (y * i))) + ((z * (x * y)) - (b * ((z * c) - (a * i))))
    else
        tmp = t_1 + (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 t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2e+101) {
		tmp = (j * (t * c)) + t_1;
	} else if (x <= 3.4e+19) {
		tmp = (j * ((t * c) - (y * i))) + ((z * (x * y)) - (b * ((z * c) - (a * i))));
	} else {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2e+101:
		tmp = (j * (t * c)) + t_1
	elif x <= 3.4e+19:
		tmp = (j * ((t * c) - (y * i))) + ((z * (x * y)) - (b * ((z * c) - (a * i))))
	else:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	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 (x <= -2e+101)
		tmp = Float64(Float64(j * Float64(t * c)) + t_1);
	elseif (x <= 3.4e+19)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(Float64(z * Float64(x * y)) - Float64(b * Float64(Float64(z * c) - Float64(a * i)))));
	else
		tmp = Float64(t_1 + 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)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2e+101)
		tmp = (j * (t * c)) + t_1;
	elseif (x <= 3.4e+19)
		tmp = (j * ((t * c) - (y * i))) + ((z * (x * y)) - (b * ((z * c) - (a * i))));
	else
		tmp = t_1 + (b * ((a * i) - (z * c)));
	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[x, -2e+101], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 3.4e+19], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e101

   1. Initial program 73.1%

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

      1. cancel-sign-sub 73.1%

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

      2. cancel-sign-sub-inv 73.1%

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

      3. *-commutative 73.1%

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

      4. *-commutative 73.1%

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

      5. remove-double-neg 73.1%

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

      6. *-commutative 73.1%

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

      7. *-commutative 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in b around 0 75.5%

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

   5. Taylor expanded in c around inf 75.5%

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

      1. associate-*r* 77.9%

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

   7. Simplified 77.9%

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

   if -2e101 < x < 3.4e19

   1. Initial program 78.8%

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

      1. cancel-sign-sub 78.8%

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

      2. cancel-sign-sub-inv 78.8%

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

      3. *-commutative 78.8%

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

      4. *-commutative 78.8%

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

      5. remove-double-neg 78.8%

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

      6. *-commutative 78.8%

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

      7. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in y around inf 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*l* 78.9%

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

      3. *-commutative 78.9%

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

   6. Simplified 78.9%

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

   if 3.4e19 < x

   1. Initial program 65.3%

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

      1. +-commutative 65.3%

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

      2. fma-def 66.8%

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

      3. *-commutative 66.8%

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

      4. *-commutative 66.8%

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

      5. *-commutative 66.8%

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

      6. *-commutative 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in j around 0 75.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4: 66.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.15 \cdot 10^{+140}:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-198} \lor \neg \left(j \leq 3 \cdot 10^{-96}\right) \land j \leq 4.6 \cdot 10^{+28}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -3.15e+140)
     (+ t_2 (* b (* a i)))
     (if (or (<= j 1.1e-198) (and (not (<= j 3e-96)) (<= j 4.6e+28)))
       (+ t_1 (* b (- (* a i) (* z c))))
       (+ 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));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.15e+140) {
		tmp = t_2 + (b * (a * i));
	} else if ((j <= 1.1e-198) || (!(j <= 3e-96) && (j <= 4.6e+28))) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1 + 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))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-3.15d+140)) then
        tmp = t_2 + (b * (a * i))
    else if ((j <= 1.1d-198) .or. (.not. (j <= 3d-96)) .and. (j <= 4.6d+28)) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = t_1 + 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));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.15e+140) {
		tmp = t_2 + (b * (a * i));
	} else if ((j <= 1.1e-198) || (!(j <= 3e-96) && (j <= 4.6e+28))) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -3.15e+140:
		tmp = t_2 + (b * (a * i))
	elif (j <= 1.1e-198) or (not (j <= 3e-96) and (j <= 4.6e+28)):
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1 + t_2
	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)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.15e+140)
		tmp = Float64(t_2 + Float64(b * Float64(a * i)));
	elseif ((j <= 1.1e-198) || (!(j <= 3e-96) && (j <= 4.6e+28)))
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 + 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));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.15e+140)
		tmp = t_2 + (b * (a * i));
	elseif ((j <= 1.1e-198) || (~((j <= 3e-96)) && (j <= 4.6e+28)))
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = t_1 + t_2;
	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]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.15e+140], N[(t$95$2 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 1.1e-198], And[N[Not[LessEqual[j, 3e-96]], $MachinePrecision], LessEqual[j, 4.6e+28]]], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.14999999999999986e140

   1. Initial program 71.4%

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

      1. cancel-sign-sub 71.4%

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

      2. cancel-sign-sub-inv 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

      5. remove-double-neg 71.4%

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

      6. *-commutative 71.4%

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

      7. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in i around inf 80.0%

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

      1. associate-*r* 82.8%

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

      2. *-commutative 82.8%

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

   6. Simplified 82.8%

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

   if -3.14999999999999986e140 < j < 1.1e-198 or 3e-96 < j < 4.59999999999999968e28

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. fma-def 73.3%

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

      3. *-commutative 73.3%

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

      4. *-commutative 73.3%

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

      5. *-commutative 73.3%

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

      6. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in j around 0 78.5%

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

   if 1.1e-198 < j < 3e-96 or 4.59999999999999968e28 < j

   1. Initial program 77.7%

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

      1. cancel-sign-sub 77.7%

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

      2. cancel-sign-sub-inv 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

      5. remove-double-neg 77.7%

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

      6. *-commutative 77.7%

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

      7. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in b around 0 72.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.15 \cdot 10^{+140}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-198} \lor \neg \left(j \leq 3 \cdot 10^{-96}\right) \land j \leq 4.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 5: 57.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -4.3 \cdot 10^{+57}:\\ \;\;\;\;t_3 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.6 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + t_1\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- (* z (* x y)) (* b (- (* z c) (* a i)))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -4.3e+57)
     (+ t_3 (* b (* a i)))
     (if (<= j -5.5e-105)
       t_2
       (if (<= j -4.6e-223)
         t_1
         (if (<= j 5.6e-198)
           t_2
           (if (<= j 9e+19)
             (+ (* j (* t c)) t_1)
             (if (<= j 1.6e+141) (* y (- (* x z) (* i j))) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (z * (x * y)) - (b * ((z * c) - (a * i)));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.3e+57) {
		tmp = t_3 + (b * (a * i));
	} else if (j <= -5.5e-105) {
		tmp = t_2;
	} else if (j <= -4.6e-223) {
		tmp = t_1;
	} else if (j <= 5.6e-198) {
		tmp = t_2;
	} else if (j <= 9e+19) {
		tmp = (j * (t * c)) + t_1;
	} else if (j <= 1.6e+141) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (z * (x * y)) - (b * ((z * c) - (a * i)))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-4.3d+57)) then
        tmp = t_3 + (b * (a * i))
    else if (j <= (-5.5d-105)) then
        tmp = t_2
    else if (j <= (-4.6d-223)) then
        tmp = t_1
    else if (j <= 5.6d-198) then
        tmp = t_2
    else if (j <= 9d+19) then
        tmp = (j * (t * c)) + t_1
    else if (j <= 1.6d+141) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (z * (x * y)) - (b * ((z * c) - (a * i)));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.3e+57) {
		tmp = t_3 + (b * (a * i));
	} else if (j <= -5.5e-105) {
		tmp = t_2;
	} else if (j <= -4.6e-223) {
		tmp = t_1;
	} else if (j <= 5.6e-198) {
		tmp = t_2;
	} else if (j <= 9e+19) {
		tmp = (j * (t * c)) + t_1;
	} else if (j <= 1.6e+141) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (z * (x * y)) - (b * ((z * c) - (a * i)))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -4.3e+57:
		tmp = t_3 + (b * (a * i))
	elif j <= -5.5e-105:
		tmp = t_2
	elif j <= -4.6e-223:
		tmp = t_1
	elif j <= 5.6e-198:
		tmp = t_2
	elif j <= 9e+19:
		tmp = (j * (t * c)) + t_1
	elif j <= 1.6e+141:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_3
	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)))
	t_2 = Float64(Float64(z * Float64(x * y)) - Float64(b * Float64(Float64(z * c) - Float64(a * i))))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -4.3e+57)
		tmp = Float64(t_3 + Float64(b * Float64(a * i)));
	elseif (j <= -5.5e-105)
		tmp = t_2;
	elseif (j <= -4.6e-223)
		tmp = t_1;
	elseif (j <= 5.6e-198)
		tmp = t_2;
	elseif (j <= 9e+19)
		tmp = Float64(Float64(j * Float64(t * c)) + t_1);
	elseif (j <= 1.6e+141)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_3;
	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));
	t_2 = (z * (x * y)) - (b * ((z * c) - (a * i)));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -4.3e+57)
		tmp = t_3 + (b * (a * i));
	elseif (j <= -5.5e-105)
		tmp = t_2;
	elseif (j <= -4.6e-223)
		tmp = t_1;
	elseif (j <= 5.6e-198)
		tmp = t_2;
	elseif (j <= 9e+19)
		tmp = (j * (t * c)) + t_1;
	elseif (j <= 1.6e+141)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.3e+57], N[(t$95$3 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.5e-105], t$95$2, If[LessEqual[j, -4.6e-223], t$95$1, If[LessEqual[j, 5.6e-198], t$95$2, If[LessEqual[j, 9e+19], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 1.6e+141], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -4.30000000000000033e57

   1. Initial program 74.1%

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

      1. cancel-sign-sub 74.1%

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

      2. cancel-sign-sub-inv 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. remove-double-neg 74.1%

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

      6. *-commutative 74.1%

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

      7. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in i around inf 72.5%

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

      1. associate-*r* 74.5%

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

      2. *-commutative 74.5%

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

   6. Simplified 74.5%

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

   if -4.30000000000000033e57 < j < -5.50000000000000029e-105 or -4.5999999999999999e-223 < j < 5.5999999999999998e-198

   1. Initial program 74.9%

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

      1. +-commutative 74.9%

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

      2. fma-def 74.9%

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

      3. *-commutative 74.9%

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

      4. *-commutative 74.9%

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

      5. *-commutative 74.9%

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

      6. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in j around 0 78.9%

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

   5. Taylor expanded in y around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l* 66.4%

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

   7. Simplified 66.4%

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

   if -5.50000000000000029e-105 < j < -4.5999999999999999e-223

   1. Initial program 64.7%

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

      1. +-commutative 64.7%

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

      2. fma-def 64.7%

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

      3. *-commutative 64.7%

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

      4. *-commutative 64.7%

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

      5. *-commutative 64.7%

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

      6. *-commutative 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in j around 0 75.6%

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

   5. Taylor expanded in x around inf 79.2%

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

   if 5.5999999999999998e-198 < j < 9e19

   1. Initial program 73.9%

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

      1. cancel-sign-sub 73.9%

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

      2. cancel-sign-sub-inv 73.9%

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

      3. *-commutative 73.9%

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

      4. *-commutative 73.9%

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

      5. remove-double-neg 73.9%

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

      6. *-commutative 73.9%

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

      7. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in b around 0 70.9%

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

   5. Taylor expanded in c around inf 70.9%

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

      1. associate-*r* 64.4%

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

   7. Simplified 64.4%

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

   if 9e19 < j < 1.60000000000000009e141

   1. Initial program 70.4%

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

      1. cancel-sign-sub 70.4%

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

      2. cancel-sign-sub-inv 70.4%

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

      3. *-commutative 70.4%

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

      4. *-commutative 70.4%

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

      5. remove-double-neg 70.4%

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

      6. *-commutative 70.4%

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

      7. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in y around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

   6. Simplified 71.3%

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

   if 1.60000000000000009e141 < j

   1. Initial program 84.0%

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

      1. cancel-sign-sub 84.0%

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

      2. cancel-sign-sub-inv 84.0%

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

      3. *-commutative 84.0%

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

      4. *-commutative 84.0%

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

      5. remove-double-neg 84.0%

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

      6. *-commutative 84.0%

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

      7. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in b around 0 73.1%

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

   5. Taylor expanded in j around inf 72.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.3 \cdot 10^{+57}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;j \leq -4.6 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-198}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 6: 53.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -0.018:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+18}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + t_1\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -0.018)
     (+ t_2 (* b (* a i)))
     (if (<= j -3.1e-245)
       t_1
       (if (<= j 6.5e-204)
         (* b (- (* a i) (* z c)))
         (if (<= j 3.4e+18)
           (+ (* j (* t c)) t_1)
           (if (<= j 3.4e+140) (* y (- (* x z) (* i j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -0.018) {
		tmp = t_2 + (b * (a * i));
	} else if (j <= -3.1e-245) {
		tmp = t_1;
	} else if (j <= 6.5e-204) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 3.4e+18) {
		tmp = (j * (t * c)) + t_1;
	} else if (j <= 3.4e+140) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-0.018d0)) then
        tmp = t_2 + (b * (a * i))
    else if (j <= (-3.1d-245)) then
        tmp = t_1
    else if (j <= 6.5d-204) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 3.4d+18) then
        tmp = (j * (t * c)) + t_1
    else if (j <= 3.4d+140) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -0.018) {
		tmp = t_2 + (b * (a * i));
	} else if (j <= -3.1e-245) {
		tmp = t_1;
	} else if (j <= 6.5e-204) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 3.4e+18) {
		tmp = (j * (t * c)) + t_1;
	} else if (j <= 3.4e+140) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -0.018:
		tmp = t_2 + (b * (a * i))
	elif j <= -3.1e-245:
		tmp = t_1
	elif j <= 6.5e-204:
		tmp = b * ((a * i) - (z * c))
	elif j <= 3.4e+18:
		tmp = (j * (t * c)) + t_1
	elif j <= 3.4e+140:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -0.018)
		tmp = Float64(t_2 + Float64(b * Float64(a * i)));
	elseif (j <= -3.1e-245)
		tmp = t_1;
	elseif (j <= 6.5e-204)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 3.4e+18)
		tmp = Float64(Float64(j * Float64(t * c)) + t_1);
	elseif (j <= 3.4e+140)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -0.018)
		tmp = t_2 + (b * (a * i));
	elseif (j <= -3.1e-245)
		tmp = t_1;
	elseif (j <= 6.5e-204)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 3.4e+18)
		tmp = (j * (t * c)) + t_1;
	elseif (j <= 3.4e+140)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -0.018], N[(t$95$2 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.1e-245], t$95$1, If[LessEqual[j, 6.5e-204], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e+18], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 3.4e+140], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -0.0179999999999999986

   1. Initial program 75.4%

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

      1. cancel-sign-sub 75.4%

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

      2. cancel-sign-sub-inv 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

      5. remove-double-neg 75.4%

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

      6. *-commutative 75.4%

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

      7. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in i around inf 72.6%

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

      1. associate-*r* 74.3%

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

      2. *-commutative 74.3%

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

   6. Simplified 74.3%

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

   if -0.0179999999999999986 < j < -3.10000000000000003e-245

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. fma-def 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

      5. *-commutative 69.7%

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

      6. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in j around 0 76.6%

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

   5. Taylor expanded in x around inf 65.1%

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

   if -3.10000000000000003e-245 < j < 6.49999999999999939e-204

   1. Initial program 75.4%

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

      1. cancel-sign-sub 75.4%

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

      2. cancel-sign-sub-inv 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

      5. remove-double-neg 75.4%

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

      6. *-commutative 75.4%

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

      7. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in b around inf 55.7%

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

   if 6.49999999999999939e-204 < j < 3.4e18

   1. Initial program 71.7%

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

      1. cancel-sign-sub 71.7%

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

      2. cancel-sign-sub-inv 71.7%

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

      3. *-commutative 71.7%

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

      4. *-commutative 71.7%

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

      5. remove-double-neg 71.7%

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

      6. *-commutative 71.7%

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

      7. *-commutative 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in b around 0 68.8%

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

   5. Taylor expanded in c around inf 68.8%

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

      1. associate-*r* 62.5%

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

   7. Simplified 62.5%

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

   if 3.4e18 < j < 3.4e140

   1. Initial program 70.4%

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

      1. cancel-sign-sub 70.4%

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

      2. cancel-sign-sub-inv 70.4%

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

      3. *-commutative 70.4%

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

      4. *-commutative 70.4%

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

      5. remove-double-neg 70.4%

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

      6. *-commutative 70.4%

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

      7. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in y around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

   6. Simplified 71.3%

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

   if 3.4e140 < j

   1. Initial program 84.0%

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

      1. cancel-sign-sub 84.0%

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

      2. cancel-sign-sub-inv 84.0%

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

      3. *-commutative 84.0%

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

      4. *-commutative 84.0%

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

      5. remove-double-neg 84.0%

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

      6. *-commutative 84.0%

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

      7. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in b around 0 73.1%

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

   5. Taylor expanded in j around inf 72.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.018:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+18}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 7: 59.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* a i) (* z c))) (* x (* t a))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.1e+85)
     t_2
     (if (<= y 4.6e-14)
       t_1
       (if (<= y 3.3e+65)
         (+ (* j (- (* t c) (* y i))) (* b (* a i)))
         (if (<= y 3.8e+80) 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))) - (x * (t * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.1e+85) {
		tmp = t_2;
	} else if (y <= 4.6e-14) {
		tmp = t_1;
	} else if (y <= 3.3e+65) {
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	} else if (y <= 3.8e+80) {
		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))) - (x * (t * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.1d+85)) then
        tmp = t_2
    else if (y <= 4.6d-14) then
        tmp = t_1
    else if (y <= 3.3d+65) then
        tmp = (j * ((t * c) - (y * i))) + (b * (a * i))
    else if (y <= 3.8d+80) 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))) - (x * (t * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.1e+85) {
		tmp = t_2;
	} else if (y <= 4.6e-14) {
		tmp = t_1;
	} else if (y <= 3.3e+65) {
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	} else if (y <= 3.8e+80) {
		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))) - (x * (t * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.1e+85:
		tmp = t_2
	elif y <= 4.6e-14:
		tmp = t_1
	elif y <= 3.3e+65:
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i))
	elif y <= 3.8e+80:
		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(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(x * Float64(t * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.1e+85)
		tmp = t_2;
	elseif (y <= 4.6e-14)
		tmp = t_1;
	elseif (y <= 3.3e+65)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(a * i)));
	elseif (y <= 3.8e+80)
		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))) - (x * (t * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.1e+85)
		tmp = t_2;
	elseif (y <= 4.6e-14)
		tmp = t_1;
	elseif (y <= 3.3e+65)
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	elseif (y <= 3.8e+80)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+85], t$95$2, If[LessEqual[y, 4.6e-14], t$95$1, If[LessEqual[y, 3.3e+65], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+80], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1000000000000001e85 or 3.79999999999999997e80 < y

   1. Initial program 55.4%

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

      1. cancel-sign-sub 55.4%

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

      2. cancel-sign-sub-inv 55.4%

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

      3. *-commutative 55.4%

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

      4. *-commutative 55.4%

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

      5. remove-double-neg 55.4%

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

      6. *-commutative 55.4%

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

      7. *-commutative 55.4%

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

   3. Simplified 55.4%

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

   4. Taylor expanded in y around inf 76.4%

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

      1. +-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

   6. Simplified 76.4%

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

   if -1.1000000000000001e85 < y < 4.59999999999999996e-14 or 3.30000000000000023e65 < y < 3.79999999999999997e80

   1. Initial program 85.8%

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

      1. +-commutative 85.8%

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

      2. fma-def 85.8%

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

      3. *-commutative 85.8%

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

      4. *-commutative 85.8%

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

      5. *-commutative 85.8%

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

      6. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in j around 0 72.8%

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

   5. Taylor expanded in y around 0 66.7%

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

      1. neg-mul-1 66.7%

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

      2. distribute-rgt-neg-in 66.7%

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

   7. Simplified 66.7%

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

   if 4.59999999999999996e-14 < y < 3.30000000000000023e65

   1. Initial program 76.5%

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

      1. cancel-sign-sub 76.5%

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

      2. cancel-sign-sub-inv 76.5%

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

      3. *-commutative 76.5%

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

      4. *-commutative 76.5%

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

      5. remove-double-neg 76.5%

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

      6. *-commutative 76.5%

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

      7. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in i around inf 71.4%

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

      1. associate-*r* 71.6%

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

      2. *-commutative 71.6%

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

   6. Simplified 71.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 8: 68.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.85 \cdot 10^{+143} \lor \neg \left(b \leq 95\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.85e+143) (not (<= b 95.0)))
   (- (* z (* x y)) (* b (- (* z c) (* a i))))
   (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y 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 ((b <= -3.85e+143) || !(b <= 95.0)) {
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 ((b <= (-3.85d+143)) .or. (.not. (b <= 95.0d0))) then
        tmp = (z * (x * y)) - (b * ((z * c) - (a * i)))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 ((b <= -3.85e+143) || !(b <= 95.0)) {
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.85e+143) or not (b <= 95.0):
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.85e+143) || !(b <= 95.0))
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.85e+143) || ~((b <= 95.0)))
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.85e+143], N[Not[LessEqual[b, 95.0]], $MachinePrecision]], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.85000000000000013e143 or 95 < b

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. fma-def 78.4%

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

      3. *-commutative 78.4%

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

      4. *-commutative 78.4%

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

      5. *-commutative 78.4%

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

      6. *-commutative 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in j around 0 80.0%

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

   5. Taylor expanded in y around inf 79.3%

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

      1. *-commutative 79.3%

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

      2. associate-*l* 76.2%

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

   7. Simplified 76.2%

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

   if -3.85000000000000013e143 < b < 95

   1. Initial program 72.3%

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

      1. cancel-sign-sub 72.3%

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

      2. cancel-sign-sub-inv 72.3%

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

      3. *-commutative 72.3%

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

      4. *-commutative 72.3%

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

      5. remove-double-neg 72.3%

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

      6. *-commutative 72.3%

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

      7. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in b around 0 67.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.85 \cdot 10^{+143} \lor \neg \left(b \leq 95\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 9: 30.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{if}\;i \leq -4 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* x t))))
   (if (<= i -4e+46)
     (* j (* y (- i)))
     (if (<= i -1.6e-122)
       (* z (* x y))
       (if (<= i 1.2e-264)
         t_1
         (if (<= i 7.8e-168)
           (* y (* x z))
           (if (<= i 2e-88)
             (* (* z b) (- c))
             (if (<= i 4.4e-50)
               (* x (* y z))
               (if (<= i 1.9e+107)
                 t_1
                 (if (<= i 3.1e+165) (* b (* a i)) (* (* i j) (- y))))))))))))

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 * (x * t);
	double tmp;
	if (i <= -4e+46) {
		tmp = j * (y * -i);
	} else if (i <= -1.6e-122) {
		tmp = z * (x * y);
	} else if (i <= 1.2e-264) {
		tmp = t_1;
	} else if (i <= 7.8e-168) {
		tmp = y * (x * z);
	} else if (i <= 2e-88) {
		tmp = (z * b) * -c;
	} else if (i <= 4.4e-50) {
		tmp = x * (y * z);
	} else if (i <= 1.9e+107) {
		tmp = t_1;
	} else if (i <= 3.1e+165) {
		tmp = b * (a * i);
	} else {
		tmp = (i * j) * -y;
	}
	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 * (x * t)
    if (i <= (-4d+46)) then
        tmp = j * (y * -i)
    else if (i <= (-1.6d-122)) then
        tmp = z * (x * y)
    else if (i <= 1.2d-264) then
        tmp = t_1
    else if (i <= 7.8d-168) then
        tmp = y * (x * z)
    else if (i <= 2d-88) then
        tmp = (z * b) * -c
    else if (i <= 4.4d-50) then
        tmp = x * (y * z)
    else if (i <= 1.9d+107) then
        tmp = t_1
    else if (i <= 3.1d+165) then
        tmp = b * (a * i)
    else
        tmp = (i * j) * -y
    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 * (x * t);
	double tmp;
	if (i <= -4e+46) {
		tmp = j * (y * -i);
	} else if (i <= -1.6e-122) {
		tmp = z * (x * y);
	} else if (i <= 1.2e-264) {
		tmp = t_1;
	} else if (i <= 7.8e-168) {
		tmp = y * (x * z);
	} else if (i <= 2e-88) {
		tmp = (z * b) * -c;
	} else if (i <= 4.4e-50) {
		tmp = x * (y * z);
	} else if (i <= 1.9e+107) {
		tmp = t_1;
	} else if (i <= 3.1e+165) {
		tmp = b * (a * i);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (x * t)
	tmp = 0
	if i <= -4e+46:
		tmp = j * (y * -i)
	elif i <= -1.6e-122:
		tmp = z * (x * y)
	elif i <= 1.2e-264:
		tmp = t_1
	elif i <= 7.8e-168:
		tmp = y * (x * z)
	elif i <= 2e-88:
		tmp = (z * b) * -c
	elif i <= 4.4e-50:
		tmp = x * (y * z)
	elif i <= 1.9e+107:
		tmp = t_1
	elif i <= 3.1e+165:
		tmp = b * (a * i)
	else:
		tmp = (i * j) * -y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(x * t))
	tmp = 0.0
	if (i <= -4e+46)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (i <= -1.6e-122)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1.2e-264)
		tmp = t_1;
	elseif (i <= 7.8e-168)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 2e-88)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (i <= 4.4e-50)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 1.9e+107)
		tmp = t_1;
	elseif (i <= 3.1e+165)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(Float64(i * j) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (x * t);
	tmp = 0.0;
	if (i <= -4e+46)
		tmp = j * (y * -i);
	elseif (i <= -1.6e-122)
		tmp = z * (x * y);
	elseif (i <= 1.2e-264)
		tmp = t_1;
	elseif (i <= 7.8e-168)
		tmp = y * (x * z);
	elseif (i <= 2e-88)
		tmp = (z * b) * -c;
	elseif (i <= 4.4e-50)
		tmp = x * (y * z);
	elseif (i <= 1.9e+107)
		tmp = t_1;
	elseif (i <= 3.1e+165)
		tmp = b * (a * i);
	else
		tmp = (i * j) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4e+46], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.6e-122], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e-264], t$95$1, If[LessEqual[i, 7.8e-168], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e-88], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[i, 4.4e-50], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.9e+107], t$95$1, If[LessEqual[i, 3.1e+165], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -4e46

   1. Initial program 61.6%

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

      1. cancel-sign-sub 61.6%

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

      2. cancel-sign-sub-inv 61.6%

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

      3. *-commutative 61.6%

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

      4. *-commutative 61.6%

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

      5. remove-double-neg 61.6%

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

      6. *-commutative 61.6%

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

      7. *-commutative 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in y around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

   6. Simplified 46.8%

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

   7. Taylor expanded in z around 0 33.5%

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

      1. mul-1-neg 33.5%

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

      2. *-commutative 33.5%

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

      3. distribute-lft-neg-in 33.5%

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

      4. distribute-lft-neg-in 33.5%

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

      5. *-commutative 33.5%

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

      6. associate-*l* 38.3%

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

      7. distribute-lft-neg-in 38.3%

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

      8. distribute-rgt-neg-in 38.3%

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

   9. Simplified 38.3%

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

   if -4e46 < i < -1.6000000000000001e-122

   1. Initial program 72.2%

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

      1. cancel-sign-sub 72.2%

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

      2. cancel-sign-sub-inv 72.2%

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

      3. *-commutative 72.2%

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

      4. *-commutative 72.2%

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

      5. remove-double-neg 72.2%

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

      6. *-commutative 72.2%

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

      7. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in b around 0 63.2%

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

   5. Taylor expanded in c around inf 54.1%

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

      1. associate-*r* 48.0%

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

   7. Simplified 48.0%

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

   8. Taylor expanded in t around 0 41.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.0%

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

      2. *-commutative 36.0%

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

      3. associate-*l* 41.9%

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

   10. Simplified 41.9%

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

   if -1.6000000000000001e-122 < i < 1.1999999999999999e-264 or 4.3999999999999998e-50 < i < 1.8999999999999999e107

   1. Initial program 80.6%

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

      1. cancel-sign-sub 80.6%

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

      2. cancel-sign-sub-inv 80.6%

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

      3. *-commutative 80.6%

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

      4. *-commutative 80.6%

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

      5. remove-double-neg 80.6%

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

      6. *-commutative 80.6%

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

      7. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in a around inf 56.3%

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

      1. distribute-lft-out-- 56.3%

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

      2. distribute-lft-out-- 56.3%

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

      3. sub-neg 56.3%

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

      4. mul-1-neg 56.3%

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

      5. remove-double-neg 56.3%

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

      6. +-commutative 56.3%

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

      7. mul-1-neg 56.3%

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

      8. unsub-neg 56.3%

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

      9. *-commutative 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in b around 0 43.9%

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

      1. neg-mul-1 43.9%

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

      2. distribute-lft-neg-in 43.9%

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

      3. *-commutative 43.9%

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

   9. Simplified 43.9%

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

   if 1.1999999999999999e-264 < i < 7.80000000000000025e-168

   1. Initial program 75.6%

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

      1. cancel-sign-sub 75.6%

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

      2. cancel-sign-sub-inv 75.6%

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

      3. *-commutative 75.6%

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

      4. *-commutative 75.6%

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

      5. remove-double-neg 75.6%

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

      6. *-commutative 75.6%

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

      7. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in y around inf 46.7%

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

      1. +-commutative 46.7%

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

      2. mul-1-neg 46.7%

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

      3. unsub-neg 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in z around inf 46.7%

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

   if 7.80000000000000025e-168 < i < 1.99999999999999987e-88

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. fma-def 93.2%

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

      3. *-commutative 93.2%

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

      4. *-commutative 93.2%

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

      5. *-commutative 93.2%

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

      6. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in j around 0 72.7%

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

   5. Taylor expanded in c around inf 38.3%

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

      1. mul-1-neg 38.3%

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

      2. distribute-rgt-neg-in 38.3%

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

      3. *-commutative 38.3%

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

   7. Simplified 38.3%

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

   if 1.99999999999999987e-88 < i < 4.3999999999999998e-50

   1. Initial program 100.0%

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

      1. cancel-sign-sub 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. *-commutative 100.0%

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

      7. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around 0 72.5%

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

   5. Taylor expanded in c around inf 72.5%

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

      1. associate-*r* 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-*l* 71.5%

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

   10. Simplified 71.5%

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

   if 1.8999999999999999e107 < i < 3.1000000000000002e165

   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. cancel-sign-sub 81.2%

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

      2. cancel-sign-sub-inv 81.2%

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

      3. *-commutative 81.2%

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

      4. *-commutative 81.2%

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

      5. remove-double-neg 81.2%

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

      6. *-commutative 81.2%

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

      7. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in b around inf 88.0%

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

   5. Taylor expanded in a around inf 81.5%

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

   if 3.1000000000000002e165 < i

   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 y around inf 80.1%

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

      1. +-commutative 80.1%

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

      2. mul-1-neg 80.1%

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

      3. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in z around 0 67.2%

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

      1. neg-mul-1 67.2%

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

      2. distribute-rgt-neg-in 67.2%

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

   9. Simplified 67.2%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-264}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+107}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]

Alternative 10: 29.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{if}\;i \leq -2.65 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -8.6 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.16 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* x t))))
   (if (<= i -2.65e+44)
     (* j (* y (- i)))
     (if (<= i -8.6e-123)
       (* z (* x y))
       (if (<= i 1.6e-265)
         t_1
         (if (<= i 1.35e-168)
           (* y (* x z))
           (if (<= i 2.16e-88)
             (* b (* z (- c)))
             (if (<= i 1.35e-48)
               (* x (* y z))
               (if (<= i 1.4e+107)
                 t_1
                 (if (<= i 1.15e+165) (* b (* a i)) (* (* i j) (- y))))))))))))

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 * (x * t);
	double tmp;
	if (i <= -2.65e+44) {
		tmp = j * (y * -i);
	} else if (i <= -8.6e-123) {
		tmp = z * (x * y);
	} else if (i <= 1.6e-265) {
		tmp = t_1;
	} else if (i <= 1.35e-168) {
		tmp = y * (x * z);
	} else if (i <= 2.16e-88) {
		tmp = b * (z * -c);
	} else if (i <= 1.35e-48) {
		tmp = x * (y * z);
	} else if (i <= 1.4e+107) {
		tmp = t_1;
	} else if (i <= 1.15e+165) {
		tmp = b * (a * i);
	} else {
		tmp = (i * j) * -y;
	}
	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 * (x * t)
    if (i <= (-2.65d+44)) then
        tmp = j * (y * -i)
    else if (i <= (-8.6d-123)) then
        tmp = z * (x * y)
    else if (i <= 1.6d-265) then
        tmp = t_1
    else if (i <= 1.35d-168) then
        tmp = y * (x * z)
    else if (i <= 2.16d-88) then
        tmp = b * (z * -c)
    else if (i <= 1.35d-48) then
        tmp = x * (y * z)
    else if (i <= 1.4d+107) then
        tmp = t_1
    else if (i <= 1.15d+165) then
        tmp = b * (a * i)
    else
        tmp = (i * j) * -y
    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 * (x * t);
	double tmp;
	if (i <= -2.65e+44) {
		tmp = j * (y * -i);
	} else if (i <= -8.6e-123) {
		tmp = z * (x * y);
	} else if (i <= 1.6e-265) {
		tmp = t_1;
	} else if (i <= 1.35e-168) {
		tmp = y * (x * z);
	} else if (i <= 2.16e-88) {
		tmp = b * (z * -c);
	} else if (i <= 1.35e-48) {
		tmp = x * (y * z);
	} else if (i <= 1.4e+107) {
		tmp = t_1;
	} else if (i <= 1.15e+165) {
		tmp = b * (a * i);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (x * t)
	tmp = 0
	if i <= -2.65e+44:
		tmp = j * (y * -i)
	elif i <= -8.6e-123:
		tmp = z * (x * y)
	elif i <= 1.6e-265:
		tmp = t_1
	elif i <= 1.35e-168:
		tmp = y * (x * z)
	elif i <= 2.16e-88:
		tmp = b * (z * -c)
	elif i <= 1.35e-48:
		tmp = x * (y * z)
	elif i <= 1.4e+107:
		tmp = t_1
	elif i <= 1.15e+165:
		tmp = b * (a * i)
	else:
		tmp = (i * j) * -y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(x * t))
	tmp = 0.0
	if (i <= -2.65e+44)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (i <= -8.6e-123)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1.6e-265)
		tmp = t_1;
	elseif (i <= 1.35e-168)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 2.16e-88)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (i <= 1.35e-48)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 1.4e+107)
		tmp = t_1;
	elseif (i <= 1.15e+165)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(Float64(i * j) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (x * t);
	tmp = 0.0;
	if (i <= -2.65e+44)
		tmp = j * (y * -i);
	elseif (i <= -8.6e-123)
		tmp = z * (x * y);
	elseif (i <= 1.6e-265)
		tmp = t_1;
	elseif (i <= 1.35e-168)
		tmp = y * (x * z);
	elseif (i <= 2.16e-88)
		tmp = b * (z * -c);
	elseif (i <= 1.35e-48)
		tmp = x * (y * z);
	elseif (i <= 1.4e+107)
		tmp = t_1;
	elseif (i <= 1.15e+165)
		tmp = b * (a * i);
	else
		tmp = (i * j) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.65e+44], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.6e-123], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e-265], t$95$1, If[LessEqual[i, 1.35e-168], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.16e-88], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e-48], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e+107], t$95$1, If[LessEqual[i, 1.15e+165], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -2.65e44

   1. Initial program 61.6%

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

      1. cancel-sign-sub 61.6%

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

      2. cancel-sign-sub-inv 61.6%

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

      3. *-commutative 61.6%

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

      4. *-commutative 61.6%

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

      5. remove-double-neg 61.6%

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

      6. *-commutative 61.6%

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

      7. *-commutative 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in y around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

   6. Simplified 46.8%

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

   7. Taylor expanded in z around 0 33.5%

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

      1. mul-1-neg 33.5%

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

      2. *-commutative 33.5%

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

      3. distribute-lft-neg-in 33.5%

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

      4. distribute-lft-neg-in 33.5%

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

      5. *-commutative 33.5%

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

      6. associate-*l* 38.3%

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

      7. distribute-lft-neg-in 38.3%

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

      8. distribute-rgt-neg-in 38.3%

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

   9. Simplified 38.3%

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

   if -2.65e44 < i < -8.60000000000000064e-123

   1. Initial program 72.2%

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

      1. cancel-sign-sub 72.2%

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

      2. cancel-sign-sub-inv 72.2%

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

      3. *-commutative 72.2%

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

      4. *-commutative 72.2%

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

      5. remove-double-neg 72.2%

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

      6. *-commutative 72.2%

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

      7. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in b around 0 63.2%

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

   5. Taylor expanded in c around inf 54.1%

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

      1. associate-*r* 48.0%

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

   7. Simplified 48.0%

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

   8. Taylor expanded in t around 0 41.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.0%

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

      2. *-commutative 36.0%

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

      3. associate-*l* 41.9%

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

   10. Simplified 41.9%

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

   if -8.60000000000000064e-123 < i < 1.6e-265 or 1.35000000000000006e-48 < i < 1.39999999999999992e107

   1. Initial program 80.6%

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

      1. cancel-sign-sub 80.6%

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

      2. cancel-sign-sub-inv 80.6%

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

      3. *-commutative 80.6%

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

      4. *-commutative 80.6%

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

      5. remove-double-neg 80.6%

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

      6. *-commutative 80.6%

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

      7. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in a around inf 56.3%

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

      1. distribute-lft-out-- 56.3%

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

      2. distribute-lft-out-- 56.3%

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

      3. sub-neg 56.3%

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

      4. mul-1-neg 56.3%

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

      5. remove-double-neg 56.3%

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

      6. +-commutative 56.3%

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

      7. mul-1-neg 56.3%

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

      8. unsub-neg 56.3%

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

      9. *-commutative 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in b around 0 43.9%

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

      1. neg-mul-1 43.9%

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

      2. distribute-lft-neg-in 43.9%

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

      3. *-commutative 43.9%

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

   9. Simplified 43.9%

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

   if 1.6e-265 < i < 1.35000000000000008e-168

   1. Initial program 75.6%

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

      1. cancel-sign-sub 75.6%

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

      2. cancel-sign-sub-inv 75.6%

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

      3. *-commutative 75.6%

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

      4. *-commutative 75.6%

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

      5. remove-double-neg 75.6%

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

      6. *-commutative 75.6%

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

      7. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in y around inf 46.7%

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

      1. +-commutative 46.7%

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

      2. mul-1-neg 46.7%

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

      3. unsub-neg 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in z around inf 46.7%

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

   if 1.35000000000000008e-168 < i < 2.1599999999999999e-88

   1. Initial program 93.2%

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

      1. cancel-sign-sub 93.2%

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

      2. cancel-sign-sub-inv 93.2%

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

      3. *-commutative 93.2%

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

      4. *-commutative 93.2%

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

      5. remove-double-neg 93.2%

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

      6. *-commutative 93.2%

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

      7. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in b around inf 51.9%

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

   5. Taylor expanded in a around 0 44.9%

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

      1. neg-mul-1 44.9%

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

      2. distribute-rgt-neg-in 44.9%

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

   7. Simplified 44.9%

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

   if 2.1599999999999999e-88 < i < 1.35000000000000006e-48

   1. Initial program 100.0%

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

      1. cancel-sign-sub 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. remove-double-neg 100.0%

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

      6. *-commutative 100.0%

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

      7. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around 0 72.5%

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

   5. Taylor expanded in c around inf 72.5%

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

      1. associate-*r* 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-*l* 71.5%

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

   10. Simplified 71.5%

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

   if 1.39999999999999992e107 < i < 1.15000000000000008e165

   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. cancel-sign-sub 81.2%

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

      2. cancel-sign-sub-inv 81.2%

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

      3. *-commutative 81.2%

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

      4. *-commutative 81.2%

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

      5. remove-double-neg 81.2%

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

      6. *-commutative 81.2%

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

      7. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in b around inf 88.0%

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

   5. Taylor expanded in a around inf 81.5%

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

   if 1.15000000000000008e165 < i

   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 y around inf 80.1%

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

      1. +-commutative 80.1%

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

      2. mul-1-neg 80.1%

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

      3. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in z around 0 67.2%

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

      1. neg-mul-1 67.2%

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

      2. distribute-rgt-neg-in 67.2%

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

   9. Simplified 67.2%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.65 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -8.6 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-265}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.16 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+107}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]

Alternative 11: 51.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.96 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 0.05:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -6.8e+142)
     t_2
     (if (<= t -1.8e+119)
       t_1
       (if (<= t -3.8e-25)
         t_2
         (if (<= t 1.96e-303)
           t_1
           (if (<= t 5e-243) (* z (* x y)) (if (<= t 0.05) 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 = i * ((a * b) - (y * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -6.8e+142) {
		tmp = t_2;
	} else if (t <= -1.8e+119) {
		tmp = t_1;
	} else if (t <= -3.8e-25) {
		tmp = t_2;
	} else if (t <= 1.96e-303) {
		tmp = t_1;
	} else if (t <= 5e-243) {
		tmp = z * (x * y);
	} else if (t <= 0.05) {
		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 = i * ((a * b) - (y * j))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-6.8d+142)) then
        tmp = t_2
    else if (t <= (-1.8d+119)) then
        tmp = t_1
    else if (t <= (-3.8d-25)) then
        tmp = t_2
    else if (t <= 1.96d-303) then
        tmp = t_1
    else if (t <= 5d-243) then
        tmp = z * (x * y)
    else if (t <= 0.05d0) 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 = i * ((a * b) - (y * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -6.8e+142) {
		tmp = t_2;
	} else if (t <= -1.8e+119) {
		tmp = t_1;
	} else if (t <= -3.8e-25) {
		tmp = t_2;
	} else if (t <= 1.96e-303) {
		tmp = t_1;
	} else if (t <= 5e-243) {
		tmp = z * (x * y);
	} else if (t <= 0.05) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -6.8e+142:
		tmp = t_2
	elif t <= -1.8e+119:
		tmp = t_1
	elif t <= -3.8e-25:
		tmp = t_2
	elif t <= 1.96e-303:
		tmp = t_1
	elif t <= 5e-243:
		tmp = z * (x * y)
	elif t <= 0.05:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -6.8e+142)
		tmp = t_2;
	elseif (t <= -1.8e+119)
		tmp = t_1;
	elseif (t <= -3.8e-25)
		tmp = t_2;
	elseif (t <= 1.96e-303)
		tmp = t_1;
	elseif (t <= 5e-243)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 0.05)
		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 = i * ((a * b) - (y * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -6.8e+142)
		tmp = t_2;
	elseif (t <= -1.8e+119)
		tmp = t_1;
	elseif (t <= -3.8e-25)
		tmp = t_2;
	elseif (t <= 1.96e-303)
		tmp = t_1;
	elseif (t <= 5e-243)
		tmp = z * (x * y);
	elseif (t <= 0.05)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+142], t$95$2, If[LessEqual[t, -1.8e+119], t$95$1, If[LessEqual[t, -3.8e-25], t$95$2, If[LessEqual[t, 1.96e-303], t$95$1, If[LessEqual[t, 5e-243], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.05], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.7999999999999996e142 or -1.80000000000000001e119 < t < -3.7999999999999998e-25 or 0.050000000000000003 < 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. cancel-sign-sub 68.4%

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

      2. cancel-sign-sub-inv 68.4%

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

      3. *-commutative 68.4%

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

      4. *-commutative 68.4%

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

      5. remove-double-neg 68.4%

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

      6. *-commutative 68.4%

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

      7. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in t around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

   6. Simplified 65.6%

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

   if -6.7999999999999996e142 < t < -1.80000000000000001e119 or -3.7999999999999998e-25 < t < 1.9600000000000001e-303 or 5e-243 < t < 0.050000000000000003

   1. Initial program 80.4%

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

      1. cancel-sign-sub 80.4%

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

      2. cancel-sign-sub-inv 80.4%

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

      3. *-commutative 80.4%

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

      4. *-commutative 80.4%

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

      5. remove-double-neg 80.4%

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

      6. *-commutative 80.4%

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

      7. *-commutative 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in i around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-*r* 52.6%

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

      3. neg-mul-1 52.6%

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

      4. cancel-sign-sub 52.6%

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

      5. +-commutative 52.6%

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

      6. mul-1-neg 52.6%

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

      7. unsub-neg 52.6%

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

      8. *-commutative 52.6%

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

   6. Simplified 52.6%

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

   if 1.9600000000000001e-303 < t < 5e-243

   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. cancel-sign-sub 69.0%

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

      2. cancel-sign-sub-inv 69.0%

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

      3. *-commutative 69.0%

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

      4. *-commutative 69.0%

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

      5. remove-double-neg 69.0%

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

      6. *-commutative 69.0%

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

      7. *-commutative 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in b around 0 69.3%

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

   5. Taylor expanded in c around inf 84.6%

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

      1. associate-*r* 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in t around 0 77.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 77.2%

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

      2. *-commutative 77.2%

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

      3. associate-*l* 77.3%

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

   10. Simplified 77.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.96 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 0.05:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 12: 52.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+143}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 0.078:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -1.65e+143)
     t_3
     (if (<= t -1.8e+119)
       t_2
       (if (<= t -1.12e-21)
         t_3
         (if (<= t -5.8e-156)
           t_1
           (if (<= t 1.22e-263) t_2 (if (<= t 0.078) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.65e+143) {
		tmp = t_3;
	} else if (t <= -1.8e+119) {
		tmp = t_2;
	} else if (t <= -1.12e-21) {
		tmp = t_3;
	} else if (t <= -5.8e-156) {
		tmp = t_1;
	} else if (t <= 1.22e-263) {
		tmp = t_2;
	} else if (t <= 0.078) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = y * ((x * z) - (i * j))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-1.65d+143)) then
        tmp = t_3
    else if (t <= (-1.8d+119)) then
        tmp = t_2
    else if (t <= (-1.12d-21)) then
        tmp = t_3
    else if (t <= (-5.8d-156)) then
        tmp = t_1
    else if (t <= 1.22d-263) then
        tmp = t_2
    else if (t <= 0.078d0) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.65e+143) {
		tmp = t_3;
	} else if (t <= -1.8e+119) {
		tmp = t_2;
	} else if (t <= -1.12e-21) {
		tmp = t_3;
	} else if (t <= -5.8e-156) {
		tmp = t_1;
	} else if (t <= 1.22e-263) {
		tmp = t_2;
	} else if (t <= 0.078) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = y * ((x * z) - (i * j))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.65e+143:
		tmp = t_3
	elif t <= -1.8e+119:
		tmp = t_2
	elif t <= -1.12e-21:
		tmp = t_3
	elif t <= -5.8e-156:
		tmp = t_1
	elif t <= 1.22e-263:
		tmp = t_2
	elif t <= 0.078:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.65e+143)
		tmp = t_3;
	elseif (t <= -1.8e+119)
		tmp = t_2;
	elseif (t <= -1.12e-21)
		tmp = t_3;
	elseif (t <= -5.8e-156)
		tmp = t_1;
	elseif (t <= 1.22e-263)
		tmp = t_2;
	elseif (t <= 0.078)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = y * ((x * z) - (i * j));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.65e+143)
		tmp = t_3;
	elseif (t <= -1.8e+119)
		tmp = t_2;
	elseif (t <= -1.12e-21)
		tmp = t_3;
	elseif (t <= -5.8e-156)
		tmp = t_1;
	elseif (t <= 1.22e-263)
		tmp = t_2;
	elseif (t <= 0.078)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+143], t$95$3, If[LessEqual[t, -1.8e+119], t$95$2, If[LessEqual[t, -1.12e-21], t$95$3, If[LessEqual[t, -5.8e-156], t$95$1, If[LessEqual[t, 1.22e-263], t$95$2, If[LessEqual[t, 0.078], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.65e143 or -1.80000000000000001e119 < t < -1.11999999999999998e-21 or 0.0779999999999999999 < 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. cancel-sign-sub 68.4%

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

      2. cancel-sign-sub-inv 68.4%

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

      3. *-commutative 68.4%

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

      4. *-commutative 68.4%

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

      5. remove-double-neg 68.4%

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

      6. *-commutative 68.4%

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

      7. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in t around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

   6. Simplified 65.6%

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

   if -1.65e143 < t < -1.80000000000000001e119 or -5.80000000000000041e-156 < t < 1.22000000000000005e-263

   1. Initial program 84.8%

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

      1. cancel-sign-sub 84.8%

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

      2. cancel-sign-sub-inv 84.8%

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

      3. *-commutative 84.8%

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

      4. *-commutative 84.8%

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

      5. remove-double-neg 84.8%

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

      6. *-commutative 84.8%

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

      7. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

   6. Simplified 65.3%

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

   if -1.11999999999999998e-21 < t < -5.80000000000000041e-156 or 1.22000000000000005e-263 < t < 0.0779999999999999999

   1. Initial program 75.3%

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

      1. cancel-sign-sub 75.3%

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

      2. cancel-sign-sub-inv 75.3%

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

      3. *-commutative 75.3%

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

      4. *-commutative 75.3%

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

      5. remove-double-neg 75.3%

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

      6. *-commutative 75.3%

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

      7. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in i around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-*r* 56.1%

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

      3. neg-mul-1 56.1%

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

      4. cancel-sign-sub 56.1%

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

      5. +-commutative 56.1%

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

      6. mul-1-neg 56.1%

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

      7. unsub-neg 56.1%

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

      8. *-commutative 56.1%

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

   6. Simplified 56.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 0.078:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 13: 53.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.42 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2700000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -1.42e+143)
     t_2
     (if (<= t -1.15e+119)
       t_1
       (if (<= t -1.62e-24)
         t_2
         (if (<= t -1.85e-156)
           (* i (- (* a b) (* y j)))
           (if (<= t 6.5e-193)
             t_1
             (if (<= t 2700000000000.0) (* 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 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.42e+143) {
		tmp = t_2;
	} else if (t <= -1.15e+119) {
		tmp = t_1;
	} else if (t <= -1.62e-24) {
		tmp = t_2;
	} else if (t <= -1.85e-156) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 6.5e-193) {
		tmp = t_1;
	} else if (t <= 2700000000000.0) {
		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 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-1.42d+143)) then
        tmp = t_2
    else if (t <= (-1.15d+119)) then
        tmp = t_1
    else if (t <= (-1.62d-24)) then
        tmp = t_2
    else if (t <= (-1.85d-156)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 6.5d-193) then
        tmp = t_1
    else if (t <= 2700000000000.0d0) 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 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.42e+143) {
		tmp = t_2;
	} else if (t <= -1.15e+119) {
		tmp = t_1;
	} else if (t <= -1.62e-24) {
		tmp = t_2;
	} else if (t <= -1.85e-156) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 6.5e-193) {
		tmp = t_1;
	} else if (t <= 2700000000000.0) {
		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 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.42e+143:
		tmp = t_2
	elif t <= -1.15e+119:
		tmp = t_1
	elif t <= -1.62e-24:
		tmp = t_2
	elif t <= -1.85e-156:
		tmp = i * ((a * b) - (y * j))
	elif t <= 6.5e-193:
		tmp = t_1
	elif t <= 2700000000000.0:
		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(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.42e+143)
		tmp = t_2;
	elseif (t <= -1.15e+119)
		tmp = t_1;
	elseif (t <= -1.62e-24)
		tmp = t_2;
	elseif (t <= -1.85e-156)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 6.5e-193)
		tmp = t_1;
	elseif (t <= 2700000000000.0)
		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 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.42e+143)
		tmp = t_2;
	elseif (t <= -1.15e+119)
		tmp = t_1;
	elseif (t <= -1.62e-24)
		tmp = t_2;
	elseif (t <= -1.85e-156)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 6.5e-193)
		tmp = t_1;
	elseif (t <= 2700000000000.0)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.42e+143], t$95$2, If[LessEqual[t, -1.15e+119], t$95$1, If[LessEqual[t, -1.62e-24], t$95$2, If[LessEqual[t, -1.85e-156], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-193], t$95$1, If[LessEqual[t, 2700000000000.0], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.42e143 or -1.15e119 < t < -1.62e-24 or 2.7e12 < t

   1. Initial program 68.2%

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

      1. cancel-sign-sub 68.2%

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

      2. cancel-sign-sub-inv 68.2%

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

      3. *-commutative 68.2%

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

      4. *-commutative 68.2%

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

      5. remove-double-neg 68.2%

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

      6. *-commutative 68.2%

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

      7. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in t around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

   6. Simplified 67.8%

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

   if -1.42e143 < t < -1.15e119 or -1.85e-156 < t < 6.5000000000000004e-193

   1. Initial program 84.5%

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

      1. cancel-sign-sub 84.5%

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

      2. cancel-sign-sub-inv 84.5%

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

      3. *-commutative 84.5%

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

      4. *-commutative 84.5%

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

      5. remove-double-neg 84.5%

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

      6. *-commutative 84.5%

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

      7. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in y around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

   6. Simplified 63.3%

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

   if -1.62e-24 < t < -1.85e-156

   1. Initial program 74.1%

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

      1. cancel-sign-sub 74.1%

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

      2. cancel-sign-sub-inv 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. remove-double-neg 74.1%

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

      6. *-commutative 74.1%

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

      7. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in i around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-*r* 60.9%

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

      3. neg-mul-1 60.9%

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

      4. cancel-sign-sub 60.9%

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

      5. +-commutative 60.9%

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

      6. mul-1-neg 60.9%

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

      7. unsub-neg 60.9%

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

      8. *-commutative 60.9%

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

   6. Simplified 60.9%

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

   if 6.5000000000000004e-193 < t < 2.7e12

   1. Initial program 71.7%

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

      1. cancel-sign-sub 71.7%

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

      2. cancel-sign-sub-inv 71.7%

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

      3. *-commutative 71.7%

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

      4. *-commutative 71.7%

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

      5. remove-double-neg 71.7%

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

      6. *-commutative 71.7%

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

      7. *-commutative 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in b around inf 59.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2700000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 14: 53.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 54000000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -3.7e+143)
     t_2
     (if (<= t -5.8e+118)
       t_1
       (if (<= t -1.7e-21)
         (- (* j (* t c)) (* a (* x t)))
         (if (<= t -3.2e-156)
           (* i (- (* a b) (* y j)))
           (if (<= t 6e-193)
             t_1
             (if (<= t 54000000000000.0) (* 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 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.7e+143) {
		tmp = t_2;
	} else if (t <= -5.8e+118) {
		tmp = t_1;
	} else if (t <= -1.7e-21) {
		tmp = (j * (t * c)) - (a * (x * t));
	} else if (t <= -3.2e-156) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 6e-193) {
		tmp = t_1;
	} else if (t <= 54000000000000.0) {
		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 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-3.7d+143)) then
        tmp = t_2
    else if (t <= (-5.8d+118)) then
        tmp = t_1
    else if (t <= (-1.7d-21)) then
        tmp = (j * (t * c)) - (a * (x * t))
    else if (t <= (-3.2d-156)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 6d-193) then
        tmp = t_1
    else if (t <= 54000000000000.0d0) 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 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.7e+143) {
		tmp = t_2;
	} else if (t <= -5.8e+118) {
		tmp = t_1;
	} else if (t <= -1.7e-21) {
		tmp = (j * (t * c)) - (a * (x * t));
	} else if (t <= -3.2e-156) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 6e-193) {
		tmp = t_1;
	} else if (t <= 54000000000000.0) {
		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 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3.7e+143:
		tmp = t_2
	elif t <= -5.8e+118:
		tmp = t_1
	elif t <= -1.7e-21:
		tmp = (j * (t * c)) - (a * (x * t))
	elif t <= -3.2e-156:
		tmp = i * ((a * b) - (y * j))
	elif t <= 6e-193:
		tmp = t_1
	elif t <= 54000000000000.0:
		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(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.7e+143)
		tmp = t_2;
	elseif (t <= -5.8e+118)
		tmp = t_1;
	elseif (t <= -1.7e-21)
		tmp = Float64(Float64(j * Float64(t * c)) - Float64(a * Float64(x * t)));
	elseif (t <= -3.2e-156)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 6e-193)
		tmp = t_1;
	elseif (t <= 54000000000000.0)
		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 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3.7e+143)
		tmp = t_2;
	elseif (t <= -5.8e+118)
		tmp = t_1;
	elseif (t <= -1.7e-21)
		tmp = (j * (t * c)) - (a * (x * t));
	elseif (t <= -3.2e-156)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 6e-193)
		tmp = t_1;
	elseif (t <= 54000000000000.0)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+143], t$95$2, If[LessEqual[t, -5.8e+118], t$95$1, If[LessEqual[t, -1.7e-21], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-156], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-193], t$95$1, If[LessEqual[t, 54000000000000.0], 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 < -3.7000000000000002e143 or 5.4e13 < 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. cancel-sign-sub 65.9%

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

      2. cancel-sign-sub-inv 65.9%

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

      3. *-commutative 65.9%

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

      4. *-commutative 65.9%

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

      5. remove-double-neg 65.9%

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

      6. *-commutative 65.9%

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

      7. *-commutative 65.9%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in t around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. unsub-neg 67.4%

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

   6. Simplified 67.4%

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

   if -3.7000000000000002e143 < t < -5.80000000000000032e118 or -3.19999999999999982e-156 < t < 5.9999999999999998e-193

   1. Initial program 84.5%

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

      1. cancel-sign-sub 84.5%

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

      2. cancel-sign-sub-inv 84.5%

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

      3. *-commutative 84.5%

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

      4. *-commutative 84.5%

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

      5. remove-double-neg 84.5%

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

      6. *-commutative 84.5%

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

      7. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in y around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

   6. Simplified 63.3%

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

   if -5.80000000000000032e118 < t < -1.7e-21

   1. Initial program 74.8%

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

      1. cancel-sign-sub 74.8%

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

      2. cancel-sign-sub-inv 74.8%

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

      3. *-commutative 74.8%

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

      4. *-commutative 74.8%

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

      5. remove-double-neg 74.8%

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

      6. *-commutative 74.8%

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

      7. *-commutative 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in b around 0 75.6%

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

   5. Taylor expanded in c around inf 68.8%

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

      1. associate-*r* 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in y around 0 72.5%

      \[\leadsto \left(c \cdot t\right) \cdot j + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 72.5%

         \[\leadsto \left(c \cdot t\right) \cdot j + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 72.5%

         \[\leadsto \left(c \cdot t\right) \cdot j + \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

   10. Simplified 72.5%

       \[\leadsto \left(c \cdot t\right) \cdot j + \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right)} \]

   if -1.7e-21 < t < -3.19999999999999982e-156

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 60.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   5. Step-by-step derivation

      1. *-commutative 60.9%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. associate-*r* 60.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot a\right) \cdot b}\right) \]

      3. neg-mul-1 60.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-a\right)} \cdot b\right) \]

      4. cancel-sign-sub 60.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + a \cdot b\right)} \]

      5. +-commutative 60.9%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 60.9%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 60.9%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      8. *-commutative 60.9%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if 5.9999999999999998e-193 < t < 5.4e13

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 59.7%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 54000000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 15: 42.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+199}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* y (* x z)))
        (t_3 (* i (- (* a b) (* y j)))))
   (if (<= z -6e+116)
     t_2
     (if (<= z -1.35e-258)
       t_1
       (if (<= z 2.25e-71)
         t_3
         (if (<= z 3.8e+22)
           t_1
           (if (<= z 8.2e+180)
             t_3
             (if (<= z 5.4e+199) (* j (* t 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 = a * ((b * i) - (x * t));
	double t_2 = y * (x * z);
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (z <= -6e+116) {
		tmp = t_2;
	} else if (z <= -1.35e-258) {
		tmp = t_1;
	} else if (z <= 2.25e-71) {
		tmp = t_3;
	} else if (z <= 3.8e+22) {
		tmp = t_1;
	} else if (z <= 8.2e+180) {
		tmp = t_3;
	} else if (z <= 5.4e+199) {
		tmp = j * (t * 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) :: t_3
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = y * (x * z)
    t_3 = i * ((a * b) - (y * j))
    if (z <= (-6d+116)) then
        tmp = t_2
    else if (z <= (-1.35d-258)) then
        tmp = t_1
    else if (z <= 2.25d-71) then
        tmp = t_3
    else if (z <= 3.8d+22) then
        tmp = t_1
    else if (z <= 8.2d+180) then
        tmp = t_3
    else if (z <= 5.4d+199) then
        tmp = j * (t * 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 = a * ((b * i) - (x * t));
	double t_2 = y * (x * z);
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (z <= -6e+116) {
		tmp = t_2;
	} else if (z <= -1.35e-258) {
		tmp = t_1;
	} else if (z <= 2.25e-71) {
		tmp = t_3;
	} else if (z <= 3.8e+22) {
		tmp = t_1;
	} else if (z <= 8.2e+180) {
		tmp = t_3;
	} else if (z <= 5.4e+199) {
		tmp = j * (t * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = y * (x * z)
	t_3 = i * ((a * b) - (y * j))
	tmp = 0
	if z <= -6e+116:
		tmp = t_2
	elif z <= -1.35e-258:
		tmp = t_1
	elif z <= 2.25e-71:
		tmp = t_3
	elif z <= 3.8e+22:
		tmp = t_1
	elif z <= 8.2e+180:
		tmp = t_3
	elif z <= 5.4e+199:
		tmp = j * (t * c)
	else:
		tmp = t_2
	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)))
	t_2 = Float64(y * Float64(x * z))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (z <= -6e+116)
		tmp = t_2;
	elseif (z <= -1.35e-258)
		tmp = t_1;
	elseif (z <= 2.25e-71)
		tmp = t_3;
	elseif (z <= 3.8e+22)
		tmp = t_1;
	elseif (z <= 8.2e+180)
		tmp = t_3;
	elseif (z <= 5.4e+199)
		tmp = Float64(j * Float64(t * 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 = a * ((b * i) - (x * t));
	t_2 = y * (x * z);
	t_3 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (z <= -6e+116)
		tmp = t_2;
	elseif (z <= -1.35e-258)
		tmp = t_1;
	elseif (z <= 2.25e-71)
		tmp = t_3;
	elseif (z <= 3.8e+22)
		tmp = t_1;
	elseif (z <= 8.2e+180)
		tmp = t_3;
	elseif (z <= 5.4e+199)
		tmp = j * (t * 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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+116], t$95$2, If[LessEqual[z, -1.35e-258], t$95$1, If[LessEqual[z, 2.25e-71], t$95$3, If[LessEqual[z, 3.8e+22], t$95$1, If[LessEqual[z, 8.2e+180], t$95$3, If[LessEqual[z, 5.4e+199], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9999999999999997e116 or 5.3999999999999998e199 < z

   1. Initial program 61.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 61.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 61.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 61.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 61.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 61.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 61.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 61.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 61.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 61.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.8%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 61.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 54.4%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -5.9999999999999997e116 < z < -1.34999999999999998e-258 or 2.2500000000000001e-71 < z < 3.8000000000000004e22

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 86.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 59.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 59.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. distribute-lft-out-- 59.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      3. sub-neg 59.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1 \cdot \left(i \cdot b\right)\right)\right)} \]

      4. mul-1-neg 59.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \left(-\color{blue}{\left(-i \cdot b\right)}\right)\right) \]

      5. remove-double-neg 59.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      6. +-commutative 59.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      7. mul-1-neg 59.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      8. unsub-neg 59.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      9. *-commutative 59.7%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 59.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -1.34999999999999998e-258 < z < 2.2500000000000001e-71 or 3.8000000000000004e22 < z < 8.2e180

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 53.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   5. Step-by-step derivation

      1. *-commutative 53.9%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. associate-*r* 53.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot a\right) \cdot b}\right) \]

      3. neg-mul-1 53.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-a\right)} \cdot b\right) \]

      4. cancel-sign-sub 53.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + a \cdot b\right)} \]

      5. +-commutative 53.9%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 53.9%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 53.9%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      8. *-commutative 53.9%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   6. Simplified 53.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]

   if 8.2e180 < z < 5.3999999999999998e199

   1. Initial program 60.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 60.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 60.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 60.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 60.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 60.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 60.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 60.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 60.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 60.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in j around inf 80.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   6. Taylor expanded in c around inf 80.0%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-258}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-71}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+180}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+199}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 16: 49.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.4 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-247}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.4e+105)
     t_1
     (if (<= j -8.2e-39)
       (+ (* z (* x y)) (* b (* a i)))
       (if (<= j -1.8e-247)
         (* x (- (* y z) (* t a)))
         (if (<= j 1.45e-199)
           (* b (- (* a i) (* z c)))
           (if (<= j 2.2e+141) (* y (- (* x z) (* i j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.4e+105) {
		tmp = t_1;
	} else if (j <= -8.2e-39) {
		tmp = (z * (x * y)) + (b * (a * i));
	} else if (j <= -1.8e-247) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.45e-199) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 2.2e+141) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.4d+105)) then
        tmp = t_1
    else if (j <= (-8.2d-39)) then
        tmp = (z * (x * y)) + (b * (a * i))
    else if (j <= (-1.8d-247)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 1.45d-199) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 2.2d+141) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.4e+105) {
		tmp = t_1;
	} else if (j <= -8.2e-39) {
		tmp = (z * (x * y)) + (b * (a * i));
	} else if (j <= -1.8e-247) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.45e-199) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 2.2e+141) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.4e+105:
		tmp = t_1
	elif j <= -8.2e-39:
		tmp = (z * (x * y)) + (b * (a * i))
	elif j <= -1.8e-247:
		tmp = x * ((y * z) - (t * a))
	elif j <= 1.45e-199:
		tmp = b * ((a * i) - (z * c))
	elif j <= 2.2e+141:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.4e+105)
		tmp = t_1;
	elseif (j <= -8.2e-39)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(a * i)));
	elseif (j <= -1.8e-247)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 1.45e-199)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 2.2e+141)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.4e+105)
		tmp = t_1;
	elseif (j <= -8.2e-39)
		tmp = (z * (x * y)) + (b * (a * i));
	elseif (j <= -1.8e-247)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 1.45e-199)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 2.2e+141)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.4e+105], t$95$1, If[LessEqual[j, -8.2e-39], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.8e-247], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e-199], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.2e+141], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.4000000000000001e105 or 2.2e141 < j

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 77.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 77.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 77.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 77.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 77.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 73.8%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in j around inf 71.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   if -1.4000000000000001e105 < j < -8.2e-39

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 79.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 76.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 79.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} - \left(c \cdot z - i \cdot a\right) \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 79.6%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} - \left(c \cdot z - i \cdot a\right) \cdot b \]

      2. associate-*l* 79.9%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} - \left(c \cdot z - i \cdot a\right) \cdot b \]

   7. Simplified 79.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} - \left(c \cdot z - i \cdot a\right) \cdot b \]

   8. Taylor expanded in c around 0 69.6%

      \[\leadsto z \cdot \left(x \cdot y\right) - \color{blue}{\left(-1 \cdot \left(a \cdot i\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. neg-mul-1 69.6%

         \[\leadsto z \cdot \left(x \cdot y\right) - \color{blue}{\left(-a \cdot i\right)} \cdot b \]

      2. distribute-rgt-neg-in 69.6%

         \[\leadsto z \cdot \left(x \cdot y\right) - \color{blue}{\left(a \cdot \left(-i\right)\right)} \cdot b \]

   10. Simplified 69.6%

       \[\leadsto z \cdot \left(x \cdot y\right) - \color{blue}{\left(a \cdot \left(-i\right)\right)} \cdot b \]

   if -8.2e-39 < j < -1.7999999999999998e-247

   1. Initial program 69.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 69.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 69.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 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 x around inf 70.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -1.7999999999999998e-247 < j < 1.45e-199

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 1.45e-199 < j < 2.2e141

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 59.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 59.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 59.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-247}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 17: 30.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{if}\;b \leq -1.42 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 185:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* x t))))
   (if (<= b -1.42e+17)
     (* (* z b) (- c))
     (if (<= b -1.8e-31)
       t_1
       (if (<= b -1.9e-158)
         (* y (* x z))
         (if (<= b 1.9e-210)
           t_1
           (if (<= b 5.6e-161)
             (* x (* y z))
             (if (<= b 185.0) 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 = -a * (x * t);
	double tmp;
	if (b <= -1.42e+17) {
		tmp = (z * b) * -c;
	} else if (b <= -1.8e-31) {
		tmp = t_1;
	} else if (b <= -1.9e-158) {
		tmp = y * (x * z);
	} else if (b <= 1.9e-210) {
		tmp = t_1;
	} else if (b <= 5.6e-161) {
		tmp = x * (y * z);
	} else if (b <= 185.0) {
		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 = -a * (x * t)
    if (b <= (-1.42d+17)) then
        tmp = (z * b) * -c
    else if (b <= (-1.8d-31)) then
        tmp = t_1
    else if (b <= (-1.9d-158)) then
        tmp = y * (x * z)
    else if (b <= 1.9d-210) then
        tmp = t_1
    else if (b <= 5.6d-161) then
        tmp = x * (y * z)
    else if (b <= 185.0d0) 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 = -a * (x * t);
	double tmp;
	if (b <= -1.42e+17) {
		tmp = (z * b) * -c;
	} else if (b <= -1.8e-31) {
		tmp = t_1;
	} else if (b <= -1.9e-158) {
		tmp = y * (x * z);
	} else if (b <= 1.9e-210) {
		tmp = t_1;
	} else if (b <= 5.6e-161) {
		tmp = x * (y * z);
	} else if (b <= 185.0) {
		tmp = t_1;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (x * t)
	tmp = 0
	if b <= -1.42e+17:
		tmp = (z * b) * -c
	elif b <= -1.8e-31:
		tmp = t_1
	elif b <= -1.9e-158:
		tmp = y * (x * z)
	elif b <= 1.9e-210:
		tmp = t_1
	elif b <= 5.6e-161:
		tmp = x * (y * z)
	elif b <= 185.0:
		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(Float64(-a) * Float64(x * t))
	tmp = 0.0
	if (b <= -1.42e+17)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (b <= -1.8e-31)
		tmp = t_1;
	elseif (b <= -1.9e-158)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.9e-210)
		tmp = t_1;
	elseif (b <= 5.6e-161)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 185.0)
		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 = -a * (x * t);
	tmp = 0.0;
	if (b <= -1.42e+17)
		tmp = (z * b) * -c;
	elseif (b <= -1.8e-31)
		tmp = t_1;
	elseif (b <= -1.9e-158)
		tmp = y * (x * z);
	elseif (b <= 1.9e-210)
		tmp = t_1;
	elseif (b <= 5.6e-161)
		tmp = x * (y * z);
	elseif (b <= 185.0)
		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[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.42e+17], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[b, -1.8e-31], t$95$1, If[LessEqual[b, -1.9e-158], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-210], t$95$1, If[LessEqual[b, 5.6e-161], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 185.0], t$95$1, N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.42e17

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 76.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 67.9%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in c around inf 39.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. distribute-rgt-neg-in 39.1%

         \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} \]

      3. *-commutative 39.1%

         \[\leadsto c \cdot \left(-\color{blue}{b \cdot z}\right) \]

   7. Simplified 39.1%

      \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

   if -1.42e17 < b < -1.80000000000000002e-31 or -1.8999999999999999e-158 < b < 1.90000000000000002e-210 or 5.59999999999999984e-161 < b < 185

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 51.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. distribute-lft-out-- 51.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      3. sub-neg 51.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1 \cdot \left(i \cdot b\right)\right)\right)} \]

      4. mul-1-neg 51.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \left(-\color{blue}{\left(-i \cdot b\right)}\right)\right) \]

      5. remove-double-neg 51.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      6. +-commutative 51.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      7. mul-1-neg 51.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      8. unsub-neg 51.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      9. *-commutative 51.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 51.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around 0 44.7%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 44.7%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 44.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 44.7%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 44.7%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -1.80000000000000002e-31 < b < -1.8999999999999999e-158

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 62.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 62.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 62.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 62.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 45.5%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if 1.90000000000000002e-210 < b < 5.59999999999999984e-161

   1. Initial program 55.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 55.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 55.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 55.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 55.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 55.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 55.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 55.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 55.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 55.1%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in c around inf 47.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]
   6. Step-by-step derivation

      1. associate-*r* 40.1%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} + \left(y \cdot z - a \cdot t\right) \cdot x \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} + \left(y \cdot z - a \cdot t\right) \cdot x \]

   8. Taylor expanded in t around 0 40.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. *-commutative 40.6%

         \[\leadsto \color{blue}{\left(x \cdot z\right)} \cdot y \]

      3. associate-*l* 47.5%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   10. Simplified 47.5%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 185 < b

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 67.7%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around inf 51.2%

      \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-31}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-210}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-161}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 185:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 18: 30.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+16}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.11 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq 206:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* x t))))
   (if (<= b -2.45e+16)
     (* (* z b) (- c))
     (if (<= b -2.3e-31)
       t_1
       (if (<= b -2e-157)
         (* y (* x z))
         (if (<= b 1.11e-203)
           t_1
           (if (<= b 1.22e-77)
             (* j (* y (- i)))
             (if (<= b 206.0) 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 = -a * (x * t);
	double tmp;
	if (b <= -2.45e+16) {
		tmp = (z * b) * -c;
	} else if (b <= -2.3e-31) {
		tmp = t_1;
	} else if (b <= -2e-157) {
		tmp = y * (x * z);
	} else if (b <= 1.11e-203) {
		tmp = t_1;
	} else if (b <= 1.22e-77) {
		tmp = j * (y * -i);
	} else if (b <= 206.0) {
		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 = -a * (x * t)
    if (b <= (-2.45d+16)) then
        tmp = (z * b) * -c
    else if (b <= (-2.3d-31)) then
        tmp = t_1
    else if (b <= (-2d-157)) then
        tmp = y * (x * z)
    else if (b <= 1.11d-203) then
        tmp = t_1
    else if (b <= 1.22d-77) then
        tmp = j * (y * -i)
    else if (b <= 206.0d0) 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 = -a * (x * t);
	double tmp;
	if (b <= -2.45e+16) {
		tmp = (z * b) * -c;
	} else if (b <= -2.3e-31) {
		tmp = t_1;
	} else if (b <= -2e-157) {
		tmp = y * (x * z);
	} else if (b <= 1.11e-203) {
		tmp = t_1;
	} else if (b <= 1.22e-77) {
		tmp = j * (y * -i);
	} else if (b <= 206.0) {
		tmp = t_1;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (x * t)
	tmp = 0
	if b <= -2.45e+16:
		tmp = (z * b) * -c
	elif b <= -2.3e-31:
		tmp = t_1
	elif b <= -2e-157:
		tmp = y * (x * z)
	elif b <= 1.11e-203:
		tmp = t_1
	elif b <= 1.22e-77:
		tmp = j * (y * -i)
	elif b <= 206.0:
		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(Float64(-a) * Float64(x * t))
	tmp = 0.0
	if (b <= -2.45e+16)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (b <= -2.3e-31)
		tmp = t_1;
	elseif (b <= -2e-157)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.11e-203)
		tmp = t_1;
	elseif (b <= 1.22e-77)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (b <= 206.0)
		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 = -a * (x * t);
	tmp = 0.0;
	if (b <= -2.45e+16)
		tmp = (z * b) * -c;
	elseif (b <= -2.3e-31)
		tmp = t_1;
	elseif (b <= -2e-157)
		tmp = y * (x * z);
	elseif (b <= 1.11e-203)
		tmp = t_1;
	elseif (b <= 1.22e-77)
		tmp = j * (y * -i);
	elseif (b <= 206.0)
		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[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.45e+16], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[b, -2.3e-31], t$95$1, If[LessEqual[b, -2e-157], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.11e-203], t$95$1, If[LessEqual[b, 1.22e-77], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 206.0], t$95$1, N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.45e16

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 76.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 67.9%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in c around inf 39.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. distribute-rgt-neg-in 39.1%

         \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} \]

      3. *-commutative 39.1%

         \[\leadsto c \cdot \left(-\color{blue}{b \cdot z}\right) \]

   7. Simplified 39.1%

      \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

   if -2.45e16 < b < -2.2999999999999998e-31 or -1.99999999999999989e-157 < b < 1.1100000000000001e-203 or 1.22000000000000001e-77 < b < 206

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 58.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. distribute-lft-out-- 58.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      3. sub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1 \cdot \left(i \cdot b\right)\right)\right)} \]

      4. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \left(-\color{blue}{\left(-i \cdot b\right)}\right)\right) \]

      5. remove-double-neg 58.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      6. +-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      7. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      8. unsub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      9. *-commutative 58.5%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around 0 49.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 49.6%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 49.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 49.6%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 49.6%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -2.2999999999999998e-31 < b < -1.99999999999999989e-157

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 62.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 62.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 62.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 62.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 45.5%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if 1.1100000000000001e-203 < b < 1.22000000000000001e-77

   1. Initial program 59.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 59.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 59.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 53.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 53.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 53.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 53.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 53.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around 0 31.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 31.2%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. *-commutative 31.2%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

      3. distribute-lft-neg-in 31.2%

         \[\leadsto \color{blue}{\left(-i \cdot j\right) \cdot y} \]

      4. distribute-lft-neg-in 31.2%

         \[\leadsto \color{blue}{\left(\left(-i\right) \cdot j\right)} \cdot y \]

      5. *-commutative 31.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(-i\right)\right)} \cdot y \]

      6. associate-*l* 34.1%

         \[\leadsto \color{blue}{j \cdot \left(\left(-i\right) \cdot y\right)} \]

      7. distribute-lft-neg-in 34.1%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      8. distribute-rgt-neg-in 34.1%

         \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(-y\right)\right)} \]

   9. Simplified 34.1%

      \[\leadsto \color{blue}{j \cdot \left(i \cdot \left(-y\right)\right)} \]

   if 206 < b

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 67.7%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around inf 51.2%

      \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+16}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-31}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.11 \cdot 10^{-203}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq 206:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 19: 51.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -0.0215:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -0.0215)
     (+ t_1 (* b (* a i)))
     (if (<= j -3.6e-245)
       (* x (- (* y z) (* t a)))
       (if (<= j 2.5e-199)
         (* b (- (* a i) (* z c)))
         (if (<= j 5.8e+140) (* y (- (* x z) (* i j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -0.0215) {
		tmp = t_1 + (b * (a * i));
	} else if (j <= -3.6e-245) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 2.5e-199) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 5.8e+140) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-0.0215d0)) then
        tmp = t_1 + (b * (a * i))
    else if (j <= (-3.6d-245)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 2.5d-199) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 5.8d+140) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -0.0215) {
		tmp = t_1 + (b * (a * i));
	} else if (j <= -3.6e-245) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 2.5e-199) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 5.8e+140) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -0.0215:
		tmp = t_1 + (b * (a * i))
	elif j <= -3.6e-245:
		tmp = x * ((y * z) - (t * a))
	elif j <= 2.5e-199:
		tmp = b * ((a * i) - (z * c))
	elif j <= 5.8e+140:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -0.0215)
		tmp = Float64(t_1 + Float64(b * Float64(a * i)));
	elseif (j <= -3.6e-245)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 2.5e-199)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 5.8e+140)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -0.0215)
		tmp = t_1 + (b * (a * i));
	elseif (j <= -3.6e-245)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 2.5e-199)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 5.8e+140)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -0.0215], N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.6e-245], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e-199], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e+140], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -0.021499999999999998

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 72.6%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 74.3%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 74.3%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -0.021499999999999998 < j < -3.59999999999999999e-245

   1. Initial program 69.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 69.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 69.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 69.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 76.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in x around inf 65.1%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -3.59999999999999999e-245 < j < 2.4999999999999998e-199

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 2.4999999999999998e-199 < j < 5.7999999999999998e140

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 59.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 59.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 59.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if 5.7999999999999998e140 < j

   1. Initial program 84.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 73.1%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in j around inf 72.2%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.0215:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 20: 30.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(x \cdot t\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;i \leq -1.66 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* x t))) (t_2 (* b (* a i))))
   (if (<= i -1.66e+106)
     t_2
     (if (<= i -3.8e-121)
       (* z (* x y))
       (if (<= i 1.4e-266)
         t_1
         (if (<= i 6.2e-47) (* y (* x z)) (if (<= i 1.32e+107) 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 = -a * (x * t);
	double t_2 = b * (a * i);
	double tmp;
	if (i <= -1.66e+106) {
		tmp = t_2;
	} else if (i <= -3.8e-121) {
		tmp = z * (x * y);
	} else if (i <= 1.4e-266) {
		tmp = t_1;
	} else if (i <= 6.2e-47) {
		tmp = y * (x * z);
	} else if (i <= 1.32e+107) {
		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 = -a * (x * t)
    t_2 = b * (a * i)
    if (i <= (-1.66d+106)) then
        tmp = t_2
    else if (i <= (-3.8d-121)) then
        tmp = z * (x * y)
    else if (i <= 1.4d-266) then
        tmp = t_1
    else if (i <= 6.2d-47) then
        tmp = y * (x * z)
    else if (i <= 1.32d+107) 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 = -a * (x * t);
	double t_2 = b * (a * i);
	double tmp;
	if (i <= -1.66e+106) {
		tmp = t_2;
	} else if (i <= -3.8e-121) {
		tmp = z * (x * y);
	} else if (i <= 1.4e-266) {
		tmp = t_1;
	} else if (i <= 6.2e-47) {
		tmp = y * (x * z);
	} else if (i <= 1.32e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (x * t)
	t_2 = b * (a * i)
	tmp = 0
	if i <= -1.66e+106:
		tmp = t_2
	elif i <= -3.8e-121:
		tmp = z * (x * y)
	elif i <= 1.4e-266:
		tmp = t_1
	elif i <= 6.2e-47:
		tmp = y * (x * z)
	elif i <= 1.32e+107:
		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(-a) * Float64(x * t))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (i <= -1.66e+106)
		tmp = t_2;
	elseif (i <= -3.8e-121)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1.4e-266)
		tmp = t_1;
	elseif (i <= 6.2e-47)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.32e+107)
		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 = -a * (x * t);
	t_2 = b * (a * i);
	tmp = 0.0;
	if (i <= -1.66e+106)
		tmp = t_2;
	elseif (i <= -3.8e-121)
		tmp = z * (x * y);
	elseif (i <= 1.4e-266)
		tmp = t_1;
	elseif (i <= 6.2e-47)
		tmp = y * (x * z);
	elseif (i <= 1.32e+107)
		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[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.66e+106], t$95$2, If[LessEqual[i, -3.8e-121], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e-266], t$95$1, If[LessEqual[i, 6.2e-47], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.32e+107], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.66e106 or 1.32000000000000003e107 < i

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 65.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 65.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 65.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 65.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 65.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 65.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 65.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 65.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 54.8%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around inf 45.2%

      \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]

   if -1.66e106 < i < -3.8000000000000001e-121

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 65.0%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in c around inf 53.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]
   6. Step-by-step derivation

      1. associate-*r* 53.4%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} + \left(y \cdot z - a \cdot t\right) \cdot x \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} + \left(y \cdot z - a \cdot t\right) \cdot x \]

   8. Taylor expanded in t around 0 37.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 34.9%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 34.9%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

      3. associate-*l* 37.2%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   10. Simplified 37.2%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if -3.8000000000000001e-121 < i < 1.4e-266 or 6.1999999999999996e-47 < i < 1.32000000000000003e107

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 56.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 56.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. distribute-lft-out-- 56.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      3. sub-neg 56.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1 \cdot \left(i \cdot b\right)\right)\right)} \]

      4. mul-1-neg 56.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \left(-\color{blue}{\left(-i \cdot b\right)}\right)\right) \]

      5. remove-double-neg 56.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      6. +-commutative 56.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      7. mul-1-neg 56.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      8. unsub-neg 56.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      9. *-commutative 56.3%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 56.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around 0 43.9%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 43.9%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-in 43.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 43.9%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 43.9%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 1.4e-266 < i < 6.1999999999999996e-47

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 45.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 45.6%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 45.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 39.6%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.66 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-266}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+107}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 21: 42.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+116} \lor \neg \left(z \leq 8.8 \cdot 10^{+184}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -7.6e+116) (not (<= z 8.8e+184)))
   (* y (* x z))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -7.6e+116) || !(z <= 8.8e+184)) {
		tmp = y * (x * z);
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-7.6d+116)) .or. (.not. (z <= 8.8d+184))) then
        tmp = y * (x * z)
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -7.6e+116) || !(z <= 8.8e+184)) {
		tmp = y * (x * z);
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -7.6e+116) or not (z <= 8.8e+184):
		tmp = y * (x * z)
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -7.6e+116) || !(z <= 8.8e+184))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -7.6e+116) || ~((z <= 8.8e+184)))
		tmp = y * (x * z);
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -7.6e+116], N[Not[LessEqual[z, 8.8e+184]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5999999999999998e116 or 8.8e184 < z

   1. Initial program 61.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 61.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 61.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 61.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 61.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 61.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 61.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 61.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 59.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 59.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.6%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 52.4%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -7.5999999999999998e116 < z < 8.8e184

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 51.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. distribute-lft-out-- 51.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      3. sub-neg 51.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1 \cdot \left(i \cdot b\right)\right)\right)} \]

      4. mul-1-neg 51.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \left(-\color{blue}{\left(-i \cdot b\right)}\right)\right) \]

      5. remove-double-neg 51.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      6. +-commutative 51.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      7. mul-1-neg 51.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      8. unsub-neg 51.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      9. *-commutative 51.5%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 51.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+116} \lor \neg \left(z \leq 8.8 \cdot 10^{+184}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 22: 30.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-17} \lor \neg \left(t \leq 7400000000000\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1e-17) (not (<= t 7400000000000.0)))
   (* c (* t j))
   (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1e-17) || !(t <= 7400000000000.0)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1d-17)) .or. (.not. (t <= 7400000000000.0d0))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1e-17) || !(t <= 7400000000000.0)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1e-17) or not (t <= 7400000000000.0):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1e-17) || !(t <= 7400000000000.0))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1e-17) || ~((t <= 7400000000000.0)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1e-17], N[Not[LessEqual[t, 7400000000000.0]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000007e-17 or 7.4e12 < t

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 68.1%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in j around inf 41.1%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   6. Taylor expanded in c around inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.00000000000000007e-17 < t < 7.4e12

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 69.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 29.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-17} \lor \neg \left(t \leq 7400000000000\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 23: 30.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+104} \lor \neg \left(x \leq 1.7 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -2.55e+104) (not (<= x 1.7e+23))) (* y (* x 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 ((x <= -2.55e+104) || !(x <= 1.7e+23)) {
		tmp = y * (x * 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 ((x <= (-2.55d+104)) .or. (.not. (x <= 1.7d+23))) then
        tmp = y * (x * 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 ((x <= -2.55e+104) || !(x <= 1.7e+23)) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -2.55e+104) or not (x <= 1.7e+23):
		tmp = y * (x * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -2.55e+104) || !(x <= 1.7e+23))
		tmp = Float64(y * Float64(x * 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 ((x <= -2.55e+104) || ~((x <= 1.7e+23)))
		tmp = y * (x * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -2.55e+104], N[Not[LessEqual[x, 1.7e+23]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5500000000000001e104 or 1.69999999999999996e23 < x

   1. Initial program 68.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 51.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.6%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 51.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 46.8%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -2.5500000000000001e104 < x < 1.69999999999999996e23

   1. Initial program 78.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 47.9%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around inf 30.4%

      \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+104} \lor \neg \left(x \leq 1.7 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 24: 29.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -7.5e+155)
   (* a (* b i))
   (if (<= b 2.4e+77) (* x (* y z)) (* i (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.5e+155) {
		tmp = a * (b * i);
	} else if (b <= 2.4e+77) {
		tmp = x * (y * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-7.5d+155)) then
        tmp = a * (b * i)
    else if (b <= 2.4d+77) then
        tmp = x * (y * z)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.5e+155) {
		tmp = a * (b * i);
	} else if (b <= 2.4e+77) {
		tmp = x * (y * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -7.5e+155:
		tmp = a * (b * i)
	elif b <= 2.4e+77:
		tmp = x * (y * z)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -7.5e+155)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 2.4e+77)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -7.5e+155)
		tmp = a * (b * i);
	elseif (b <= 2.4e+77)
		tmp = x * (y * z);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -7.5e+155], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+77], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.4999999999999999e155

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 80.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 47.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -7.4999999999999999e155 < b < 2.3999999999999999e77

   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. cancel-sign-sub 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 65.7%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j + \left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in c around inf 57.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} + \left(y \cdot z - a \cdot t\right) \cdot x \]
   6. Step-by-step derivation

      1. associate-*r* 57.2%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} + \left(y \cdot z - a \cdot t\right) \cdot x \]

   7. Simplified 57.2%

      \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} + \left(y \cdot z - a \cdot t\right) \cdot x \]

   8. Taylor expanded in t around 0 29.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   9. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. *-commutative 29.9%

         \[\leadsto \color{blue}{\left(x \cdot z\right)} \cdot y \]

      3. associate-*l* 29.4%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   10. Simplified 29.4%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 2.3999999999999999e77 < b

   1. Initial program 85.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 85.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 55.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 55.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. distribute-lft-out-- 55.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      3. sub-neg 55.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1 \cdot \left(i \cdot b\right)\right)\right)} \]

      4. mul-1-neg 55.2%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \left(-\color{blue}{\left(-i \cdot b\right)}\right)\right) \]

      5. remove-double-neg 55.2%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      6. +-commutative 55.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      7. mul-1-neg 55.2%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      8. unsub-neg 55.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      9. *-commutative 55.2%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 55.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 57.3%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 25: 29.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.3e+154)
   (* a (* b i))
   (if (<= b 7.8e+79) (* y (* x z)) (* i (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.3e+154) {
		tmp = a * (b * i);
	} else if (b <= 7.8e+79) {
		tmp = y * (x * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.3d+154)) then
        tmp = a * (b * i)
    else if (b <= 7.8d+79) then
        tmp = y * (x * z)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.3e+154) {
		tmp = a * (b * i);
	} else if (b <= 7.8e+79) {
		tmp = y * (x * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.3e+154:
		tmp = a * (b * i)
	elif b <= 7.8e+79:
		tmp = y * (x * z)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.3e+154)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 7.8e+79)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.3e+154)
		tmp = a * (b * i);
	elseif (b <= 7.8e+79)
		tmp = y * (x * z);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.3e+154], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+79], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.29999999999999994e154

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 80.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 47.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -1.29999999999999994e154 < b < 7.7999999999999994e79

   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. cancel-sign-sub 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 46.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 46.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 46.6%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 46.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 46.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 29.9%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if 7.7999999999999994e79 < b

   1. Initial program 85.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 85.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 85.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 55.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 55.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. distribute-lft-out-- 55.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      3. sub-neg 55.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1 \cdot \left(i \cdot b\right)\right)\right)} \]

      4. mul-1-neg 55.2%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \left(-\color{blue}{\left(-i \cdot b\right)}\right)\right) \]

      5. remove-double-neg 55.2%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      6. +-commutative 55.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      7. mul-1-neg 55.2%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      8. unsub-neg 55.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      9. *-commutative 55.2%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 55.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 57.3%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 26: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 74.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-def 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 65.1%

   \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

5. Taylor expanded in i around inf 22.8%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

6. Final simplification 22.8%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.3% 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 2023242 
(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)))))