Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.2% → 80.8%

Time: 31.1s

Alternatives: 23

Speedup: 0.5×

• 57.1% 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: 80.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_2 + \left(t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\right) \leq \infty:\\ \;\;\;\;t\_2 + \left(x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= (+ t_2 (+ t_1 (* x (- (* y z) (* t a))))) INFINITY)
     (+ t_2 (+ (* x (fma y z (* t (- a)))) t_1))
     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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if ((t_2 + (t_1 + (x * ((y * z) - (t * a))))) <= ((double) INFINITY)) {
		tmp = t_2 + ((x * fma(y, z, (t * -a))) + t_1);
	} else {
		tmp = t_1;
	}
	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(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (Float64(t_2 + Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))))) <= Inf)
		tmp = Float64(t_2 + Float64(Float64(x * fma(y, z, Float64(t * Float64(-a)))) + t_1));
	else
		tmp = t_1;
	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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 + N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$2 + N[(N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$1]]]

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 90.9%

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

      1. cancel-sign-sub-inv 90.9%

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

      2. cancel-sign-sub 90.9%

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

      3. *-commutative 90.9%

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

      4. fma-neg 90.9%

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

      5. distribute-rgt-neg-in 90.9%

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

      6. remove-double-neg 90.9%

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

      7. *-commutative 90.9%

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

      8. *-commutative 90.9%

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

      9. sub-neg 90.9%

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

      10. sub-neg 90.9%

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

      11. *-commutative 90.9%

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

      12. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   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. Add Preprocessing

   3. Taylor expanded in b around inf 57.7%

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

      1. *-commutative 57.7%

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

   5. Simplified 57.7%

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

4. Final simplification 84.9%

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

Alternative 2: 80.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\right)\\ \mathbf{if}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (j * ((t * c) - (y * i))) + (t_1 + (x * ((y * z) - (t * a))))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	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(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a)))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = (j * ((t * c) - (y * i))) + (t_1 + (x * ((y * z) - (t * a))));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

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 90.9%

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

   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. Add Preprocessing

   3. Taylor expanded in b around inf 57.7%

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

      1. *-commutative 57.7%

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

   5. Simplified 57.7%

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

4. Final simplification 84.9%

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

Alternative 3: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+167}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -132000000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -6400:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+95}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(b \cdot \left(x \cdot \frac{y}{b} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -9.2e+167)
     t_2
     (if (<= b -3.8e+129)
       t_1
       (if (<= b -5e+88)
         t_2
         (if (<= b -3.45e+72)
           t_1
           (if (<= b -132000000.0)
             (* c (- (* t j) (* z b)))
             (if (<= b -6400.0)
               (* a (- (* b i) (* x t)))
               (if (<= b 3.9e+57)
                 t_1
                 (if (<= b 1.35e+95)
                   (* i (- (* a b) (* y j)))
                   (if (<= b 1.05e+138)
                     (* z (* b (- (* x (/ y b)) 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 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.2e+167) {
		tmp = t_2;
	} else if (b <= -3.8e+129) {
		tmp = t_1;
	} else if (b <= -5e+88) {
		tmp = t_2;
	} else if (b <= -3.45e+72) {
		tmp = t_1;
	} else if (b <= -132000000.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= -6400.0) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= 3.9e+57) {
		tmp = t_1;
	} else if (b <= 1.35e+95) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= 1.05e+138) {
		tmp = z * (b * ((x * (y / b)) - 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 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-9.2d+167)) then
        tmp = t_2
    else if (b <= (-3.8d+129)) then
        tmp = t_1
    else if (b <= (-5d+88)) then
        tmp = t_2
    else if (b <= (-3.45d+72)) then
        tmp = t_1
    else if (b <= (-132000000.0d0)) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= (-6400.0d0)) then
        tmp = a * ((b * i) - (x * t))
    else if (b <= 3.9d+57) then
        tmp = t_1
    else if (b <= 1.35d+95) then
        tmp = i * ((a * b) - (y * j))
    else if (b <= 1.05d+138) then
        tmp = z * (b * ((x * (y / b)) - 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 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.2e+167) {
		tmp = t_2;
	} else if (b <= -3.8e+129) {
		tmp = t_1;
	} else if (b <= -5e+88) {
		tmp = t_2;
	} else if (b <= -3.45e+72) {
		tmp = t_1;
	} else if (b <= -132000000.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= -6400.0) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= 3.9e+57) {
		tmp = t_1;
	} else if (b <= 1.35e+95) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= 1.05e+138) {
		tmp = z * (b * ((x * (y / b)) - c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -9.2e+167:
		tmp = t_2
	elif b <= -3.8e+129:
		tmp = t_1
	elif b <= -5e+88:
		tmp = t_2
	elif b <= -3.45e+72:
		tmp = t_1
	elif b <= -132000000.0:
		tmp = c * ((t * j) - (z * b))
	elif b <= -6400.0:
		tmp = a * ((b * i) - (x * t))
	elif b <= 3.9e+57:
		tmp = t_1
	elif b <= 1.35e+95:
		tmp = i * ((a * b) - (y * j))
	elif b <= 1.05e+138:
		tmp = z * (b * ((x * (y / b)) - c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.2e+167)
		tmp = t_2;
	elseif (b <= -3.8e+129)
		tmp = t_1;
	elseif (b <= -5e+88)
		tmp = t_2;
	elseif (b <= -3.45e+72)
		tmp = t_1;
	elseif (b <= -132000000.0)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= -6400.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (b <= 3.9e+57)
		tmp = t_1;
	elseif (b <= 1.35e+95)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (b <= 1.05e+138)
		tmp = Float64(z * Float64(b * Float64(Float64(x * Float64(y / b)) - 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 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.2e+167)
		tmp = t_2;
	elseif (b <= -3.8e+129)
		tmp = t_1;
	elseif (b <= -5e+88)
		tmp = t_2;
	elseif (b <= -3.45e+72)
		tmp = t_1;
	elseif (b <= -132000000.0)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= -6400.0)
		tmp = a * ((b * i) - (x * t));
	elseif (b <= 3.9e+57)
		tmp = t_1;
	elseif (b <= 1.35e+95)
		tmp = i * ((a * b) - (y * j));
	elseif (b <= 1.05e+138)
		tmp = z * (b * ((x * (y / b)) - c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+167], t$95$2, If[LessEqual[b, -3.8e+129], t$95$1, If[LessEqual[b, -5e+88], t$95$2, If[LessEqual[b, -3.45e+72], t$95$1, If[LessEqual[b, -132000000.0], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6400.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.9e+57], t$95$1, If[LessEqual[b, 1.35e+95], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+138], N[(z * N[(b * N[(N[(x * N[(y / b), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.19999999999999952e167 or -3.80000000000000005e129 < b < -4.99999999999999997e88 or 1.05000000000000003e138 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -9.19999999999999952e167 < b < -3.80000000000000005e129 or -4.99999999999999997e88 < b < -3.45000000000000017e72 or -6400 < b < 3.89999999999999968e57

   1. Initial program 78.2%

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

   3. Taylor expanded in b around 0 80.4%

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

   if -3.45000000000000017e72 < b < -1.32e8

   1. Initial program 79.8%

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

   3. Taylor expanded in c around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if -1.32e8 < b < -6400

   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. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

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

      1. distribute-lft-out-- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 3.89999999999999968e57 < b < 1.35e95

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.8%

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

   4. Taylor expanded in x around inf 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

      4. associate-/l* 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in y around 0 60.6%

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

   9. Simplified 59.7%

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

   10. Taylor expanded in i around inf 89.5%

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

       1. sub-neg 89.5%

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

       2. neg-mul-1 89.5%

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

       3. mul-1-neg 89.5%

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

       4. remove-double-neg 89.5%

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

       5. +-commutative 89.5%

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

       6. unsub-neg 89.5%

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

       7. *-commutative 89.5%

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

   12. Simplified 89.5%

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

   if 1.35e95 < b < 1.05000000000000003e138

   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. Add Preprocessing

   3. Taylor expanded in z around inf 86.4%

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

      1. *-commutative 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in b around inf 86.4%

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

      1. associate-/l* 86.4%

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

   8. Simplified 86.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+167}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{+129}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{+72}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -132000000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -6400:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+57}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+95}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(b \cdot \left(x \cdot \frac{y}{b} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -3.1e+232)
     t_2
     (if (<= b -2.2e+132)
       t_1
       (if (<= b -1.3e-52)
         t_2
         (if (<= b 2.4e-160)
           (* x (- (* y z) (* t a)))
           (if (<= b 5.5e+56)
             (* t (- (* c j) (* x a)))
             (if (<= b 4.4e+96)
               t_1
               (if (<= b 1.5e+132) (* c (- (* t j) (* z b))) 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.1e+232) {
		tmp = t_2;
	} else if (b <= -2.2e+132) {
		tmp = t_1;
	} else if (b <= -1.3e-52) {
		tmp = t_2;
	} else if (b <= 2.4e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 5.5e+56) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.4e+96) {
		tmp = t_1;
	} else if (b <= 1.5e+132) {
		tmp = c * ((t * j) - (z * b));
	} 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 = b * ((a * i) - (z * c))
    if (b <= (-3.1d+232)) then
        tmp = t_2
    else if (b <= (-2.2d+132)) then
        tmp = t_1
    else if (b <= (-1.3d-52)) then
        tmp = t_2
    else if (b <= 2.4d-160) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 5.5d+56) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 4.4d+96) then
        tmp = t_1
    else if (b <= 1.5d+132) then
        tmp = c * ((t * j) - (z * b))
    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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.1e+232) {
		tmp = t_2;
	} else if (b <= -2.2e+132) {
		tmp = t_1;
	} else if (b <= -1.3e-52) {
		tmp = t_2;
	} else if (b <= 2.4e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 5.5e+56) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.4e+96) {
		tmp = t_1;
	} else if (b <= 1.5e+132) {
		tmp = c * ((t * j) - (z * b));
	} 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 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.1e+232:
		tmp = t_2
	elif b <= -2.2e+132:
		tmp = t_1
	elif b <= -1.3e-52:
		tmp = t_2
	elif b <= 2.4e-160:
		tmp = x * ((y * z) - (t * a))
	elif b <= 5.5e+56:
		tmp = t * ((c * j) - (x * a))
	elif b <= 4.4e+96:
		tmp = t_1
	elif b <= 1.5e+132:
		tmp = c * ((t * j) - (z * b))
	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(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.1e+232)
		tmp = t_2;
	elseif (b <= -2.2e+132)
		tmp = t_1;
	elseif (b <= -1.3e-52)
		tmp = t_2;
	elseif (b <= 2.4e-160)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 5.5e+56)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 4.4e+96)
		tmp = t_1;
	elseif (b <= 1.5e+132)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.1e+232)
		tmp = t_2;
	elseif (b <= -2.2e+132)
		tmp = t_1;
	elseif (b <= -1.3e-52)
		tmp = t_2;
	elseif (b <= 2.4e-160)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 5.5e+56)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 4.4e+96)
		tmp = t_1;
	elseif (b <= 1.5e+132)
		tmp = c * ((t * j) - (z * b));
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+232], t$95$2, If[LessEqual[b, -2.2e+132], t$95$1, If[LessEqual[b, -1.3e-52], t$95$2, If[LessEqual[b, 2.4e-160], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+56], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e+96], t$95$1, If[LessEqual[b, 1.5e+132], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.09999999999999983e232 or -2.19999999999999989e132 < b < -1.2999999999999999e-52 or 1.4999999999999999e132 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -3.09999999999999983e232 < b < -2.19999999999999989e132 or 5.5000000000000002e56 < b < 4.3999999999999998e96

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 70.8%

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

   4. Taylor expanded in x around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. associate-/l* 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around 0 59.4%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in i around inf 73.7%

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

       1. sub-neg 73.7%

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

       2. neg-mul-1 73.7%

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

       3. mul-1-neg 73.7%

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

       4. remove-double-neg 73.7%

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

       5. +-commutative 73.7%

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

       6. unsub-neg 73.7%

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

       7. *-commutative 73.7%

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

   12. Simplified 73.7%

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

   if -1.2999999999999999e-52 < b < 2.39999999999999991e-160

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 76.0%

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

   4. Taylor expanded in x around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. +-commutative 57.9%

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

      4. sub-neg 57.9%

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

   6. Simplified 57.9%

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

   if 2.39999999999999991e-160 < b < 5.5000000000000002e56

   1. Initial program 86.0%

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

   3. Taylor expanded in t around inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. *-commutative 60.5%

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

      5. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   if 4.3999999999999998e96 < b < 1.4999999999999999e132

   1. Initial program 70.0%

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

   3. Taylor expanded in c around inf 80.4%

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

      1. *-commutative 80.4%

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

      2. *-commutative 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.45e+235)
     t_1
     (if (<= b -2.4e+132)
       (* i (- (* a b) (* y j)))
       (if (<= b -1.25e-52)
         t_1
         (if (<= b 3.7e-160)
           (* x (- (* y z) (* t a)))
           (if (<= b 8.5e+31)
             (* t (- (* c j) (* x a)))
             (if (<= b 3.8e+107)
               (* y (- (* x z) (* i j)))
               (if (<= b 3.4e+135) (* c (- (* t j) (* z b))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.45e+235) {
		tmp = t_1;
	} else if (b <= -2.4e+132) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= -1.25e-52) {
		tmp = t_1;
	} else if (b <= 3.7e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 8.5e+31) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 3.8e+107) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 3.4e+135) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.45d+235)) then
        tmp = t_1
    else if (b <= (-2.4d+132)) then
        tmp = i * ((a * b) - (y * j))
    else if (b <= (-1.25d-52)) then
        tmp = t_1
    else if (b <= 3.7d-160) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 8.5d+31) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 3.8d+107) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 3.4d+135) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.45e+235) {
		tmp = t_1;
	} else if (b <= -2.4e+132) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= -1.25e-52) {
		tmp = t_1;
	} else if (b <= 3.7e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 8.5e+31) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 3.8e+107) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 3.4e+135) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.45e+235:
		tmp = t_1
	elif b <= -2.4e+132:
		tmp = i * ((a * b) - (y * j))
	elif b <= -1.25e-52:
		tmp = t_1
	elif b <= 3.7e-160:
		tmp = x * ((y * z) - (t * a))
	elif b <= 8.5e+31:
		tmp = t * ((c * j) - (x * a))
	elif b <= 3.8e+107:
		tmp = y * ((x * z) - (i * j))
	elif b <= 3.4e+135:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.45e+235)
		tmp = t_1;
	elseif (b <= -2.4e+132)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (b <= -1.25e-52)
		tmp = t_1;
	elseif (b <= 3.7e-160)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 8.5e+31)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 3.8e+107)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 3.4e+135)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.45e+235)
		tmp = t_1;
	elseif (b <= -2.4e+132)
		tmp = i * ((a * b) - (y * j));
	elseif (b <= -1.25e-52)
		tmp = t_1;
	elseif (b <= 3.7e-160)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 8.5e+31)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 3.8e+107)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 3.4e+135)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+235], t$95$1, If[LessEqual[b, -2.4e+132], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e-52], t$95$1, If[LessEqual[b, 3.7e-160], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+31], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+107], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+135], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.45000000000000011e235 or -2.4000000000000001e132 < b < -1.25e-52 or 3.4000000000000001e135 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -1.45000000000000011e235 < b < -2.4000000000000001e132

   1. Initial program 72.7%

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

   3. Taylor expanded in y around 0 64.0%

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

   4. Taylor expanded in x around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

      4. associate-/l* 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in y around 0 55.2%

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

   9. Simplified 50.3%

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

   10. Taylor expanded in i around inf 68.6%

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

       1. sub-neg 68.6%

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

       2. neg-mul-1 68.6%

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

       3. mul-1-neg 68.6%

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

       4. remove-double-neg 68.6%

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

       5. +-commutative 68.6%

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

       6. unsub-neg 68.6%

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

       7. *-commutative 68.6%

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

   12. Simplified 68.6%

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

   if -1.25e-52 < b < 3.69999999999999977e-160

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 76.0%

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

   4. Taylor expanded in x around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. +-commutative 57.9%

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

      4. sub-neg 57.9%

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

   6. Simplified 57.9%

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

   if 3.69999999999999977e-160 < b < 8.49999999999999947e31

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. unsub-neg 63.6%

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

      4. *-commutative 63.6%

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

      5. *-commutative 63.6%

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

   5. Simplified 63.6%

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

   if 8.49999999999999947e31 < b < 3.7999999999999998e107

   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. Add Preprocessing

   3. Taylor expanded in y around 0 74.0%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

   6. Simplified 66.3%

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

   if 3.7999999999999998e107 < b < 3.4000000000000001e135

   1. Initial program 83.3%

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

   3. Taylor expanded in c around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+235}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-269}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -8.4e+138)
     t_2
     (if (<= z -1.4e-100)
       t_1
       (if (<= z -1.2e-269)
         (* i (- (* a b) (* y j)))
         (if (<= z 5.4e-297)
           t_1
           (if (<= z 3.05e-78)
             (* j (- (* t c) (* y i)))
             (if (<= z 5e-24)
               t_1
               (if (<= z 6.2e+108) (* 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 = t * ((c * j) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -8.4e+138) {
		tmp = t_2;
	} else if (z <= -1.4e-100) {
		tmp = t_1;
	} else if (z <= -1.2e-269) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 5.4e-297) {
		tmp = t_1;
	} else if (z <= 3.05e-78) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 5e-24) {
		tmp = t_1;
	} else if (z <= 6.2e+108) {
		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 = t * ((c * j) - (x * a))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-8.4d+138)) then
        tmp = t_2
    else if (z <= (-1.4d-100)) then
        tmp = t_1
    else if (z <= (-1.2d-269)) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 5.4d-297) then
        tmp = t_1
    else if (z <= 3.05d-78) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 5d-24) then
        tmp = t_1
    else if (z <= 6.2d+108) 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 = t * ((c * j) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -8.4e+138) {
		tmp = t_2;
	} else if (z <= -1.4e-100) {
		tmp = t_1;
	} else if (z <= -1.2e-269) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 5.4e-297) {
		tmp = t_1;
	} else if (z <= 3.05e-78) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 5e-24) {
		tmp = t_1;
	} else if (z <= 6.2e+108) {
		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 = t * ((c * j) - (x * a))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -8.4e+138:
		tmp = t_2
	elif z <= -1.4e-100:
		tmp = t_1
	elif z <= -1.2e-269:
		tmp = i * ((a * b) - (y * j))
	elif z <= 5.4e-297:
		tmp = t_1
	elif z <= 3.05e-78:
		tmp = j * ((t * c) - (y * i))
	elif z <= 5e-24:
		tmp = t_1
	elif z <= 6.2e+108:
		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(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -8.4e+138)
		tmp = t_2;
	elseif (z <= -1.4e-100)
		tmp = t_1;
	elseif (z <= -1.2e-269)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 5.4e-297)
		tmp = t_1;
	elseif (z <= 3.05e-78)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 5e-24)
		tmp = t_1;
	elseif (z <= 6.2e+108)
		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 = t * ((c * j) - (x * a));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -8.4e+138)
		tmp = t_2;
	elseif (z <= -1.4e-100)
		tmp = t_1;
	elseif (z <= -1.2e-269)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 5.4e-297)
		tmp = t_1;
	elseif (z <= 3.05e-78)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 5e-24)
		tmp = t_1;
	elseif (z <= 6.2e+108)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.4e+138], t$95$2, If[LessEqual[z, -1.4e-100], t$95$1, If[LessEqual[z, -1.2e-269], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-297], t$95$1, If[LessEqual[z, 3.05e-78], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-24], t$95$1, If[LessEqual[z, 6.2e+108], 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 z < -8.40000000000000028e138 or 6.2000000000000003e108 < z

   1. Initial program 54.2%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -8.40000000000000028e138 < z < -1.39999999999999998e-100 or -1.20000000000000005e-269 < z < 5.4000000000000002e-297 or 3.05000000000000003e-78 < z < 4.9999999999999998e-24

   1. Initial program 77.6%

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

   3. Taylor expanded in t around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

      4. *-commutative 62.3%

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

      5. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -1.39999999999999998e-100 < z < -1.20000000000000005e-269

   1. Initial program 81.4%

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

   3. Taylor expanded in y around 0 85.5%

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

   4. Taylor expanded in x around inf 81.5%

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

      1. +-commutative 81.5%

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

      2. mul-1-neg 81.5%

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

      3. unsub-neg 81.5%

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

      4. associate-/l* 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in y around 0 79.5%

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

   9. Simplified 75.1%

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

   10. Taylor expanded in i around inf 64.1%

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

       1. sub-neg 64.1%

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

       2. neg-mul-1 64.1%

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

       3. mul-1-neg 64.1%

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

       4. remove-double-neg 64.1%

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

       5. +-commutative 64.1%

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

       6. unsub-neg 64.1%

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

       7. *-commutative 64.1%

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

   12. Simplified 64.1%

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

   if 5.4000000000000002e-297 < z < 3.05000000000000003e-78

   1. Initial program 88.4%

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

   3. Taylor expanded in j around inf 62.8%

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

   if 4.9999999999999998e-24 < z < 6.2000000000000003e108

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-269}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t\_2 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -5.1 \cdot 10^{+15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+205}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (- (* c j) (* x a))) (* z (- (* x y) (* b c)))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (+ t_2 (* x (- (* y z) (* t a))))))
   (if (<= j -5.1e+15)
     t_3
     (if (<= j 2.4e-216)
       t_1
       (if (<= j 5.8e-93)
         (* b (- (* a i) (* z c)))
         (if (<= j 4.5e+19) t_1 (if (<= j 2.5e+205) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 + (x * ((y * z) - (t * a)));
	double tmp;
	if (j <= -5.1e+15) {
		tmp = t_3;
	} else if (j <= 2.4e-216) {
		tmp = t_1;
	} else if (j <= 5.8e-93) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 4.5e+19) {
		tmp = t_1;
	} else if (j <= 2.5e+205) {
		tmp = t_3;
	} 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 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
    t_2 = j * ((t * c) - (y * i))
    t_3 = t_2 + (x * ((y * z) - (t * a)))
    if (j <= (-5.1d+15)) then
        tmp = t_3
    else if (j <= 2.4d-216) then
        tmp = t_1
    else if (j <= 5.8d-93) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 4.5d+19) then
        tmp = t_1
    else if (j <= 2.5d+205) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 + (x * ((y * z) - (t * a)));
	double tmp;
	if (j <= -5.1e+15) {
		tmp = t_3;
	} else if (j <= 2.4e-216) {
		tmp = t_1;
	} else if (j <= 5.8e-93) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 4.5e+19) {
		tmp = t_1;
	} else if (j <= 2.5e+205) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
	t_2 = j * ((t * c) - (y * i))
	t_3 = t_2 + (x * ((y * z) - (t * a)))
	tmp = 0
	if j <= -5.1e+15:
		tmp = t_3
	elif j <= 2.4e-216:
		tmp = t_1
	elif j <= 5.8e-93:
		tmp = b * ((a * i) - (z * c))
	elif j <= 4.5e+19:
		tmp = t_1
	elif j <= 2.5e+205:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(t_2 + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (j <= -5.1e+15)
		tmp = t_3;
	elseif (j <= 2.4e-216)
		tmp = t_1;
	elseif (j <= 5.8e-93)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 4.5e+19)
		tmp = t_1;
	elseif (j <= 2.5e+205)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	t_2 = j * ((t * c) - (y * i));
	t_3 = t_2 + (x * ((y * z) - (t * a)));
	tmp = 0.0;
	if (j <= -5.1e+15)
		tmp = t_3;
	elseif (j <= 2.4e-216)
		tmp = t_1;
	elseif (j <= 5.8e-93)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 4.5e+19)
		tmp = t_1;
	elseif (j <= 2.5e+205)
		tmp = t_3;
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.1e+15], t$95$3, If[LessEqual[j, 2.4e-216], t$95$1, If[LessEqual[j, 5.8e-93], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e+19], t$95$1, If[LessEqual[j, 2.5e+205], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.1e15 or 4.5e19 < j < 2.5000000000000001e205

   1. Initial program 78.5%

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

   3. Taylor expanded in b around 0 77.1%

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

   if -5.1e15 < j < 2.40000000000000004e-216 or 5.7999999999999997e-93 < j < 4.5e19

   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. Add Preprocessing

   3. Taylor expanded in y around 0 82.7%

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

   4. Taylor expanded in x around inf 79.7%

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

      1. +-commutative 79.7%

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

      2. mul-1-neg 79.7%

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

      3. unsub-neg 79.7%

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

      4. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in i around 0 65.6%

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

      1. sub-neg 65.6%

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

      2. associate-+r+ 65.6%

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

      3. associate-+l+ 65.6%

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

      4. +-commutative 65.6%

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

      5. mul-1-neg 65.6%

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

      6. associate-*r* 65.3%

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

      7. *-commutative 65.3%

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

      8. associate-*r* 67.4%

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

      9. distribute-lft-neg-in 67.4%

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

      10. mul-1-neg 67.4%

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

      11. distribute-rgt-in 67.4%

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

      12. mul-1-neg 67.4%

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

      13. unsub-neg 67.4%

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

      14. *-commutative 67.4%

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

      15. *-commutative 67.4%

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

   9. Simplified 78.3%

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

   if 2.40000000000000004e-216 < j < 5.7999999999999997e-93

   1. Initial program 63.8%

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

   3. Taylor expanded in b around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if 2.5000000000000001e205 < j

   1. Initial program 68.0%

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

   3. Taylor expanded in j around inf 70.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.1 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+205}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right) + t\_1\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(b \cdot \left(x \cdot \frac{y}{b} - c\right)\right)\\ \mathbf{elif}\;z \leq -3700000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-111}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* t c) (* y i))) t_1))
        (t_3 (+ (* b (- (* a i) (* z c))) t_1)))
   (if (<= z -1.32e+138)
     (* z (* b (- (* x (/ y b)) c)))
     (if (<= z -3700000.0)
       t_2
       (if (<= z -6.6e-111)
         t_3
         (if (<= z 1.25e-20)
           t_2
           (if (<= z 4.9e+153) t_3 (* z (- (* x y) (* b 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 t_2 = (j * ((t * c) - (y * i))) + t_1;
	double t_3 = (b * ((a * i) - (z * c))) + t_1;
	double tmp;
	if (z <= -1.32e+138) {
		tmp = z * (b * ((x * (y / b)) - c));
	} else if (z <= -3700000.0) {
		tmp = t_2;
	} else if (z <= -6.6e-111) {
		tmp = t_3;
	} else if (z <= 1.25e-20) {
		tmp = t_2;
	} else if (z <= 4.9e+153) {
		tmp = t_3;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (j * ((t * c) - (y * i))) + t_1
    t_3 = (b * ((a * i) - (z * c))) + t_1
    if (z <= (-1.32d+138)) then
        tmp = z * (b * ((x * (y / b)) - c))
    else if (z <= (-3700000.0d0)) then
        tmp = t_2
    else if (z <= (-6.6d-111)) then
        tmp = t_3
    else if (z <= 1.25d-20) then
        tmp = t_2
    else if (z <= 4.9d+153) then
        tmp = t_3
    else
        tmp = z * ((x * y) - (b * 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 t_2 = (j * ((t * c) - (y * i))) + t_1;
	double t_3 = (b * ((a * i) - (z * c))) + t_1;
	double tmp;
	if (z <= -1.32e+138) {
		tmp = z * (b * ((x * (y / b)) - c));
	} else if (z <= -3700000.0) {
		tmp = t_2;
	} else if (z <= -6.6e-111) {
		tmp = t_3;
	} else if (z <= 1.25e-20) {
		tmp = t_2;
	} else if (z <= 4.9e+153) {
		tmp = t_3;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	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))) + t_1
	t_3 = (b * ((a * i) - (z * c))) + t_1
	tmp = 0
	if z <= -1.32e+138:
		tmp = z * (b * ((x * (y / b)) - c))
	elif z <= -3700000.0:
		tmp = t_2
	elif z <= -6.6e-111:
		tmp = t_3
	elif z <= 1.25e-20:
		tmp = t_2
	elif z <= 4.9e+153:
		tmp = t_3
	else:
		tmp = z * ((x * y) - (b * 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)))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1)
	t_3 = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + t_1)
	tmp = 0.0
	if (z <= -1.32e+138)
		tmp = Float64(z * Float64(b * Float64(Float64(x * Float64(y / b)) - c)));
	elseif (z <= -3700000.0)
		tmp = t_2;
	elseif (z <= -6.6e-111)
		tmp = t_3;
	elseif (z <= 1.25e-20)
		tmp = t_2;
	elseif (z <= 4.9e+153)
		tmp = t_3;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * 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));
	t_2 = (j * ((t * c) - (y * i))) + t_1;
	t_3 = (b * ((a * i) - (z * c))) + t_1;
	tmp = 0.0;
	if (z <= -1.32e+138)
		tmp = z * (b * ((x * (y / b)) - c));
	elseif (z <= -3700000.0)
		tmp = t_2;
	elseif (z <= -6.6e-111)
		tmp = t_3;
	elseif (z <= 1.25e-20)
		tmp = t_2;
	elseif (z <= 4.9e+153)
		tmp = t_3;
	else
		tmp = z * ((x * y) - (b * 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]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[z, -1.32e+138], N[(z * N[(b * N[(N[(x * N[(y / b), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3700000.0], t$95$2, If[LessEqual[z, -6.6e-111], t$95$3, If[LessEqual[z, 1.25e-20], t$95$2, If[LessEqual[z, 4.9e+153], t$95$3, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.32000000000000001e138

   1. Initial program 57.8%

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

   3. Taylor expanded in z around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in b around inf 87.4%

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

      1. associate-/l* 85.4%

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

   8. Simplified 85.4%

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

   if -1.32000000000000001e138 < z < -3.7e6 or -6.6e-111 < z < 1.25e-20

   1. Initial program 78.3%

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

   3. Taylor expanded in b around 0 72.4%

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

   if -3.7e6 < z < -6.6e-111 or 1.25e-20 < z < 4.90000000000000002e153

   1. Initial program 90.6%

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

   3. Taylor expanded in j around 0 79.7%

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

      1. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   if 4.90000000000000002e153 < z

   1. Initial program 46.3%

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

   3. Taylor expanded in z around inf 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(b \cdot \left(x \cdot \frac{y}{b} - c\right)\right)\\ \mathbf{elif}\;z \leq -3700000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-111}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* a i) (* z c))) (- (* i (* y j)) (* c (* t j)))))
        (t_2 (+ (* t (- (* c j) (* x a))) (* z (- (* x y) (* b c))))))
   (if (<= x -1.6e-45)
     t_2
     (if (<= x 1.4e-61)
       t_1
       (if (<= x 5.6e+101)
         (+ (- (* y (- (* x z) (* i j))) (* a (* x t))) (* a (* b i)))
         (if (<= x 1.15e+145)
           t_1
           (if (<= x 1.08e+182)
             t_2
             (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	double t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (x <= -1.6e-45) {
		tmp = t_2;
	} else if (x <= 1.4e-61) {
		tmp = t_1;
	} else if (x <= 5.6e+101) {
		tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i));
	} else if (x <= 1.15e+145) {
		tmp = t_1;
	} else if (x <= 1.08e+182) {
		tmp = t_2;
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)))
    t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
    if (x <= (-1.6d-45)) then
        tmp = t_2
    else if (x <= 1.4d-61) then
        tmp = t_1
    else if (x <= 5.6d+101) then
        tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i))
    else if (x <= 1.15d+145) then
        tmp = t_1
    else if (x <= 1.08d+182) then
        tmp = t_2
    else
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	double t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (x <= -1.6e-45) {
		tmp = t_2;
	} else if (x <= 1.4e-61) {
		tmp = t_1;
	} else if (x <= 5.6e+101) {
		tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i));
	} else if (x <= 1.15e+145) {
		tmp = t_1;
	} else if (x <= 1.08e+182) {
		tmp = t_2;
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)))
	t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
	tmp = 0
	if x <= -1.6e-45:
		tmp = t_2
	elif x <= 1.4e-61:
		tmp = t_1
	elif x <= 5.6e+101:
		tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i))
	elif x <= 1.15e+145:
		tmp = t_1
	elif x <= 1.08e+182:
		tmp = t_2
	else:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	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(Float64(i * Float64(y * j)) - Float64(c * Float64(t * j))))
	t_2 = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (x <= -1.6e-45)
		tmp = t_2;
	elseif (x <= 1.4e-61)
		tmp = t_1;
	elseif (x <= 5.6e+101)
		tmp = Float64(Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(a * Float64(x * t))) + Float64(a * Float64(b * i)));
	elseif (x <= 1.15e+145)
		tmp = t_1;
	elseif (x <= 1.08e+182)
		tmp = t_2;
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	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))) - ((i * (y * j)) - (c * (t * j)));
	t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (x <= -1.6e-45)
		tmp = t_2;
	elseif (x <= 1.4e-61)
		tmp = t_1;
	elseif (x <= 5.6e+101)
		tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i));
	elseif (x <= 1.15e+145)
		tmp = t_1;
	elseif (x <= 1.08e+182)
		tmp = t_2;
	else
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	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[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e-45], t$95$2, If[LessEqual[x, 1.4e-61], t$95$1, If[LessEqual[x, 5.6e+101], N[(N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+145], t$95$1, If[LessEqual[x, 1.08e+182], t$95$2, N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.60000000000000004e-45 or 1.15e145 < x < 1.08000000000000003e182

   1. Initial program 67.9%

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

   3. Taylor expanded in y around 0 66.4%

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

   4. Taylor expanded in x around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. associate-/l* 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in i around 0 63.5%

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

      1. sub-neg 63.5%

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

      2. associate-+r+ 63.5%

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

      3. associate-+l+ 63.5%

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

      4. +-commutative 63.5%

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

      5. mul-1-neg 63.5%

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

      6. associate-*r* 65.1%

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

      7. *-commutative 65.1%

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

      8. associate-*r* 68.1%

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

      9. distribute-lft-neg-in 68.1%

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

      10. mul-1-neg 68.1%

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

      11. distribute-rgt-in 69.6%

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

      12. mul-1-neg 69.6%

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

      13. unsub-neg 69.6%

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

      14. *-commutative 69.6%

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

      15. *-commutative 69.6%

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

   9. Simplified 74.2%

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

   if -1.60000000000000004e-45 < x < 1.4000000000000001e-61 or 5.59999999999999962e101 < x < 1.15e145

   1. Initial program 72.0%

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

   3. Taylor expanded in y around 0 83.8%

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

   4. Taylor expanded in x around 0 77.6%

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

   if 1.4000000000000001e-61 < x < 5.59999999999999962e101

   1. Initial program 78.1%

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

   3. Taylor expanded in y around 0 77.6%

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

   4. Taylor expanded in c around 0 82.3%

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

   if 1.08000000000000003e182 < x

   1. Initial program 96.3%

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

   3. Taylor expanded in b around 0 92.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-64} \lor \neg \left(x \leq 1.6 \cdot 10^{+32}\right) \land x \leq 4.6 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -7.5e-51)
   (+ (* t (- (* c j) (* x a))) (* z (- (* x y) (* b c))))
   (if (or (<= x 2.55e-64) (and (not (<= x 1.6e+32)) (<= x 4.6e+143)))
     (- (* b (- (* a i) (* z c))) (- (* i (* y j)) (* c (* t j))))
     (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))))

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 <= -7.5e-51) {
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	} else if ((x <= 2.55e-64) || (!(x <= 1.6e+32) && (x <= 4.6e+143))) {
		tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-7.5d-51)) then
        tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
    else if ((x <= 2.55d-64) .or. (.not. (x <= 1.6d+32)) .and. (x <= 4.6d+143)) then
        tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)))
    else
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -7.5e-51) {
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	} else if ((x <= 2.55e-64) || (!(x <= 1.6e+32) && (x <= 4.6e+143))) {
		tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -7.5e-51:
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
	elif (x <= 2.55e-64) or (not (x <= 1.6e+32) and (x <= 4.6e+143)):
		tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)))
	else:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -7.5e-51)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif ((x <= 2.55e-64) || (!(x <= 1.6e+32) && (x <= 4.6e+143)))
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(Float64(i * Float64(y * j)) - Float64(c * Float64(t * j))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -7.5e-51)
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	elseif ((x <= 2.55e-64) || (~((x <= 1.6e+32)) && (x <= 4.6e+143)))
		tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	else
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -7.5e-51], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.55e-64], And[N[Not[LessEqual[x, 1.6e+32]], $MachinePrecision], LessEqual[x, 4.6e+143]]], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999976e-51

   1. Initial program 66.9%

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

   3. Taylor expanded in y around 0 65.2%

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

   4. Taylor expanded in x around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in i around 0 62.1%

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

      1. sub-neg 62.1%

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

      2. associate-+r+ 62.1%

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

      3. associate-+l+ 62.1%

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

      4. +-commutative 62.1%

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

      5. mul-1-neg 62.1%

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

      6. associate-*r* 63.8%

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

      7. *-commutative 63.8%

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

      8. associate-*r* 65.5%

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

      9. distribute-lft-neg-in 65.5%

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

      10. mul-1-neg 65.5%

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

      11. distribute-rgt-in 67.1%

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

      12. mul-1-neg 67.1%

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

      13. unsub-neg 67.1%

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

      14. *-commutative 67.1%

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

      15. *-commutative 67.1%

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

   9. Simplified 72.1%

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

   if -7.49999999999999976e-51 < x < 2.54999999999999992e-64 or 1.5999999999999999e32 < x < 4.5999999999999999e143

   1. Initial program 71.8%

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

   3. Taylor expanded in y around 0 82.5%

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

   4. Taylor expanded in x around 0 76.7%

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

   if 2.54999999999999992e-64 < x < 1.5999999999999999e32 or 4.5999999999999999e143 < x

   1. Initial program 90.8%

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

   3. Taylor expanded in b around 0 86.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-64} \lor \neg \left(x \leq 1.6 \cdot 10^{+32}\right) \land x \leq 4.6 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := \left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-236}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 4.45 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* z (* x y)))
        (t_3 (* (* y j) (- i))))
   (if (<= x -2.9e-25)
     t_2
     (if (<= x 2.2e-300)
       t_1
       (if (<= x 1.6e-236)
         t_3
         (if (<= x 4.45e-7)
           t_1
           (if (<= x 7.1e+78) t_3 (if (<= x 5.8e+143) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = z * (x * y);
	double t_3 = (y * j) * -i;
	double tmp;
	if (x <= -2.9e-25) {
		tmp = t_2;
	} else if (x <= 2.2e-300) {
		tmp = t_1;
	} else if (x <= 1.6e-236) {
		tmp = t_3;
	} else if (x <= 4.45e-7) {
		tmp = t_1;
	} else if (x <= 7.1e+78) {
		tmp = t_3;
	} else if (x <= 5.8e+143) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = z * (x * y)
    t_3 = (y * j) * -i
    if (x <= (-2.9d-25)) then
        tmp = t_2
    else if (x <= 2.2d-300) then
        tmp = t_1
    else if (x <= 1.6d-236) then
        tmp = t_3
    else if (x <= 4.45d-7) then
        tmp = t_1
    else if (x <= 7.1d+78) then
        tmp = t_3
    else if (x <= 5.8d+143) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = z * (x * y);
	double t_3 = (y * j) * -i;
	double tmp;
	if (x <= -2.9e-25) {
		tmp = t_2;
	} else if (x <= 2.2e-300) {
		tmp = t_1;
	} else if (x <= 1.6e-236) {
		tmp = t_3;
	} else if (x <= 4.45e-7) {
		tmp = t_1;
	} else if (x <= 7.1e+78) {
		tmp = t_3;
	} else if (x <= 5.8e+143) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = z * (x * y)
	t_3 = (y * j) * -i
	tmp = 0
	if x <= -2.9e-25:
		tmp = t_2
	elif x <= 2.2e-300:
		tmp = t_1
	elif x <= 1.6e-236:
		tmp = t_3
	elif x <= 4.45e-7:
		tmp = t_1
	elif x <= 7.1e+78:
		tmp = t_3
	elif x <= 5.8e+143:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(z * Float64(x * y))
	t_3 = Float64(Float64(y * j) * Float64(-i))
	tmp = 0.0
	if (x <= -2.9e-25)
		tmp = t_2;
	elseif (x <= 2.2e-300)
		tmp = t_1;
	elseif (x <= 1.6e-236)
		tmp = t_3;
	elseif (x <= 4.45e-7)
		tmp = t_1;
	elseif (x <= 7.1e+78)
		tmp = t_3;
	elseif (x <= 5.8e+143)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = z * (x * y);
	t_3 = (y * j) * -i;
	tmp = 0.0;
	if (x <= -2.9e-25)
		tmp = t_2;
	elseif (x <= 2.2e-300)
		tmp = t_1;
	elseif (x <= 1.6e-236)
		tmp = t_3;
	elseif (x <= 4.45e-7)
		tmp = t_1;
	elseif (x <= 7.1e+78)
		tmp = t_3;
	elseif (x <= 5.8e+143)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]}, If[LessEqual[x, -2.9e-25], t$95$2, If[LessEqual[x, 2.2e-300], t$95$1, If[LessEqual[x, 1.6e-236], t$95$3, If[LessEqual[x, 4.45e-7], t$95$1, If[LessEqual[x, 7.1e+78], t$95$3, If[LessEqual[x, 5.8e+143], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9000000000000001e-25 or 5.7999999999999996e143 < x

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 54.5%

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

      1. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if -2.9000000000000001e-25 < x < 2.20000000000000002e-300 or 1.6e-236 < x < 4.45e-7 or 7.09999999999999992e78 < x < 5.7999999999999996e143

   1. Initial program 71.9%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   if 2.20000000000000002e-300 < x < 1.6e-236 or 4.45e-7 < x < 7.09999999999999992e78

   1. Initial program 76.8%

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

   3. Taylor expanded in y around 0 81.6%

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

   4. Taylor expanded in x around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. associate-/l* 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in i around inf 68.0%

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

      1. sub-neg 68.0%

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

      2. associate-*r* 68.0%

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

      3. mul-1-neg 68.0%

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

      4. neg-mul-1 68.0%

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

      5. remove-double-neg 68.0%

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

      6. *-commutative 68.0%

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

   9. Simplified 68.0%

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

   10. Taylor expanded in j around inf 56.9%

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

       1. neg-mul-1 56.9%

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

       2. *-commutative 56.9%

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

   12. Simplified 56.9%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-236}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;x \leq 4.45 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+78}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -3.1e+232)
     t_2
     (if (<= b -1.5e+131)
       t_1
       (if (<= b -3.3e-80)
         t_2
         (if (<= b 5.8e+51)
           (* t (- (* c j) (* x a)))
           (if (<= b 4e+96)
             t_1
             (if (<= b 5.4e+132) (* c (- (* t j) (* z b))) 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.1e+232) {
		tmp = t_2;
	} else if (b <= -1.5e+131) {
		tmp = t_1;
	} else if (b <= -3.3e-80) {
		tmp = t_2;
	} else if (b <= 5.8e+51) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4e+96) {
		tmp = t_1;
	} else if (b <= 5.4e+132) {
		tmp = c * ((t * j) - (z * b));
	} 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 = b * ((a * i) - (z * c))
    if (b <= (-3.1d+232)) then
        tmp = t_2
    else if (b <= (-1.5d+131)) then
        tmp = t_1
    else if (b <= (-3.3d-80)) then
        tmp = t_2
    else if (b <= 5.8d+51) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 4d+96) then
        tmp = t_1
    else if (b <= 5.4d+132) then
        tmp = c * ((t * j) - (z * b))
    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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.1e+232) {
		tmp = t_2;
	} else if (b <= -1.5e+131) {
		tmp = t_1;
	} else if (b <= -3.3e-80) {
		tmp = t_2;
	} else if (b <= 5.8e+51) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4e+96) {
		tmp = t_1;
	} else if (b <= 5.4e+132) {
		tmp = c * ((t * j) - (z * b));
	} 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 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.1e+232:
		tmp = t_2
	elif b <= -1.5e+131:
		tmp = t_1
	elif b <= -3.3e-80:
		tmp = t_2
	elif b <= 5.8e+51:
		tmp = t * ((c * j) - (x * a))
	elif b <= 4e+96:
		tmp = t_1
	elif b <= 5.4e+132:
		tmp = c * ((t * j) - (z * b))
	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(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.1e+232)
		tmp = t_2;
	elseif (b <= -1.5e+131)
		tmp = t_1;
	elseif (b <= -3.3e-80)
		tmp = t_2;
	elseif (b <= 5.8e+51)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 4e+96)
		tmp = t_1;
	elseif (b <= 5.4e+132)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.1e+232)
		tmp = t_2;
	elseif (b <= -1.5e+131)
		tmp = t_1;
	elseif (b <= -3.3e-80)
		tmp = t_2;
	elseif (b <= 5.8e+51)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 4e+96)
		tmp = t_1;
	elseif (b <= 5.4e+132)
		tmp = c * ((t * j) - (z * b));
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+232], t$95$2, If[LessEqual[b, -1.5e+131], t$95$1, If[LessEqual[b, -3.3e-80], t$95$2, If[LessEqual[b, 5.8e+51], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+96], t$95$1, If[LessEqual[b, 5.4e+132], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.09999999999999983e232 or -1.5000000000000001e131 < b < -3.3e-80 or 5.3999999999999999e132 < b

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -3.09999999999999983e232 < b < -1.5000000000000001e131 or 5.7999999999999997e51 < b < 4.0000000000000002e96

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 70.8%

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

   4. Taylor expanded in x around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. associate-/l* 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around 0 59.4%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in i around inf 73.7%

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

       1. sub-neg 73.7%

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

       2. neg-mul-1 73.7%

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

       3. mul-1-neg 73.7%

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

       4. remove-double-neg 73.7%

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

       5. +-commutative 73.7%

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

       6. unsub-neg 73.7%

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

       7. *-commutative 73.7%

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

   12. Simplified 73.7%

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

   if -3.3e-80 < b < 5.7999999999999997e51

   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. Add Preprocessing

   3. Taylor expanded in t around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

      5. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   if 4.0000000000000002e96 < b < 5.3999999999999999e132

   1. Initial program 70.0%

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

   3. Taylor expanded in c around inf 80.4%

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

      1. *-commutative 80.4%

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

      2. *-commutative 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+131}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -61:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b \cdot \left(j \cdot \frac{t}{b} - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.25e+52)
   (* c (- (* t j) (* z b)))
   (if (<= c -61.0)
     (* t (- (* c j) (* x a)))
     (if (<= c -6.5e-147)
       (* y (- (* x z) (* i j)))
       (if (<= c 8.2e-66)
         (* a (- (* b i) (* x t)))
         (if (<= c 2.2e+31)
           (* i (- (* a b) (* y j)))
           (* c (* b (- (* j (/ t b)) z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.25e+52) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= -61.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -6.5e-147) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 8.2e-66) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.2e+31) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * (b * ((j * (t / b)) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.25d+52)) then
        tmp = c * ((t * j) - (z * b))
    else if (c <= (-61.0d0)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-6.5d-147)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 8.2d-66) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 2.2d+31) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = c * (b * ((j * (t / b)) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.25e+52) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= -61.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -6.5e-147) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 8.2e-66) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.2e+31) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * (b * ((j * (t / b)) - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.25e+52:
		tmp = c * ((t * j) - (z * b))
	elif c <= -61.0:
		tmp = t * ((c * j) - (x * a))
	elif c <= -6.5e-147:
		tmp = y * ((x * z) - (i * j))
	elif c <= 8.2e-66:
		tmp = a * ((b * i) - (x * t))
	elif c <= 2.2e+31:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = c * (b * ((j * (t / b)) - z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.25e+52)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (c <= -61.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -6.5e-147)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 8.2e-66)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 2.2e+31)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(c * Float64(b * Float64(Float64(j * Float64(t / b)) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.25e+52)
		tmp = c * ((t * j) - (z * b));
	elseif (c <= -61.0)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -6.5e-147)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 8.2e-66)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 2.2e+31)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * (b * ((j * (t / b)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.25e+52], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -61.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.5e-147], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.2e-66], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+31], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(b * N[(N[(j * N[(t / b), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.25e52

   1. Initial program 63.0%

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

   3. Taylor expanded in c around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   if -1.25e52 < c < -61

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -61 < c < -6.49999999999999967e-147

   1. Initial program 79.6%

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

   3. Taylor expanded in y around 0 82.8%

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

   4. Taylor expanded in y around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -6.49999999999999967e-147 < c < 8.19999999999999996e-66

   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. Add Preprocessing

   3. Taylor expanded in a around inf 59.8%

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

      1. distribute-lft-out-- 59.8%

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

      2. *-commutative 59.8%

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

      3. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   if 8.19999999999999996e-66 < c < 2.2000000000000001e31

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0 71.6%

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

   4. Taylor expanded in x around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in y around 0 64.0%

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

   9. Simplified 71.4%

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

   10. Taylor expanded in i around inf 70.2%

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

       1. sub-neg 70.2%

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

       2. neg-mul-1 70.2%

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

       3. mul-1-neg 70.2%

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

       4. remove-double-neg 70.2%

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

       5. +-commutative 70.2%

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

       6. unsub-neg 70.2%

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

       7. *-commutative 70.2%

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

   12. Simplified 70.2%

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

   if 2.2000000000000001e31 < c

   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. Add Preprocessing

   3. Taylor expanded in c around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in b around inf 66.8%

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

      1. associate-/l* 68.6%

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

   8. Simplified 68.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -61:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b \cdot \left(j \cdot \frac{t}{b} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -57:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -1.66 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-65}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+32}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -2e+53)
     t_1
     (if (<= c -57.0)
       (* t (- (* c j) (* x a)))
       (if (<= c -1.66e-146)
         (* y (- (* x z) (* i j)))
         (if (<= c 2.9e-65)
           (* a (- (* b i) (* x t)))
           (if (<= c 3.4e+32) (* i (- (* a b) (* y 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2e+53) {
		tmp = t_1;
	} else if (c <= -57.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -1.66e-146) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.9e-65) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.4e+32) {
		tmp = i * ((a * b) - (y * 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 = c * ((t * j) - (z * b))
    if (c <= (-2d+53)) then
        tmp = t_1
    else if (c <= (-57.0d0)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-1.66d-146)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 2.9d-65) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 3.4d+32) then
        tmp = i * ((a * b) - (y * 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2e+53) {
		tmp = t_1;
	} else if (c <= -57.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -1.66e-146) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.9e-65) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.4e+32) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2e+53:
		tmp = t_1
	elif c <= -57.0:
		tmp = t * ((c * j) - (x * a))
	elif c <= -1.66e-146:
		tmp = y * ((x * z) - (i * j))
	elif c <= 2.9e-65:
		tmp = a * ((b * i) - (x * t))
	elif c <= 3.4e+32:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2e+53)
		tmp = t_1;
	elseif (c <= -57.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -1.66e-146)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 2.9e-65)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 3.4e+32)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * 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 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2e+53)
		tmp = t_1;
	elseif (c <= -57.0)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -1.66e-146)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 2.9e-65)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 3.4e+32)
		tmp = i * ((a * b) - (y * 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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2e+53], t$95$1, If[LessEqual[c, -57.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.66e-146], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-65], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+32], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2e53 or 3.39999999999999979e32 < c

   1. Initial program 67.3%

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

   3. Taylor expanded in c around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if -2e53 < c < -57

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -57 < c < -1.66e-146

   1. Initial program 79.6%

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

   3. Taylor expanded in y around 0 82.8%

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

   4. Taylor expanded in y around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -1.66e-146 < c < 2.8999999999999998e-65

   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. Add Preprocessing

   3. Taylor expanded in a around inf 59.8%

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

      1. distribute-lft-out-- 59.8%

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

      2. *-commutative 59.8%

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

      3. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   if 2.8999999999999998e-65 < c < 3.39999999999999979e32

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0 71.6%

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

   4. Taylor expanded in x around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in y around 0 64.0%

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

   9. Simplified 71.4%

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

   10. Taylor expanded in i around inf 70.2%

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

       1. sub-neg 70.2%

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

       2. neg-mul-1 70.2%

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

       3. mul-1-neg 70.2%

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

       4. remove-double-neg 70.2%

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

       5. +-commutative 70.2%

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

       6. unsub-neg 70.2%

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

       7. *-commutative 70.2%

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

   12. Simplified 70.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -57:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -1.66 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-65}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+32}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-155}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+209} \lor \neg \left(c \leq 7.2 \cdot 10^{+267}\right):\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -1.9e+137)
     t_1
     (if (<= c -3.3e-155)
       (* z (* x y))
       (if (<= c 4.8e+69)
         (* b (* a i))
         (if (or (<= c 6.2e+209) (not (<= c 7.2e+267)))
           (* c (* z (- b)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -1.9e+137) {
		tmp = t_1;
	} else if (c <= -3.3e-155) {
		tmp = z * (x * y);
	} else if (c <= 4.8e+69) {
		tmp = b * (a * i);
	} else if ((c <= 6.2e+209) || !(c <= 7.2e+267)) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (c <= (-1.9d+137)) then
        tmp = t_1
    else if (c <= (-3.3d-155)) then
        tmp = z * (x * y)
    else if (c <= 4.8d+69) then
        tmp = b * (a * i)
    else if ((c <= 6.2d+209) .or. (.not. (c <= 7.2d+267))) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -1.9e+137) {
		tmp = t_1;
	} else if (c <= -3.3e-155) {
		tmp = z * (x * y);
	} else if (c <= 4.8e+69) {
		tmp = b * (a * i);
	} else if ((c <= 6.2e+209) || !(c <= 7.2e+267)) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -1.9e+137:
		tmp = t_1
	elif c <= -3.3e-155:
		tmp = z * (x * y)
	elif c <= 4.8e+69:
		tmp = b * (a * i)
	elif (c <= 6.2e+209) or not (c <= 7.2e+267):
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -1.9e+137)
		tmp = t_1;
	elseif (c <= -3.3e-155)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 4.8e+69)
		tmp = Float64(b * Float64(a * i));
	elseif ((c <= 6.2e+209) || !(c <= 7.2e+267))
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (c <= -1.9e+137)
		tmp = t_1;
	elseif (c <= -3.3e-155)
		tmp = z * (x * y);
	elseif (c <= 4.8e+69)
		tmp = b * (a * i);
	elseif ((c <= 6.2e+209) || ~((c <= 7.2e+267)))
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.9e+137], t$95$1, If[LessEqual[c, -3.3e-155], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+69], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 6.2e+209], N[Not[LessEqual[c, 7.2e+267]], $MachinePrecision]], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.89999999999999981e137 or 6.2000000000000002e209 < c < 7.19999999999999999e267

   1. Initial program 61.4%

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

   3. Taylor expanded in c around inf 73.1%

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

      1. *-commutative 73.1%

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

      2. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around inf 53.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 57.9%

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

      2. *-commutative 57.9%

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

   8. Simplified 57.9%

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

   if -1.89999999999999981e137 < c < -3.29999999999999986e-155

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf 46.8%

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

      1. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in x around inf 32.4%

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

      1. *-commutative 32.4%

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

   8. Simplified 32.4%

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

   if -3.29999999999999986e-155 < c < 4.8000000000000003e69

   1. Initial program 79.7%

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

   3. Taylor expanded in b around inf 39.0%

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

      1. *-commutative 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in a around inf 34.9%

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

      1. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   if 4.8000000000000003e69 < c < 6.2000000000000002e209 or 7.19999999999999999e267 < c

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in t around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. *-commutative 55.0%

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

      3. distribute-rgt-neg-in 55.0%

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

   8. Simplified 55.0%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-155}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+209} \lor \neg \left(c \leq 7.2 \cdot 10^{+267}\right):\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot j\right) \cdot \left(-i\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -8.4 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* y j) (- i))) (t_2 (* z (* x y))))
   (if (<= x -8.4e-26)
     t_2
     (if (<= x 3.6e-265)
       (* c (* t j))
       (if (<= x 4.7e-170)
         t_1
         (if (<= x 6.9e-59) (* b (* a i)) (if (<= x 3.9e+88) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * j) * -i;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -8.4e-26) {
		tmp = t_2;
	} else if (x <= 3.6e-265) {
		tmp = c * (t * j);
	} else if (x <= 4.7e-170) {
		tmp = t_1;
	} else if (x <= 6.9e-59) {
		tmp = b * (a * i);
	} else if (x <= 3.9e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * j) * -i
    t_2 = z * (x * y)
    if (x <= (-8.4d-26)) then
        tmp = t_2
    else if (x <= 3.6d-265) then
        tmp = c * (t * j)
    else if (x <= 4.7d-170) then
        tmp = t_1
    else if (x <= 6.9d-59) then
        tmp = b * (a * i)
    else if (x <= 3.9d+88) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * j) * -i;
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -8.4e-26) {
		tmp = t_2;
	} else if (x <= 3.6e-265) {
		tmp = c * (t * j);
	} else if (x <= 4.7e-170) {
		tmp = t_1;
	} else if (x <= 6.9e-59) {
		tmp = b * (a * i);
	} else if (x <= 3.9e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * j) * -i
	t_2 = z * (x * y)
	tmp = 0
	if x <= -8.4e-26:
		tmp = t_2
	elif x <= 3.6e-265:
		tmp = c * (t * j)
	elif x <= 4.7e-170:
		tmp = t_1
	elif x <= 6.9e-59:
		tmp = b * (a * i)
	elif x <= 3.9e+88:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * j) * Float64(-i))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -8.4e-26)
		tmp = t_2;
	elseif (x <= 3.6e-265)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 4.7e-170)
		tmp = t_1;
	elseif (x <= 6.9e-59)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 3.9e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * j) * -i;
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -8.4e-26)
		tmp = t_2;
	elseif (x <= 3.6e-265)
		tmp = c * (t * j);
	elseif (x <= 4.7e-170)
		tmp = t_1;
	elseif (x <= 6.9e-59)
		tmp = b * (a * i);
	elseif (x <= 3.9e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.4e-26], t$95$2, If[LessEqual[x, 3.6e-265], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7e-170], t$95$1, If[LessEqual[x, 6.9e-59], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+88], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.40000000000000032e-26 or 3.9000000000000001e88 < x

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf 54.1%

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

      1. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in x around inf 48.2%

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

      1. *-commutative 48.2%

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

   8. Simplified 48.2%

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

   if -8.40000000000000032e-26 < x < 3.6000000000000002e-265

   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. Add Preprocessing

   3. Taylor expanded in b around 0 48.7%

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

   4. Taylor expanded in c around inf 35.3%

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

   if 3.6000000000000002e-265 < x < 4.7000000000000002e-170 or 6.89999999999999982e-59 < x < 3.9000000000000001e88

   1. Initial program 76.4%

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

   3. Taylor expanded in y around 0 79.0%

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

   4. Taylor expanded in x around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

      4. associate-/l* 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in i around inf 57.5%

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

      1. sub-neg 57.5%

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

      2. associate-*r* 57.5%

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

      3. mul-1-neg 57.5%

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

      4. neg-mul-1 57.5%

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

      5. remove-double-neg 57.5%

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

      6. *-commutative 57.5%

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

   9. Simplified 57.5%

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

   10. Taylor expanded in j around inf 44.4%

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

       1. neg-mul-1 44.4%

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

       2. *-commutative 44.4%

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

   12. Simplified 44.4%

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

   if 4.7000000000000002e-170 < x < 6.89999999999999982e-59

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in a around inf 44.5%

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

      1. *-commutative 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-170}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+88}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* z (* x y))))
   (if (<= x -8.8e-28)
     t_2
     (if (<= x 4.8e-118)
       t_1
       (if (<= x 1.3e+40)
         (* a (* b i))
         (if (<= x 1.55e+72) t_1 (if (<= x 3.1e+140) (* b (* a i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -8.8e-28) {
		tmp = t_2;
	} else if (x <= 4.8e-118) {
		tmp = t_1;
	} else if (x <= 1.3e+40) {
		tmp = a * (b * i);
	} else if (x <= 1.55e+72) {
		tmp = t_1;
	} else if (x <= 3.1e+140) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = z * (x * y)
    if (x <= (-8.8d-28)) then
        tmp = t_2
    else if (x <= 4.8d-118) then
        tmp = t_1
    else if (x <= 1.3d+40) then
        tmp = a * (b * i)
    else if (x <= 1.55d+72) then
        tmp = t_1
    else if (x <= 3.1d+140) then
        tmp = b * (a * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -8.8e-28) {
		tmp = t_2;
	} else if (x <= 4.8e-118) {
		tmp = t_1;
	} else if (x <= 1.3e+40) {
		tmp = a * (b * i);
	} else if (x <= 1.55e+72) {
		tmp = t_1;
	} else if (x <= 3.1e+140) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -8.8e-28:
		tmp = t_2
	elif x <= 4.8e-118:
		tmp = t_1
	elif x <= 1.3e+40:
		tmp = a * (b * i)
	elif x <= 1.55e+72:
		tmp = t_1
	elif x <= 3.1e+140:
		tmp = b * (a * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -8.8e-28)
		tmp = t_2;
	elseif (x <= 4.8e-118)
		tmp = t_1;
	elseif (x <= 1.3e+40)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 1.55e+72)
		tmp = t_1;
	elseif (x <= 3.1e+140)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -8.8e-28)
		tmp = t_2;
	elseif (x <= 4.8e-118)
		tmp = t_1;
	elseif (x <= 1.3e+40)
		tmp = a * (b * i);
	elseif (x <= 1.55e+72)
		tmp = t_1;
	elseif (x <= 3.1e+140)
		tmp = b * (a * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.8e-28], t$95$2, If[LessEqual[x, 4.8e-118], t$95$1, If[LessEqual[x, 1.3e+40], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+72], t$95$1, If[LessEqual[x, 3.1e+140], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.79999999999999984e-28 or 3.1e140 < x

   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. Add Preprocessing

   3. Taylor expanded in z around inf 54.4%

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

      1. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if -8.79999999999999984e-28 < x < 4.8000000000000003e-118 or 1.3e40 < x < 1.54999999999999994e72

   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. Add Preprocessing

   3. Taylor expanded in b around 0 52.9%

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

   4. Taylor expanded in c around inf 35.1%

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

   if 4.8000000000000003e-118 < x < 1.3e40

   1. Initial program 83.2%

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

   3. Taylor expanded in b around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in a around inf 38.9%

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

      1. *-commutative 38.9%

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

   8. Simplified 38.9%

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

   if 1.54999999999999994e72 < x < 3.1e140

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in a around inf 29.3%

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

      1. *-commutative 29.3%

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

   8. Simplified 29.3%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+103} \lor \neg \left(i \leq -2.7 \cdot 10^{+51}\right) \land \left(i \leq -1.9 \cdot 10^{-33} \lor \neg \left(i \leq 3 \cdot 10^{+75}\right)\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -3.3e+103)
         (and (not (<= i -2.7e+51)) (or (<= i -1.9e-33) (not (<= i 3e+75)))))
   (* i (- (* a b) (* y j)))
   (* c (- (* t j) (* z 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 ((i <= -3.3e+103) || (!(i <= -2.7e+51) && ((i <= -1.9e-33) || !(i <= 3e+75)))) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * 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 ((i <= (-3.3d+103)) .or. (.not. (i <= (-2.7d+51))) .and. (i <= (-1.9d-33)) .or. (.not. (i <= 3d+75))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = c * ((t * j) - (z * 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 ((i <= -3.3e+103) || (!(i <= -2.7e+51) && ((i <= -1.9e-33) || !(i <= 3e+75)))) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -3.3e+103) or (not (i <= -2.7e+51) and ((i <= -1.9e-33) or not (i <= 3e+75))):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -3.3e+103) || (!(i <= -2.7e+51) && ((i <= -1.9e-33) || !(i <= 3e+75))))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -3.3e+103) || (~((i <= -2.7e+51)) && ((i <= -1.9e-33) || ~((i <= 3e+75)))))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -3.3e+103], And[N[Not[LessEqual[i, -2.7e+51]], $MachinePrecision], Or[LessEqual[i, -1.9e-33], N[Not[LessEqual[i, 3e+75]], $MachinePrecision]]]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.30000000000000009e103 or -2.69999999999999992e51 < i < -1.89999999999999997e-33 or 3e75 < i

   1. Initial program 69.9%

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

   3. Taylor expanded in y around 0 67.2%

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

   4. Taylor expanded in x around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. associate-/l* 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in y around 0 61.3%

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

   9. Simplified 64.7%

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

   10. Taylor expanded in i around inf 64.7%

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

       1. sub-neg 64.7%

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

       2. neg-mul-1 64.7%

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

       3. mul-1-neg 64.7%

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

       4. remove-double-neg 64.7%

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

       5. +-commutative 64.7%

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

       6. unsub-neg 64.7%

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

       7. *-commutative 64.7%

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

   12. Simplified 64.7%

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

   if -3.30000000000000009e103 < i < -2.69999999999999992e51 or -1.89999999999999997e-33 < i < 3e75

   1. Initial program 78.2%

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

   3. Taylor expanded in c around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. *-commutative 50.9%

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

   5. Simplified 50.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+103} \lor \neg \left(i \leq -2.7 \cdot 10^{+51}\right) \land \left(i \leq -1.9 \cdot 10^{-33} \lor \neg \left(i \leq 3 \cdot 10^{+75}\right)\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 43.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-269}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+186}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.45e-101)
   (* c (- (* t j) (* z b)))
   (if (<= z -8.2e-269)
     (* i (- (* a b) (* y j)))
     (if (<= z 1.05e-21)
       (* j (- (* t c) (* y i)))
       (if (<= z 1.5e+186) (* b (- (* a i) (* z c))) (* z (* x y)))))))

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 <= -2.45e-101) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= -8.2e-269) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.05e-21) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 1.5e+186) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = z * (x * 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) :: tmp
    if (z <= (-2.45d-101)) then
        tmp = c * ((t * j) - (z * b))
    else if (z <= (-8.2d-269)) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 1.05d-21) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 1.5d+186) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = z * (x * 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 tmp;
	if (z <= -2.45e-101) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= -8.2e-269) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.05e-21) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 1.5e+186) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.45e-101:
		tmp = c * ((t * j) - (z * b))
	elif z <= -8.2e-269:
		tmp = i * ((a * b) - (y * j))
	elif z <= 1.05e-21:
		tmp = j * ((t * c) - (y * i))
	elif z <= 1.5e+186:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.45e-101)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (z <= -8.2e-269)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 1.05e-21)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 1.5e+186)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.45e-101)
		tmp = c * ((t * j) - (z * b));
	elseif (z <= -8.2e-269)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 1.05e-21)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 1.5e+186)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.45e-101], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.2e-269], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-21], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+186], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.45e-101

   1. Initial program 70.0%

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

   3. Taylor expanded in c around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   if -2.45e-101 < z < -8.2000000000000006e-269

   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. Add Preprocessing

   3. Taylor expanded in y around 0 87.0%

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

   4. Taylor expanded in x around inf 80.7%

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

      1. +-commutative 80.7%

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

      2. mul-1-neg 80.7%

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

      3. unsub-neg 80.7%

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

      4. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in y around 0 80.7%

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

   9. Simplified 76.1%

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

   10. Taylor expanded in i around inf 65.2%

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

       1. sub-neg 65.2%

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

       2. neg-mul-1 65.2%

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

       3. mul-1-neg 65.2%

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

       4. remove-double-neg 65.2%

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

       5. +-commutative 65.2%

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

       6. unsub-neg 65.2%

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

       7. *-commutative 65.2%

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

   12. Simplified 65.2%

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

   if -8.2000000000000006e-269 < z < 1.05000000000000006e-21

   1. Initial program 85.4%

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

   3. Taylor expanded in j around inf 56.7%

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

   if 1.05000000000000006e-21 < z < 1.49999999999999991e186

   1. Initial program 76.8%

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

   3. Taylor expanded in b around inf 61.5%

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

      1. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   if 1.49999999999999991e186 < z

   1. Initial program 52.6%

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

   3. Taylor expanded in z around inf 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in x around inf 54.9%

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

      1. *-commutative 54.9%

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

   8. Simplified 54.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-269}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+186}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 45.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{-65} \lor \neg \left(c \leq 2.4 \cdot 10^{+38}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.55e-65) (not (<= c 2.4e+38)))
   (* c (- (* t j) (* z b)))
   (* b (- (* a i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.55e-65) || !(c <= 2.4e+38)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-1.55d-65)) .or. (.not. (c <= 2.4d+38))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.55e-65) || !(c <= 2.4e+38)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.55e-65) or not (c <= 2.4e+38):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.55e-65) || !(c <= 2.4e+38))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.55e-65) || ~((c <= 2.4e+38)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.55e-65], N[Not[LessEqual[c, 2.4e+38]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.55000000000000008e-65 or 2.40000000000000017e38 < c

   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. Add Preprocessing

   3. Taylor expanded in c around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   if -1.55000000000000008e-65 < c < 2.40000000000000017e38

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{-65} \lor \neg \left(c \leq 2.4 \cdot 10^{+38}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-64} \lor \neg \left(c \leq 3.2 \cdot 10^{+41}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.5e-64) (not (<= c 3.2e+41))) (* c (* t j)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.5e-64) || !(c <= 3.2e+41)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2.5d-64)) .or. (.not. (c <= 3.2d+41))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.5e-64) || !(c <= 3.2e+41)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.5e-64) or not (c <= 3.2e+41):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.5e-64) || !(c <= 3.2e+41))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.5e-64) || ~((c <= 3.2e+41)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.5e-64], N[Not[LessEqual[c, 3.2e+41]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.50000000000000017e-64 or 3.2000000000000001e41 < c

   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. Add Preprocessing

   3. Taylor expanded in b around 0 64.7%

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

   4. Taylor expanded in c around inf 33.3%

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

   if -2.50000000000000017e-64 < c < 3.2000000000000001e41

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

   6. Taylor expanded in a around inf 32.9%

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

      1. *-commutative 32.9%

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

   8. Simplified 32.9%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-64} \lor \neg \left(c \leq 3.2 \cdot 10^{+41}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.6%

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

3. Taylor expanded in b around inf 39.3%

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

   1. *-commutative 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in a around inf 21.1%

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

   1. *-commutative 21.1%

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

8. Simplified 21.1%

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

9. Final simplification 21.1%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Alternative 23: 23.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.6%

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

3. Taylor expanded in b around inf 39.3%

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

   1. *-commutative 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in a around inf 22.1%

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

   1. *-commutative 22.1%

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

8. Simplified 22.1%

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

9. Final simplification 22.1%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
10. Add Preprocessing

Developer target: 68.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (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)))))