Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.7% → 81.2%

Time: 28.5s

Alternatives: 20

Speedup: 0.5×

• 58.1% 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: 73.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. fma-def 92.8%

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

      3. *-commutative 92.8%

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

      4. *-commutative 92.8%

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

      5. cancel-sign-sub-inv 92.8%

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

      6. cancel-sign-sub 92.8%

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

      7. fma-neg 92.8%

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

      8. distribute-rgt-neg-out 92.8%

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

      9. remove-double-neg 92.8%

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

      10. *-commutative 92.8%

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

      11. *-commutative 92.8%

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

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   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 x around 0 38.1%

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

      1. *-commutative 38.1%

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

   5. Simplified 38.1%

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

   6. Taylor expanded in t around 0 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

   8. Simplified 57.1%

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

4. Final simplification 85.4%

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

Alternative 2: 81.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	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 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1 - (i * (y * j));
	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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.8%

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

   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 x around 0 38.1%

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

      1. *-commutative 38.1%

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

   5. Simplified 38.1%

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

   6. Taylor expanded in t around 0 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

   8. Simplified 57.1%

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

4. Final simplification 85.4%

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

Alternative 3: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c\right) + t_1\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;t_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (+ (* j (* t c)) t_1)))
   (if (<= b -8.5e+61)
     (- t_1 (* i (* y j)))
     (if (<= b -4.8e-18)
       t_2
       (if (<= b -5e-54)
         t_1
         (if (<= b 2e+118)
           (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (j * (t * c)) + t_1;
	double tmp;
	if (b <= -8.5e+61) {
		tmp = t_1 - (i * (y * j));
	} else if (b <= -4.8e-18) {
		tmp = t_2;
	} else if (b <= -5e-54) {
		tmp = t_1;
	} else if (b <= 2e+118) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (j * (t * c)) + t_1
    if (b <= (-8.5d+61)) then
        tmp = t_1 - (i * (y * j))
    else if (b <= (-4.8d-18)) then
        tmp = t_2
    else if (b <= (-5d-54)) then
        tmp = t_1
    else if (b <= 2d+118) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (j * (t * c)) + t_1;
	double tmp;
	if (b <= -8.5e+61) {
		tmp = t_1 - (i * (y * j));
	} else if (b <= -4.8e-18) {
		tmp = t_2;
	} else if (b <= -5e-54) {
		tmp = t_1;
	} else if (b <= 2e+118) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (j * (t * c)) + t_1
	tmp = 0
	if b <= -8.5e+61:
		tmp = t_1 - (i * (y * j))
	elif b <= -4.8e-18:
		tmp = t_2
	elif b <= -5e-54:
		tmp = t_1
	elif b <= 2e+118:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(j * Float64(t * c)) + t_1)
	tmp = 0.0
	if (b <= -8.5e+61)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (b <= -4.8e-18)
		tmp = t_2;
	elseif (b <= -5e-54)
		tmp = t_1;
	elseif (b <= 2e+118)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = (j * (t * c)) + t_1;
	tmp = 0.0;
	if (b <= -8.5e+61)
		tmp = t_1 - (i * (y * j));
	elseif (b <= -4.8e-18)
		tmp = t_2;
	elseif (b <= -5e-54)
		tmp = t_1;
	elseif (b <= 2e+118)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -8.5e+61], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-18], t$95$2, If[LessEqual[b, -5e-54], t$95$1, If[LessEqual[b, 2e+118], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.50000000000000035e61

   1. Initial program 74.9%

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

   3. Taylor expanded in x around 0 73.0%

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

      1. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in t around 0 75.4%

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

      1. associate-*r* 75.4%

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

      2. neg-mul-1 75.4%

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

   8. Simplified 75.4%

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

   if -8.50000000000000035e61 < b < -4.79999999999999988e-18 or 1.99999999999999993e118 < b

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 87.6%

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

      1. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in c around inf 84.5%

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

   if -4.79999999999999988e-18 < b < -5.00000000000000015e-54

   1. Initial program 50.0%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -5.00000000000000015e-54 < b < 1.99999999999999993e118

   1. Initial program 72.3%

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

   3. Taylor expanded in b around 0 69.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* t c)) (* b (- (* a i) (* z c)))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -4.2e+32)
     t_2
     (if (<= y -4.1e-100)
       t_1
       (if (<= y -2.55e-120)
         (* t (- (* c j) (* x a)))
         (if (<= y 1.25e+156) 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 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.2e+32) {
		tmp = t_2;
	} else if (y <= -4.1e-100) {
		tmp = t_1;
	} else if (y <= -2.55e-120) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.25e+156) {
		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 = (j * (t * c)) + (b * ((a * i) - (z * c)))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-4.2d+32)) then
        tmp = t_2
    else if (y <= (-4.1d-100)) then
        tmp = t_1
    else if (y <= (-2.55d-120)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 1.25d+156) 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 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.2e+32) {
		tmp = t_2;
	} else if (y <= -4.1e-100) {
		tmp = t_1;
	} else if (y <= -2.55e-120) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.25e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (t * c)) + (b * ((a * i) - (z * c)))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4.2e+32:
		tmp = t_2
	elif y <= -4.1e-100:
		tmp = t_1
	elif y <= -2.55e-120:
		tmp = t * ((c * j) - (x * a))
	elif y <= 1.25e+156:
		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(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -4.2e+32)
		tmp = t_2;
	elseif (y <= -4.1e-100)
		tmp = t_1;
	elseif (y <= -2.55e-120)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 1.25e+156)
		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 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -4.2e+32)
		tmp = t_2;
	elseif (y <= -4.1e-100)
		tmp = t_1;
	elseif (y <= -2.55e-120)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 1.25e+156)
		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[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+32], t$95$2, If[LessEqual[y, -4.1e-100], t$95$1, If[LessEqual[y, -2.55e-120], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+156], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000001e32 or 1.24999999999999998e156 < y

   1. Initial program 66.2%

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

   3. Taylor expanded in y around -inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. +-commutative 71.8%

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

      5. mul-1-neg 71.8%

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

      6. unsub-neg 71.8%

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

   5. Simplified 71.8%

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

   if -4.2000000000000001e32 < y < -4.0999999999999999e-100 or -2.5499999999999999e-120 < y < 1.24999999999999998e156

   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 x around 0 74.4%

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

      1. *-commutative 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in c around inf 71.5%

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

   if -4.0999999999999999e-100 < y < -2.5499999999999999e-120

   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 t around inf 77.8%

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

   4. Taylor expanded in a around 0 64.6%

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

      1. associate-*r* 77.1%

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

      2. +-commutative 77.1%

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

      3. associate-*r* 77.1%

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

      4. neg-mul-1 77.1%

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

      5. cancel-sign-sub-inv 77.1%

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

      6. *-commutative 77.1%

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

      7. associate-*l* 77.8%

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

      8. distribute-rgt-out-- 77.8%

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

      9. *-commutative 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -6e+144)
     t_2
     (if (<= j -1.45e+71)
       t_1
       (if (<= j -1.1e-39)
         t_2
         (if (<= j -1.15e-81) (* x (* y z)) (if (<= j 9.4e-20) 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6e+144) {
		tmp = t_2;
	} else if (j <= -1.45e+71) {
		tmp = t_1;
	} else if (j <= -1.1e-39) {
		tmp = t_2;
	} else if (j <= -1.15e-81) {
		tmp = x * (y * z);
	} else if (j <= 9.4e-20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-6d+144)) then
        tmp = t_2
    else if (j <= (-1.45d+71)) then
        tmp = t_1
    else if (j <= (-1.1d-39)) then
        tmp = t_2
    else if (j <= (-1.15d-81)) then
        tmp = x * (y * z)
    else if (j <= 9.4d-20) 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6e+144) {
		tmp = t_2;
	} else if (j <= -1.45e+71) {
		tmp = t_1;
	} else if (j <= -1.1e-39) {
		tmp = t_2;
	} else if (j <= -1.15e-81) {
		tmp = x * (y * z);
	} else if (j <= 9.4e-20) {
		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 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -6e+144:
		tmp = t_2
	elif j <= -1.45e+71:
		tmp = t_1
	elif j <= -1.1e-39:
		tmp = t_2
	elif j <= -1.15e-81:
		tmp = x * (y * z)
	elif j <= 9.4e-20:
		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(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6e+144)
		tmp = t_2;
	elseif (j <= -1.45e+71)
		tmp = t_1;
	elseif (j <= -1.1e-39)
		tmp = t_2;
	elseif (j <= -1.15e-81)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 9.4e-20)
		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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -6e+144)
		tmp = t_2;
	elseif (j <= -1.45e+71)
		tmp = t_1;
	elseif (j <= -1.1e-39)
		tmp = t_2;
	elseif (j <= -1.15e-81)
		tmp = x * (y * z);
	elseif (j <= 9.4e-20)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6e+144], t$95$2, If[LessEqual[j, -1.45e+71], t$95$1, If[LessEqual[j, -1.1e-39], t$95$2, If[LessEqual[j, -1.15e-81], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.4e-20], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.9999999999999998e144 or -1.45000000000000004e71 < j < -1.1e-39 or 9.4000000000000003e-20 < j

   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 x around 0 77.9%

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

      1. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in j around inf 67.8%

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

   if -5.9999999999999998e144 < j < -1.45000000000000004e71 or -1.14999999999999996e-81 < j < 9.4000000000000003e-20

   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 b around inf 59.4%

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

      1. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if -1.1e-39 < j < -1.14999999999999996e-81

   1. Initial program 85.7%

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

   3. Taylor expanded in z around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in y around inf 58.6%

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

   7. Taylor expanded in z around 0 71.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 27.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-89}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= a -4e+168)
     t_1
     (if (<= a -4.2e+39)
       (* c (* t j))
       (if (<= a -4e-15)
         (* x (* y z))
         (if (<= a -2.4e-89)
           (* j (* t c))
           (if (<= a 2.85e+149) (* b (* z (- c))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -4e+168) {
		tmp = t_1;
	} else if (a <= -4.2e+39) {
		tmp = c * (t * j);
	} else if (a <= -4e-15) {
		tmp = x * (y * z);
	} else if (a <= -2.4e-89) {
		tmp = j * (t * c);
	} else if (a <= 2.85e+149) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (a <= (-4d+168)) then
        tmp = t_1
    else if (a <= (-4.2d+39)) then
        tmp = c * (t * j)
    else if (a <= (-4d-15)) then
        tmp = x * (y * z)
    else if (a <= (-2.4d-89)) then
        tmp = j * (t * c)
    else if (a <= 2.85d+149) then
        tmp = b * (z * -c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -4e+168) {
		tmp = t_1;
	} else if (a <= -4.2e+39) {
		tmp = c * (t * j);
	} else if (a <= -4e-15) {
		tmp = x * (y * z);
	} else if (a <= -2.4e-89) {
		tmp = j * (t * c);
	} else if (a <= 2.85e+149) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if a <= -4e+168:
		tmp = t_1
	elif a <= -4.2e+39:
		tmp = c * (t * j)
	elif a <= -4e-15:
		tmp = x * (y * z)
	elif a <= -2.4e-89:
		tmp = j * (t * c)
	elif a <= 2.85e+149:
		tmp = b * (z * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (a <= -4e+168)
		tmp = t_1;
	elseif (a <= -4.2e+39)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= -4e-15)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= -2.4e-89)
		tmp = Float64(j * Float64(t * c));
	elseif (a <= 2.85e+149)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (a <= -4e+168)
		tmp = t_1;
	elseif (a <= -4.2e+39)
		tmp = c * (t * j);
	elseif (a <= -4e-15)
		tmp = x * (y * z);
	elseif (a <= -2.4e-89)
		tmp = j * (t * c);
	elseif (a <= 2.85e+149)
		tmp = b * (z * -c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+168], t$95$1, If[LessEqual[a, -4.2e+39], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4e-15], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-89], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.85e+149], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.9999999999999997e168 or 2.84999999999999983e149 < a

   1. Initial program 59.8%

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

   3. Taylor expanded in b around inf 62.1%

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

      1. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in i around inf 54.0%

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

   if -3.9999999999999997e168 < a < -4.1999999999999997e39

   1. Initial program 64.9%

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

   3. Taylor expanded in t around inf 57.0%

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

   4. Taylor expanded in a around 0 40.7%

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

      1. *-commutative 40.7%

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

   6. Simplified 40.7%

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

   if -4.1999999999999997e39 < a < -4.0000000000000003e-15

   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 z around inf 42.9%

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

      1. *-commutative 42.9%

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

      2. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in y around inf 34.8%

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

   7. Taylor expanded in z around 0 42.6%

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

   if -4.0000000000000003e-15 < a < -2.40000000000000016e-89

   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 x around 0 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in c around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-*l* 69.5%

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

   8. Simplified 69.5%

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

   9. Taylor expanded in t around inf 44.4%

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

       1. *-commutative 44.4%

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

       2. associate-*l* 53.7%

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

   11. Simplified 53.7%

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

   if -2.40000000000000016e-89 < a < 2.84999999999999983e149

   1. Initial program 81.6%

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

   3. Taylor expanded in b around inf 45.8%

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

      1. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in i around 0 38.1%

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

      1. mul-1-neg 38.1%

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

      2. distribute-rgt-neg-out 38.1%

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

   8. Simplified 38.1%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-89}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -4.9e+42)
     t_1
     (if (<= t 1.8e-148)
       (* b (- (* a i) (* z c)))
       (if (<= t 2.45e-88)
         (* z (* x y))
         (if (<= t 1.45e+70) (* j (- (* t c) (* y i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.9e+42) {
		tmp = t_1;
	} else if (t <= 1.8e-148) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 2.45e-88) {
		tmp = z * (x * y);
	} else if (t <= 1.45e+70) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-4.9d+42)) then
        tmp = t_1
    else if (t <= 1.8d-148) then
        tmp = b * ((a * i) - (z * c))
    else if (t <= 2.45d-88) then
        tmp = z * (x * y)
    else if (t <= 1.45d+70) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.9e+42) {
		tmp = t_1;
	} else if (t <= 1.8e-148) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 2.45e-88) {
		tmp = z * (x * y);
	} else if (t <= 1.45e+70) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -4.9e+42:
		tmp = t_1
	elif t <= 1.8e-148:
		tmp = b * ((a * i) - (z * c))
	elif t <= 2.45e-88:
		tmp = z * (x * y)
	elif t <= 1.45e+70:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4.9e+42)
		tmp = t_1;
	elseif (t <= 1.8e-148)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (t <= 2.45e-88)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 1.45e+70)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -4.9e+42)
		tmp = t_1;
	elseif (t <= 1.8e-148)
		tmp = b * ((a * i) - (z * c));
	elseif (t <= 2.45e-88)
		tmp = z * (x * y);
	elseif (t <= 1.45e+70)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e+42], t$95$1, If[LessEqual[t, 1.8e-148], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e-88], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+70], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.9000000000000002e42 or 1.4499999999999999e70 < t

   1. Initial program 63.7%

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

   3. Taylor expanded in t around inf 64.3%

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

   4. Taylor expanded in a around 0 51.3%

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

      1. associate-*r* 56.3%

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

      2. +-commutative 56.3%

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

      3. associate-*r* 56.3%

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

      4. neg-mul-1 56.3%

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

      5. cancel-sign-sub-inv 56.3%

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

      6. *-commutative 56.3%

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

      7. associate-*l* 61.6%

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

      8. distribute-rgt-out-- 64.3%

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

      9. *-commutative 64.3%

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

   6. Simplified 64.3%

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

   if -4.9000000000000002e42 < t < 1.7999999999999999e-148

   1. Initial program 86.9%

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

   3. Taylor expanded in b around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   if 1.7999999999999999e-148 < t < 2.45000000000000014e-88

   1. Initial program 60.7%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in y around inf 67.3%

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

   if 2.45000000000000014e-88 < t < 1.4499999999999999e70

   1. Initial program 72.6%

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

   3. Taylor expanded in x around 0 62.9%

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

      1. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in j around inf 56.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-150}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 10^{+73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -2.3e+44)
     t_1
     (if (<= t 1.3e-150)
       (* b (- (* a i) (* z c)))
       (if (<= t 1.5e-88)
         (* z (- (* x y) (* b c)))
         (if (<= t 1e+73) (* j (- (* t c) (* y i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.3e+44) {
		tmp = t_1;
	} else if (t <= 1.3e-150) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 1.5e-88) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1e+73) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-2.3d+44)) then
        tmp = t_1
    else if (t <= 1.3d-150) then
        tmp = b * ((a * i) - (z * c))
    else if (t <= 1.5d-88) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1d+73) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.3e+44) {
		tmp = t_1;
	} else if (t <= 1.3e-150) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 1.5e-88) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1e+73) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.3e+44:
		tmp = t_1
	elif t <= 1.3e-150:
		tmp = b * ((a * i) - (z * c))
	elif t <= 1.5e-88:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1e+73:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.3e+44)
		tmp = t_1;
	elseif (t <= 1.3e-150)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (t <= 1.5e-88)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1e+73)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.3e+44)
		tmp = t_1;
	elseif (t <= 1.3e-150)
		tmp = b * ((a * i) - (z * c));
	elseif (t <= 1.5e-88)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1e+73)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+44], t$95$1, If[LessEqual[t, 1.3e-150], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-88], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+73], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.30000000000000004e44 or 9.99999999999999983e72 < t

   1. Initial program 63.7%

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

   3. Taylor expanded in t around inf 64.3%

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

   4. Taylor expanded in a around 0 51.3%

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

      1. associate-*r* 56.3%

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

      2. +-commutative 56.3%

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

      3. associate-*r* 56.3%

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

      4. neg-mul-1 56.3%

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

      5. cancel-sign-sub-inv 56.3%

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

      6. *-commutative 56.3%

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

      7. associate-*l* 61.6%

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

      8. distribute-rgt-out-- 64.3%

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

      9. *-commutative 64.3%

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

   6. Simplified 64.3%

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

   if -2.30000000000000004e44 < t < 1.2999999999999999e-150

   1. Initial program 86.9%

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

   3. Taylor expanded in b around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   if 1.2999999999999999e-150 < t < 1.5e-88

   1. Initial program 60.7%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   if 1.5e-88 < t < 9.99999999999999983e72

   1. Initial program 72.6%

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

   3. Taylor expanded in x around 0 62.9%

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

      1. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in j around inf 56.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-150}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 10^{+73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1e+190)
     t_1
     (if (<= j -5e+107)
       (* c (- (* t j) (* z b)))
       (if (<= j -9.5e-75)
         (* y (- (* x z) (* i j)))
         (if (<= j 3.5e-20) (* b (- (* a i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1e+190) {
		tmp = t_1;
	} else if (j <= -5e+107) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -9.5e-75) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 3.5e-20) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1d+190)) then
        tmp = t_1
    else if (j <= (-5d+107)) then
        tmp = c * ((t * j) - (z * b))
    else if (j <= (-9.5d-75)) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= 3.5d-20) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1e+190) {
		tmp = t_1;
	} else if (j <= -5e+107) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -9.5e-75) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 3.5e-20) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1e+190:
		tmp = t_1
	elif j <= -5e+107:
		tmp = c * ((t * j) - (z * b))
	elif j <= -9.5e-75:
		tmp = y * ((x * z) - (i * j))
	elif j <= 3.5e-20:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1e+190)
		tmp = t_1;
	elseif (j <= -5e+107)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (j <= -9.5e-75)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= 3.5e-20)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1e+190)
		tmp = t_1;
	elseif (j <= -5e+107)
		tmp = c * ((t * j) - (z * b));
	elseif (j <= -9.5e-75)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= 3.5e-20)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1e+190], t$95$1, If[LessEqual[j, -5e+107], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.5e-75], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-20], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.0000000000000001e190 or 3.50000000000000003e-20 < j

   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 x around 0 79.1%

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

      1. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in j around inf 70.3%

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

   if -1.0000000000000001e190 < j < -5.0000000000000002e107

   1. Initial program 77.7%

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

   3. Taylor expanded in c around inf 83.5%

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

      1. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   if -5.0000000000000002e107 < j < -9.4999999999999991e-75

   1. Initial program 85.7%

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

   3. Taylor expanded in y around -inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. *-commutative 65.1%

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

      3. distribute-rgt-neg-in 65.1%

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

      4. +-commutative 65.1%

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

      5. mul-1-neg 65.1%

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

      6. unsub-neg 65.1%

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

   5. Simplified 65.1%

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

   if -9.4999999999999991e-75 < j < 3.50000000000000003e-20

   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 b around inf 58.8%

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

      1. *-commutative 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+190}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{-64} \lor \neg \left(b \leq 2.2 \cdot 10^{+118}\right):\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (or (<= b -1.15e-64) (not (<= b 2.2e+118)))
     (+ t_1 (* b (- (* a i) (* z c))))
     (+ (* x (- (* y z) (* t a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if ((b <= -1.15e-64) || !(b <= 2.2e+118)) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if ((b <= (-1.15d-64)) .or. (.not. (b <= 2.2d+118))) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = (x * ((y * z) - (t * a))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if ((b <= -1.15e-64) || !(b <= 2.2e+118)) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if (b <= -1.15e-64) or not (b <= 2.2e+118):
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = (x * ((y * z) - (t * a))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if ((b <= -1.15e-64) || !(b <= 2.2e+118))
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if ((b <= -1.15e-64) || ~((b <= 2.2e+118)))
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = (x * ((y * z) - (t * a))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.15e-64], N[Not[LessEqual[b, 2.2e+118]], $MachinePrecision]], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1500000000000001e-64 or 2.19999999999999986e118 < b

   1. Initial program 75.3%

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

   3. Taylor expanded in x around 0 79.9%

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

      1. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   if -1.1500000000000001e-64 < b < 2.19999999999999986e118

   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 b around 0 69.9%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-64} \lor \neg \left(b \leq 2.2 \cdot 10^{+118}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7.8 \cdot 10^{+143}:\\ \;\;\;\;t_2 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \end{array} \]

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 (<= j -7.8e+143)
     (- t_2 (* c (* z b)))
     (if (<= j 2.25e-5) (+ (* x (- (* y z) (* t a))) t_1) (+ 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));
	double tmp;
	if (j <= -7.8e+143) {
		tmp = t_2 - (c * (z * b));
	} else if (j <= 2.25e-5) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-7.8d+143)) then
        tmp = t_2 - (c * (z * b))
    else if (j <= 2.25d-5) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = t_2 + 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 t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7.8e+143) {
		tmp = t_2 - (c * (z * b));
	} else if (j <= 2.25e-5) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_2 + 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))
	tmp = 0
	if j <= -7.8e+143:
		tmp = t_2 - (c * (z * b))
	elif j <= 2.25e-5:
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = t_2 + 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 (j <= -7.8e+143)
		tmp = Float64(t_2 - Float64(c * Float64(z * b)));
	elseif (j <= 2.25e-5)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(t_2 + 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));
	tmp = 0.0;
	if (j <= -7.8e+143)
		tmp = t_2 - (c * (z * b));
	elseif (j <= 2.25e-5)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = t_2 + 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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.8e+143], N[(t$95$2 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.25e-5], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.7999999999999997e143

   1. Initial program 75.1%

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

   3. Taylor expanded in x around 0 84.5%

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

      1. *-commutative 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in c around inf 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l* 84.9%

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

   8. Simplified 84.9%

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

   if -7.7999999999999997e143 < j < 2.25000000000000014e-5

   1. Initial program 73.3%

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

   3. Taylor expanded in j around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if 2.25000000000000014e-5 < j

   1. Initial program 73.5%

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

   3. Taylor expanded in x around 0 79.7%

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

      1. *-commutative 79.7%

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

   5. Simplified 79.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.8 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -9.1 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-182}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= y -1.12e+29)
     (* z (* x y))
     (if (<= y -9.1e-262)
       t_1
       (if (<= y 5.2e-182)
         (* b (* a i))
         (if (<= y 3.9e+158) t_1 (* i (* y (- j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double tmp;
	if (y <= -1.12e+29) {
		tmp = z * (x * y);
	} else if (y <= -9.1e-262) {
		tmp = t_1;
	} else if (y <= 5.2e-182) {
		tmp = b * (a * i);
	} else if (y <= 3.9e+158) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * -c)
    if (y <= (-1.12d+29)) then
        tmp = z * (x * y)
    else if (y <= (-9.1d-262)) then
        tmp = t_1
    else if (y <= 5.2d-182) then
        tmp = b * (a * i)
    else if (y <= 3.9d+158) then
        tmp = t_1
    else
        tmp = i * (y * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double tmp;
	if (y <= -1.12e+29) {
		tmp = z * (x * y);
	} else if (y <= -9.1e-262) {
		tmp = t_1;
	} else if (y <= 5.2e-182) {
		tmp = b * (a * i);
	} else if (y <= 3.9e+158) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if y <= -1.12e+29:
		tmp = z * (x * y)
	elif y <= -9.1e-262:
		tmp = t_1
	elif y <= 5.2e-182:
		tmp = b * (a * i)
	elif y <= 3.9e+158:
		tmp = t_1
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (y <= -1.12e+29)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -9.1e-262)
		tmp = t_1;
	elseif (y <= 5.2e-182)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 3.9e+158)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	tmp = 0.0;
	if (y <= -1.12e+29)
		tmp = z * (x * y);
	elseif (y <= -9.1e-262)
		tmp = t_1;
	elseif (y <= 5.2e-182)
		tmp = b * (a * i);
	elseif (y <= 3.9e+158)
		tmp = t_1;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+29], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.1e-262], t$95$1, If[LessEqual[y, 5.2e-182], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+158], t$95$1, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1200000000000001e29

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in y around inf 47.6%

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

   if -1.1200000000000001e29 < y < -9.10000000000000018e-262 or 5.20000000000000011e-182 < y < 3.9e158

   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 b around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in i around 0 37.1%

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

      1. mul-1-neg 37.1%

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

      2. distribute-rgt-neg-out 37.1%

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

   8. Simplified 37.1%

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

   if -9.10000000000000018e-262 < y < 5.20000000000000011e-182

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in i around inf 47.1%

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

   if 3.9e158 < y

   1. Initial program 64.2%

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

   3. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in y around inf 44.2%

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

      1. associate-*r* 44.2%

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

      2. neg-mul-1 44.2%

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

   8. Simplified 44.2%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -9.1 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-182}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+158}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;y \leq -8.9 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -9.1 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= y -8.9e+30)
     (* z (* x y))
     (if (<= y -9.1e-262)
       t_1
       (if (<= y 1.05e-184)
         (* b (* a i))
         (if (<= y 1.1e+158) t_1 (* y (* i (- j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double tmp;
	if (y <= -8.9e+30) {
		tmp = z * (x * y);
	} else if (y <= -9.1e-262) {
		tmp = t_1;
	} else if (y <= 1.05e-184) {
		tmp = b * (a * i);
	} else if (y <= 1.1e+158) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * -c)
    if (y <= (-8.9d+30)) then
        tmp = z * (x * y)
    else if (y <= (-9.1d-262)) then
        tmp = t_1
    else if (y <= 1.05d-184) then
        tmp = b * (a * i)
    else if (y <= 1.1d+158) then
        tmp = t_1
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double tmp;
	if (y <= -8.9e+30) {
		tmp = z * (x * y);
	} else if (y <= -9.1e-262) {
		tmp = t_1;
	} else if (y <= 1.05e-184) {
		tmp = b * (a * i);
	} else if (y <= 1.1e+158) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if y <= -8.9e+30:
		tmp = z * (x * y)
	elif y <= -9.1e-262:
		tmp = t_1
	elif y <= 1.05e-184:
		tmp = b * (a * i)
	elif y <= 1.1e+158:
		tmp = t_1
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (y <= -8.9e+30)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -9.1e-262)
		tmp = t_1;
	elseif (y <= 1.05e-184)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 1.1e+158)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	tmp = 0.0;
	if (y <= -8.9e+30)
		tmp = z * (x * y);
	elseif (y <= -9.1e-262)
		tmp = t_1;
	elseif (y <= 1.05e-184)
		tmp = b * (a * i);
	elseif (y <= 1.1e+158)
		tmp = t_1;
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.9e+30], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.1e-262], t$95$1, If[LessEqual[y, 1.05e-184], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+158], t$95$1, N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.90000000000000049e30

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in y around inf 47.6%

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

   if -8.90000000000000049e30 < y < -9.10000000000000018e-262 or 1.0499999999999999e-184 < y < 1.1000000000000001e158

   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 b around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in i around 0 37.1%

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

      1. mul-1-neg 37.1%

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

      2. distribute-rgt-neg-out 37.1%

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

   8. Simplified 37.1%

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

   if -9.10000000000000018e-262 < y < 1.0499999999999999e-184

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in i around inf 47.1%

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

   if 1.1000000000000001e158 < y

   1. Initial program 64.2%

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

   3. Taylor expanded in y around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. *-commutative 64.5%

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

      3. distribute-rgt-neg-in 64.5%

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

      4. +-commutative 64.5%

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

      5. mul-1-neg 64.5%

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

      6. unsub-neg 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in i around inf 46.9%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -9.1 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+158}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+200}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{+121} \lor \neg \left(j \leq 4.5 \cdot 10^{-33}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.6e+200)
   (* y (* i (- j)))
   (if (or (<= j -9.5e+121) (not (<= j 4.5e-33)))
     (* 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 (j <= -1.6e+200) {
		tmp = y * (i * -j);
	} else if ((j <= -9.5e+121) || !(j <= 4.5e-33)) {
		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 (j <= (-1.6d+200)) then
        tmp = y * (i * -j)
    else if ((j <= (-9.5d+121)) .or. (.not. (j <= 4.5d-33))) 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 (j <= -1.6e+200) {
		tmp = y * (i * -j);
	} else if ((j <= -9.5e+121) || !(j <= 4.5e-33)) {
		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 j <= -1.6e+200:
		tmp = y * (i * -j)
	elif (j <= -9.5e+121) or not (j <= 4.5e-33):
		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 (j <= -1.6e+200)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif ((j <= -9.5e+121) || !(j <= 4.5e-33))
		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 (j <= -1.6e+200)
		tmp = y * (i * -j);
	elseif ((j <= -9.5e+121) || ~((j <= 4.5e-33)))
		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[LessEqual[j, -1.6e+200], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, -9.5e+121], N[Not[LessEqual[j, 4.5e-33]], $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 3 regimes

2. if j < -1.60000000000000016e200

   1. Initial program 74.1%

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

   3. Taylor expanded in y around -inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

      4. +-commutative 57.4%

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

      5. mul-1-neg 57.4%

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

      6. unsub-neg 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in i around inf 57.2%

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

   if -1.60000000000000016e200 < j < -9.49999999999999949e121 or 4.49999999999999991e-33 < j

   1. Initial program 74.3%

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

   3. Taylor expanded in c around inf 56.2%

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

      1. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   if -9.49999999999999949e121 < j < 4.49999999999999991e-33

   1. Initial program 73.1%

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

   3. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   5. Simplified 55.3%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+200}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{+121} \lor \neg \left(j \leq 4.5 \cdot 10^{-33}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.62 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.62e+156)
   (* i (* y (- j)))
   (if (<= j 7.5e+101) (* b (- (* a i) (* z c))) (* t (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.62e+156) {
		tmp = i * (y * -j);
	} else if (j <= 7.5e+101) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.62d+156)) then
        tmp = i * (y * -j)
    else if (j <= 7.5d+101) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.62e+156) {
		tmp = i * (y * -j);
	} else if (j <= 7.5e+101) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.62e+156:
		tmp = i * (y * -j)
	elif j <= 7.5e+101:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.62e+156)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (j <= 7.5e+101)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.62e+156)
		tmp = i * (y * -j);
	elseif (j <= 7.5e+101)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.62e+156], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e+101], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.62000000000000006e156

   1. Initial program 76.0%

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

   3. Taylor expanded in x around 0 82.9%

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

      1. *-commutative 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in y around inf 56.6%

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

      1. associate-*r* 56.6%

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

      2. neg-mul-1 56.6%

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

   8. Simplified 56.6%

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

   if -1.62000000000000006e156 < j < 7.4999999999999995e101

   1. Initial program 72.1%

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

   3. Taylor expanded in b around inf 54.1%

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

      1. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   if 7.4999999999999995e101 < j

   1. Initial program 77.3%

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

   3. Taylor expanded in t around inf 53.9%

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

   4. Taylor expanded in a around 0 50.2%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.62 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 21.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-68} \lor \neg \left(i \leq 2.95 \cdot 10^{+23}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -4.2e-68) (not (<= i 2.95e+23))) (* a (* b i)) (* a (* x t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4.2e-68) || !(i <= 2.95e+23)) {
		tmp = a * (b * i);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-4.2d-68)) .or. (.not. (i <= 2.95d+23))) then
        tmp = a * (b * i)
    else
        tmp = a * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4.2e-68) || !(i <= 2.95e+23)) {
		tmp = a * (b * i);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -4.2e-68) or not (i <= 2.95e+23):
		tmp = a * (b * i)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -4.2e-68) || !(i <= 2.95e+23))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -4.2e-68) || ~((i <= 2.95e+23)))
		tmp = a * (b * i);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -4.2e-68], N[Not[LessEqual[i, 2.95e+23]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -4.20000000000000016e-68 or 2.94999999999999994e23 < i

   1. Initial program 67.0%

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

   3. Taylor expanded in b around inf 55.1%

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

      1. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in i around inf 38.0%

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

   if -4.20000000000000016e-68 < i < 2.94999999999999994e23

   1. Initial program 80.7%

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

   3. Taylor expanded in t around inf 47.0%

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

   4. Taylor expanded in a around inf 20.2%

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

      1. associate-*r* 20.2%

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

      2. neg-mul-1 20.2%

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

      3. *-commutative 20.2%

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

   6. Simplified 20.2%

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

      1. expm1-log1p-u 8.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(-a\right) \cdot \left(x \cdot t\right)\right)\right)} \]

      2. expm1-udef 7.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(-a\right) \cdot \left(x \cdot t\right)\right)} - 1} \]

      3. add-sqr-sqrt 3.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot t\right)\right)} - 1 \]

      4. sqrt-unprod 6.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot t\right)\right)} - 1 \]

      5. sqr-neg 6.0%

         \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot t\right)\right)} - 1 \]

      6. sqrt-unprod 3.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot t\right)\right)} - 1 \]

      7. add-sqr-sqrt 7.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{a} \cdot \left(x \cdot t\right)\right)} - 1 \]

      8. *-commutative 7.1%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(t \cdot x\right)}\right)} - 1 \]

   8. Applied egg-rr 7.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(t \cdot x\right)\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 7.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 11.7%

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

   10. Simplified 11.7%

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

4. Final simplification 25.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-68} \lor \neg \left(i \leq 2.95 \cdot 10^{+23}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{-255}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.85e-255)
   (* b (* a i))
   (if (<= i 2.15e+23) (* a (* x t)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.85e-255) {
		tmp = b * (a * i);
	} else if (i <= 2.15e+23) {
		tmp = a * (x * t);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.85d-255)) then
        tmp = b * (a * i)
    else if (i <= 2.15d+23) then
        tmp = a * (x * t)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.85e-255) {
		tmp = b * (a * i);
	} else if (i <= 2.15e+23) {
		tmp = a * (x * t);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.85e-255:
		tmp = b * (a * i)
	elif i <= 2.15e+23:
		tmp = a * (x * t)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.85e-255)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 2.15e+23)
		tmp = Float64(a * Float64(x * t));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.85e-255)
		tmp = b * (a * i);
	elseif (i <= 2.15e+23)
		tmp = a * (x * t);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.85e-255], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.15e+23], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.8500000000000001e-255

   1. Initial program 72.4%

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

   3. Taylor expanded in b around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in i around inf 29.2%

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

   if -1.8500000000000001e-255 < i < 2.1499999999999999e23

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf 46.7%

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

   4. Taylor expanded in a around inf 21.4%

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

      1. associate-*r* 21.4%

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

      2. neg-mul-1 21.4%

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

      3. *-commutative 21.4%

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

   6. Simplified 21.4%

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

      1. expm1-log1p-u 9.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(-a\right) \cdot \left(x \cdot t\right)\right)\right)} \]

      2. expm1-udef 9.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(-a\right) \cdot \left(x \cdot t\right)\right)} - 1} \]

      3. add-sqr-sqrt 5.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \left(x \cdot t\right)\right)} - 1 \]

      4. sqrt-unprod 7.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \left(x \cdot t\right)\right)} - 1 \]

      5. sqr-neg 7.0%

         \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{a \cdot a}} \cdot \left(x \cdot t\right)\right)} - 1 \]

      6. sqrt-unprod 4.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \left(x \cdot t\right)\right)} - 1 \]

      7. add-sqr-sqrt 8.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{a} \cdot \left(x \cdot t\right)\right)} - 1 \]

      8. *-commutative 8.4%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(t \cdot x\right)}\right)} - 1 \]

   8. Applied egg-rr 8.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(t \cdot x\right)\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 8.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 14.1%

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

   10. Simplified 14.1%

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

   if 2.1499999999999999e23 < i

   1. Initial program 63.1%

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

   3. Taylor expanded in b around inf 55.1%

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

      1. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in i around inf 44.5%

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

4. Final simplification 27.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{-255}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.7 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.7e-54)
   (* b (* a i))
   (if (<= i 1.65e+100) (* c (* t j)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.7e-54) {
		tmp = b * (a * i);
	} else if (i <= 1.65e+100) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-4.7d-54)) then
        tmp = b * (a * i)
    else if (i <= 1.65d+100) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.7e-54) {
		tmp = b * (a * i);
	} else if (i <= 1.65e+100) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -4.7e-54:
		tmp = b * (a * i)
	elif i <= 1.65e+100:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -4.7e-54)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 1.65e+100)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -4.7e-54)
		tmp = b * (a * i);
	elseif (i <= 1.65e+100)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -4.7e-54], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.65e+100], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.7e-54

   1. Initial program 69.5%

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

   3. Taylor expanded in b around inf 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in i around inf 41.2%

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

   if -4.7e-54 < i < 1.6500000000000001e100

   1. Initial program 79.0%

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

   3. Taylor expanded in t around inf 48.5%

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

   4. Taylor expanded in a around 0 27.7%

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

      1. *-commutative 27.7%

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

   6. Simplified 27.7%

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

   if 1.6500000000000001e100 < i

   1. Initial program 61.6%

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

   3. Taylor expanded in b around inf 59.6%

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

      1. *-commutative 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in i around inf 51.5%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.7 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -9.6 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -9.6e-59)
   (* b (* a i))
   (if (<= i 1.5e+99) (* j (* t c)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -9.6e-59) {
		tmp = b * (a * i);
	} else if (i <= 1.5e+99) {
		tmp = j * (t * c);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-9.6d-59)) then
        tmp = b * (a * i)
    else if (i <= 1.5d+99) then
        tmp = j * (t * c)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -9.6e-59) {
		tmp = b * (a * i);
	} else if (i <= 1.5e+99) {
		tmp = j * (t * c);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -9.6e-59:
		tmp = b * (a * i)
	elif i <= 1.5e+99:
		tmp = j * (t * c)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -9.6e-59)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 1.5e+99)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -9.6e-59)
		tmp = b * (a * i);
	elseif (i <= 1.5e+99)
		tmp = j * (t * c);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -9.6e-59], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.5e+99], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.6000000000000006e-59

   1. Initial program 69.5%

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

   3. Taylor expanded in b around inf 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in i around inf 41.2%

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

   if -9.6000000000000006e-59 < i < 1.50000000000000007e99

   1. Initial program 79.0%

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

   3. Taylor expanded in x around 0 64.8%

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

      1. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in c around inf 60.8%

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

      1. *-commutative 60.8%

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

      2. associate-*l* 58.2%

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

   8. Simplified 58.2%

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

   9. Taylor expanded in t around inf 27.7%

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

       1. *-commutative 27.7%

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

       2. associate-*l* 32.2%

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

   11. Simplified 32.2%

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

   if 1.50000000000000007e99 < i

   1. Initial program 61.6%

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

   3. Taylor expanded in b around inf 59.6%

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

      1. *-commutative 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in i around inf 51.5%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.6 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 22.7% 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 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 b around inf 47.2%

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

   1. *-commutative 47.2%

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

5. Simplified 47.2%

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

6. Taylor expanded in i around inf 21.9%

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

7. Final simplification 21.9%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.8% 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 2024020 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))