Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.6% → 82.2%

Time: 39.6s

Alternatives: 27

Speedup: 0.5×

• 57.5% 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: 73.6% 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: 82.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(j * t$95$2), $MachinePrecision] + N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + N[(t$95$1 - N[(b * N[(z * c + N[(a * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $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 93.0%

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

      1. +-commutative 93.0%

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

      2. fma-def 93.0%

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

      3. *-commutative 93.0%

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

      4. *-commutative 93.0%

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

      5. cancel-sign-sub-inv 93.0%

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

      6. cancel-sign-sub 93.0%

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

      7. remove-double-neg 93.0%

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

      8. *-commutative 93.0%

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

      9. fma-neg 93.0%

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

      10. distribute-rgt-neg-out 93.0%

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

   3. Simplified 93.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around -inf 8.8%

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

   3. Taylor expanded in i around inf 51.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} - b \cdot \left(c \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.4%

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

Alternative 2: 82.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $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 93.0%

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

   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. Taylor expanded in a around -inf 8.8%

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

   3. Taylor expanded in i around inf 51.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} - b \cdot \left(c \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.4%

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

Alternative 3: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(z \cdot c\right)\\ t_3 := \left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - t_2\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{-48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 920000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - t_2\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t_1\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{+141}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* b (* z c)))
        (t_3 (- (+ (* j (- (* t c) (* y i))) (* x (* y z))) t_2)))
   (if (<= j -2.2e-48)
     t_3
     (if (<= j 920000000.0)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (if (<= j 3.8e+70)
         (- (* i (- (* a b) (* y j))) t_2)
         (if (<= j 5.4e+111)
           (+ (* t (- (* c j) (* x a))) t_1)
           (if (<= j 1.32e+141) (+ (* a (* b i)) t_1) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * (z * c);
	double t_3 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_2;
	double tmp;
	if (j <= -2.2e-48) {
		tmp = t_3;
	} else if (j <= 920000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 3.8e+70) {
		tmp = (i * ((a * b) - (y * j))) - t_2;
	} else if (j <= 5.4e+111) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else if (j <= 1.32e+141) {
		tmp = (a * (b * i)) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = b * (z * c)
    t_3 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_2
    if (j <= (-2.2d-48)) then
        tmp = t_3
    else if (j <= 920000000.0d0) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (j <= 3.8d+70) then
        tmp = (i * ((a * b) - (y * j))) - t_2
    else if (j <= 5.4d+111) then
        tmp = (t * ((c * j) - (x * a))) + t_1
    else if (j <= 1.32d+141) then
        tmp = (a * (b * i)) + t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * (z * c);
	double t_3 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_2;
	double tmp;
	if (j <= -2.2e-48) {
		tmp = t_3;
	} else if (j <= 920000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 3.8e+70) {
		tmp = (i * ((a * b) - (y * j))) - t_2;
	} else if (j <= 5.4e+111) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else if (j <= 1.32e+141) {
		tmp = (a * (b * i)) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * (z * c)
	t_3 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_2
	tmp = 0
	if j <= -2.2e-48:
		tmp = t_3
	elif j <= 920000000.0:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif j <= 3.8e+70:
		tmp = (i * ((a * b) - (y * j))) - t_2
	elif j <= 5.4e+111:
		tmp = (t * ((c * j) - (x * a))) + t_1
	elif j <= 1.32e+141:
		tmp = (a * (b * i)) + t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(z * c))
	t_3 = Float64(Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z))) - t_2)
	tmp = 0.0
	if (j <= -2.2e-48)
		tmp = t_3;
	elseif (j <= 920000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 3.8e+70)
		tmp = Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) - t_2);
	elseif (j <= 5.4e+111)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_1);
	elseif (j <= 1.32e+141)
		tmp = Float64(Float64(a * Float64(b * i)) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * (z * c);
	t_3 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_2;
	tmp = 0.0;
	if (j <= -2.2e-48)
		tmp = t_3;
	elseif (j <= 920000000.0)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (j <= 3.8e+70)
		tmp = (i * ((a * b) - (y * j))) - t_2;
	elseif (j <= 5.4e+111)
		tmp = (t * ((c * j) - (x * a))) + t_1;
	elseif (j <= 1.32e+141)
		tmp = (a * (b * i)) + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[j, -2.2e-48], t$95$3, If[LessEqual[j, 920000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e+70], N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[j, 5.4e+111], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 1.32e+141], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.20000000000000013e-48 or 1.3200000000000001e141 < j

   1. Initial program 77.6%

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

   2. Taylor expanded in a around 0 75.5%

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

   if -2.20000000000000013e-48 < j < 9.2e8

   1. Initial program 78.0%

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

   2. Taylor expanded in j around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. *-commutative 79.9%

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

      3. *-commutative 79.9%

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

   4. Simplified 79.9%

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

   if 9.2e8 < j < 3.7999999999999998e70

   1. Initial program 60.6%

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

   2. Taylor expanded in a around -inf 68.7%

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

   3. Taylor expanded in i around inf 73.8%

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

   if 3.7999999999999998e70 < j < 5.3999999999999998e111

   1. Initial program 80.0%

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

   2. Taylor expanded in y around -inf 90.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around 0 90.5%

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

   if 5.3999999999999998e111 < j < 1.3200000000000001e141

   1. Initial program 33.3%

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

   2. Taylor expanded in z around 0 49.7%

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

   3. Taylor expanded in y around inf 83.3%

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

      1. +-commutative 83.3%

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

      2. *-commutative 83.3%

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

      3. mul-1-neg 83.3%

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

      4. unsub-neg 83.3%

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

      5. *-commutative 83.3%

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

   5. Simplified 83.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{-48}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 920000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{+141}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 4: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ t_2 := \left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - t_1\\ \mathbf{if}\;j \leq -8 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 920000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{+66}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - t_1\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+141}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + a \cdot \left(b \cdot i - x \cdot t\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z c)))
        (t_2 (- (+ (* j (- (* t c) (* y i))) (* x (* y z))) t_1)))
   (if (<= j -8e-48)
     t_2
     (if (<= j 920000000.0)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (if (<= j 6.3e+66)
         (- (* i (- (* a b) (* y j))) t_1)
         (if (<= j 5.4e+111)
           (+ (* t (- (* c j) (* x a))) (* y (- (* x z) (* i j))))
           (if (<= j 1.45e+141)
             (- (+ (* y (* x z)) (* a (- (* b i) (* x t)))) 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 * (z * c);
	double t_2 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_1;
	double tmp;
	if (j <= -8e-48) {
		tmp = t_2;
	} else if (j <= 920000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 6.3e+66) {
		tmp = (i * ((a * b) - (y * j))) - t_1;
	} else if (j <= 5.4e+111) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (j <= 1.45e+141) {
		tmp = ((y * (x * z)) + (a * ((b * i) - (x * t)))) - 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 * (z * c)
    t_2 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_1
    if (j <= (-8d-48)) then
        tmp = t_2
    else if (j <= 920000000.0d0) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (j <= 6.3d+66) then
        tmp = (i * ((a * b) - (y * j))) - t_1
    else if (j <= 5.4d+111) then
        tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
    else if (j <= 1.45d+141) then
        tmp = ((y * (x * z)) + (a * ((b * i) - (x * t)))) - 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 * (z * c);
	double t_2 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_1;
	double tmp;
	if (j <= -8e-48) {
		tmp = t_2;
	} else if (j <= 920000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 6.3e+66) {
		tmp = (i * ((a * b) - (y * j))) - t_1;
	} else if (j <= 5.4e+111) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (j <= 1.45e+141) {
		tmp = ((y * (x * z)) + (a * ((b * i) - (x * t)))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * c)
	t_2 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_1
	tmp = 0
	if j <= -8e-48:
		tmp = t_2
	elif j <= 920000000.0:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif j <= 6.3e+66:
		tmp = (i * ((a * b) - (y * j))) - t_1
	elif j <= 5.4e+111:
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	elif j <= 1.45e+141:
		tmp = ((y * (x * z)) + (a * ((b * i) - (x * t)))) - 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(z * c))
	t_2 = Float64(Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z))) - t_1)
	tmp = 0.0
	if (j <= -8e-48)
		tmp = t_2;
	elseif (j <= 920000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 6.3e+66)
		tmp = Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) - t_1);
	elseif (j <= 5.4e+111)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (j <= 1.45e+141)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) + Float64(a * Float64(Float64(b * i) - Float64(x * t)))) - 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 * (z * c);
	t_2 = ((j * ((t * c) - (y * i))) + (x * (y * z))) - t_1;
	tmp = 0.0;
	if (j <= -8e-48)
		tmp = t_2;
	elseif (j <= 920000000.0)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (j <= 6.3e+66)
		tmp = (i * ((a * b) - (y * j))) - t_1;
	elseif (j <= 5.4e+111)
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	elseif (j <= 1.45e+141)
		tmp = ((y * (x * z)) + (a * ((b * i) - (x * t)))) - 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[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[j, -8e-48], t$95$2, If[LessEqual[j, 920000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.3e+66], N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, 5.4e+111], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e+141], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7.9999999999999998e-48 or 1.45000000000000003e141 < j

   1. Initial program 77.6%

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

   2. Taylor expanded in a around 0 75.5%

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

   if -7.9999999999999998e-48 < j < 9.2e8

   1. Initial program 78.0%

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

   2. Taylor expanded in j around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. *-commutative 79.9%

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

      3. *-commutative 79.9%

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

   4. Simplified 79.9%

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

   if 9.2e8 < j < 6.2999999999999998e66

   1. Initial program 60.6%

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

   2. Taylor expanded in a around -inf 68.7%

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

   3. Taylor expanded in i around inf 73.8%

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

   if 6.2999999999999998e66 < j < 5.3999999999999998e111

   1. Initial program 80.0%

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

   2. Taylor expanded in y around -inf 90.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around 0 90.5%

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

   if 5.3999999999999998e111 < j < 1.45000000000000003e141

   1. Initial program 33.3%

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

   2. Taylor expanded in a around -inf 33.3%

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

   3. Taylor expanded in j around 0 50.0%

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

      1. +-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. *-commutative 50.0%

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

      4. *-commutative 50.0%

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

      5. fma-neg 50.0%

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

      6. unsub-neg 50.0%

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

      7. associate-*r* 83.1%

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

      8. *-commutative 83.1%

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

      9. associate-*r* 83.3%

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

      10. fma-neg 83.3%

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

   5. Simplified 83.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{-48}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 920000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{+66}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+141}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + a \cdot \left(b \cdot i - x \cdot t\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 5: 70.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 205:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) + t_1\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \left(c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1)))
   (if (<= x -1.32e-6)
     t_2
     (if (<= x 205.0)
       (+ (* j (- (* t c) (* y i))) (+ (* y (* x z)) t_1))
       (if (<= x 1.3e+28)
         (+ (* t (- (* c j) (* x a))) (* y (- (* x z) (* i j))))
         (if (<= x 2.55e+113)
           (+ (* a (* b i)) (- (* c (* t j)) (* z (- (* b c) (* x y)))))
           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 = (x * ((y * z) - (t * a))) + t_1;
	double tmp;
	if (x <= -1.32e-6) {
		tmp = t_2;
	} else if (x <= 205.0) {
		tmp = (j * ((t * c) - (y * i))) + ((y * (x * z)) + t_1);
	} else if (x <= 1.3e+28) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (x <= 2.55e+113) {
		tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))));
	} 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 = (x * ((y * z) - (t * a))) + t_1
    if (x <= (-1.32d-6)) then
        tmp = t_2
    else if (x <= 205.0d0) then
        tmp = (j * ((t * c) - (y * i))) + ((y * (x * z)) + t_1)
    else if (x <= 1.3d+28) then
        tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
    else if (x <= 2.55d+113) then
        tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))))
    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 = (x * ((y * z) - (t * a))) + t_1;
	double tmp;
	if (x <= -1.32e-6) {
		tmp = t_2;
	} else if (x <= 205.0) {
		tmp = (j * ((t * c) - (y * i))) + ((y * (x * z)) + t_1);
	} else if (x <= 1.3e+28) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (x <= 2.55e+113) {
		tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))));
	} 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 = (x * ((y * z) - (t * a))) + t_1
	tmp = 0
	if x <= -1.32e-6:
		tmp = t_2
	elif x <= 205.0:
		tmp = (j * ((t * c) - (y * i))) + ((y * (x * z)) + t_1)
	elif x <= 1.3e+28:
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	elif x <= 2.55e+113:
		tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))))
	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(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	tmp = 0.0
	if (x <= -1.32e-6)
		tmp = t_2;
	elseif (x <= 205.0)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(Float64(y * Float64(x * z)) + t_1));
	elseif (x <= 1.3e+28)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (x <= 2.55e+113)
		tmp = Float64(Float64(a * Float64(b * i)) + Float64(Float64(c * Float64(t * j)) - Float64(z * Float64(Float64(b * c) - Float64(x * y)))));
	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 = (x * ((y * z) - (t * a))) + t_1;
	tmp = 0.0;
	if (x <= -1.32e-6)
		tmp = t_2;
	elseif (x <= 205.0)
		tmp = (j * ((t * c) - (y * i))) + ((y * (x * z)) + t_1);
	elseif (x <= 1.3e+28)
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	elseif (x <= 2.55e+113)
		tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[x, -1.32e-6], t$95$2, If[LessEqual[x, 205.0], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+28], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e+113], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.3200000000000001e-6 or 2.54999999999999997e113 < x

   1. Initial program 81.0%

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

   2. Taylor expanded in j around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   if -1.3200000000000001e-6 < x < 205

   1. Initial program 74.0%

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

   2. Taylor expanded in y around inf 72.7%

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

      1. *-commutative 72.7%

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

      2. associate-*r* 77.5%

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

   4. Simplified 77.5%

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

   if 205 < x < 1.3000000000000001e28

   1. Initial program 40.0%

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

   2. Taylor expanded in y around -inf 40.0%

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

   4. Simplified 39.7%

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

   5. Taylor expanded in b around 0 99.7%

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

   if 1.3000000000000001e28 < x < 2.54999999999999997e113

   1. Initial program 51.3%

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

   2. Taylor expanded in z around 0 75.5%

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

   3. Taylor expanded in a around 0 88.0%

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

   4. Taylor expanded in i around 0 99.2%

      \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 205:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \left(c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 6: 71.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-5} \lor \neg \left(x \leq 9.6 \cdot 10^{+114}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -8.6e-5) (not (<= x 9.6e+114)))
   (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
   (+ (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b 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 ((x <= -8.6e-5) || !(x <= 9.6e+114)) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = ((j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))) + (a * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-8.6d-5)) .or. (.not. (x <= 9.6d+114))) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = ((j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))) + (a * (b * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -8.6e-5) || !(x <= 9.6e+114)) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = ((j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))) + (a * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -8.6e-5) or not (x <= 9.6e+114):
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = ((j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))) + (a * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -8.6e-5) || !(x <= 9.6e+114))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c)))) + Float64(a * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -8.6e-5) || ~((x <= 9.6e+114)))
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = ((j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))) + (a * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -8.6e-5], N[Not[LessEqual[x, 9.6e+114]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.6000000000000003e-5 or 9.6e114 < x

   1. Initial program 81.0%

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

   2. Taylor expanded in j around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   if -8.6000000000000003e-5 < x < 9.6e114

   1. Initial program 71.4%

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

   2. Taylor expanded in z around 0 80.9%

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

   3. Taylor expanded in a around 0 77.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-5} \lor \neg \left(x \leq 9.6 \cdot 10^{+114}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 7: 66.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.001 \lor \neg \left(b \leq 5.2 \cdot 10^{-250} \lor \neg \left(b \leq 1.1 \cdot 10^{-94}\right) \land b \leq 4.1 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -0.001)
         (not (or (<= b 5.2e-250) (and (not (<= b 1.1e-94)) (<= b 4.1e+33)))))
   (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
   (+ (* t (- (* c j) (* x a))) (* y (- (* x z) (* i j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -0.001) || !((b <= 5.2e-250) || (!(b <= 1.1e-94) && (b <= 4.1e+33)))) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (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) :: tmp
    if ((b <= (-0.001d0)) .or. (.not. (b <= 5.2d-250) .or. (.not. (b <= 1.1d-94)) .and. (b <= 4.1d+33))) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (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 tmp;
	if ((b <= -0.001) || !((b <= 5.2e-250) || (!(b <= 1.1e-94) && (b <= 4.1e+33)))) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -0.001) or not ((b <= 5.2e-250) or (not (b <= 1.1e-94) and (b <= 4.1e+33))):
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -0.001) || !((b <= 5.2e-250) || (!(b <= 1.1e-94) && (b <= 4.1e+33))))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -0.001) || ~(((b <= 5.2e-250) || (~((b <= 1.1e-94)) && (b <= 4.1e+33)))))
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -0.001], N[Not[Or[LessEqual[b, 5.2e-250], And[N[Not[LessEqual[b, 1.1e-94]], $MachinePrecision], LessEqual[b, 4.1e+33]]]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1e-3 or 5.20000000000000016e-250 < b < 1.10000000000000001e-94 or 4.09999999999999995e33 < b

   1. Initial program 82.1%

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

   2. Taylor expanded in j around 0 82.2%

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

      1. *-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. *-commutative 82.2%

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

   4. Simplified 82.2%

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

   if -1e-3 < b < 5.20000000000000016e-250 or 1.10000000000000001e-94 < b < 4.09999999999999995e33

   1. Initial program 67.8%

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

   2. Taylor expanded in y around -inf 60.2%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in b around 0 72.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + t \cdot \left(c \cdot j - a \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.001 \lor \neg \left(b \leq 5.2 \cdot 10^{-250} \lor \neg \left(b \leq 1.1 \cdot 10^{-94}\right) \land b \leq 4.1 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 8: 68.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 6000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \left(c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (+ (* j (- (* t c) (* y i))) (* x (* y z))) (* b (* z c)))))
   (if (<= j -2.9e-47)
     t_1
     (if (<= j 6000000000.0)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (if (<= j 7.2e+149)
         (+ (* a (* b i)) (- (* c (* t j)) (* z (- (* b c) (* x y)))))
         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))) + (x * (y * z))) - (b * (z * c));
	double tmp;
	if (j <= -2.9e-47) {
		tmp = t_1;
	} else if (j <= 6000000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 7.2e+149) {
		tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))));
	} 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))) + (x * (y * z))) - (b * (z * c))
    if (j <= (-2.9d-47)) then
        tmp = t_1
    else if (j <= 6000000000.0d0) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (j <= 7.2d+149) then
        tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))))
    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))) + (x * (y * z))) - (b * (z * c));
	double tmp;
	if (j <= -2.9e-47) {
		tmp = t_1;
	} else if (j <= 6000000000.0) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 7.2e+149) {
		tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))));
	} 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))) + (x * (y * z))) - (b * (z * c))
	tmp = 0
	if j <= -2.9e-47:
		tmp = t_1
	elif j <= 6000000000.0:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif j <= 7.2e+149:
		tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z))) - Float64(b * Float64(z * c)))
	tmp = 0.0
	if (j <= -2.9e-47)
		tmp = t_1;
	elseif (j <= 6000000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 7.2e+149)
		tmp = Float64(Float64(a * Float64(b * i)) + Float64(Float64(c * Float64(t * j)) - Float64(z * Float64(Float64(b * c) - Float64(x * y)))));
	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))) + (x * (y * z))) - (b * (z * c));
	tmp = 0.0;
	if (j <= -2.9e-47)
		tmp = t_1;
	elseif (j <= 6000000000.0)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (j <= 7.2e+149)
		tmp = (a * (b * i)) + ((c * (t * j)) - (z * ((b * c) - (x * y))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e-47], t$95$1, If[LessEqual[j, 6000000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e+149], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.9e-47 or 7.1999999999999999e149 < j

   1. Initial program 77.6%

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

   2. Taylor expanded in a around 0 75.5%

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

   if -2.9e-47 < j < 6e9

   1. Initial program 78.0%

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

   2. Taylor expanded in j around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. *-commutative 79.9%

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

      3. *-commutative 79.9%

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

   4. Simplified 79.9%

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

   if 6e9 < j < 7.1999999999999999e149

   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. Taylor expanded in z around 0 87.4%

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

   3. Taylor expanded in a around 0 84.2%

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

   4. Taylor expanded in i around 0 68.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{-47}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 6000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+149}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \left(c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 9: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;j \leq -10500000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-116}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-256}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1150000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (* a i)))))
   (if (<= j -10500000000000.0)
     (* j (- (* t c) (* y i)))
     (if (<= j -2.7e-116)
       (* c (- (* t j) (* z b)))
       (if (<= j -1.2e-277)
         t_1
         (if (<= j 3.1e-256)
           (* z (- (* x y) (* b c)))
           (if (<= j 1150000000.0)
             t_1
             (- (* y (- (* x z) (* i j))) (* b (* z c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * (a * i));
	double tmp;
	if (j <= -10500000000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else if (j <= -2.7e-116) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -1.2e-277) {
		tmp = t_1;
	} else if (j <= 3.1e-256) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1150000000.0) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (b * (a * i))
    if (j <= (-10500000000000.0d0)) then
        tmp = j * ((t * c) - (y * i))
    else if (j <= (-2.7d-116)) then
        tmp = c * ((t * j) - (z * b))
    else if (j <= (-1.2d-277)) then
        tmp = t_1
    else if (j <= 3.1d-256) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 1150000000.0d0) then
        tmp = t_1
    else
        tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * (a * i));
	double tmp;
	if (j <= -10500000000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else if (j <= -2.7e-116) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -1.2e-277) {
		tmp = t_1;
	} else if (j <= 3.1e-256) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1150000000.0) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (b * (a * i))
	tmp = 0
	if j <= -10500000000000.0:
		tmp = j * ((t * c) - (y * i))
	elif j <= -2.7e-116:
		tmp = c * ((t * j) - (z * b))
	elif j <= -1.2e-277:
		tmp = t_1
	elif j <= 3.1e-256:
		tmp = z * ((x * y) - (b * c))
	elif j <= 1150000000.0:
		tmp = t_1
	else:
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(a * i)))
	tmp = 0.0
	if (j <= -10500000000000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (j <= -2.7e-116)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (j <= -1.2e-277)
		tmp = t_1;
	elseif (j <= 3.1e-256)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 1150000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (b * (a * i));
	tmp = 0.0;
	if (j <= -10500000000000.0)
		tmp = j * ((t * c) - (y * i));
	elseif (j <= -2.7e-116)
		tmp = c * ((t * j) - (z * b));
	elseif (j <= -1.2e-277)
		tmp = t_1;
	elseif (j <= 3.1e-256)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 1150000000.0)
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -10500000000000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.7e-116], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.2e-277], t$95$1, If[LessEqual[j, 3.1e-256], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1150000000.0], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.05e13

   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. Taylor expanded in j around inf 62.1%

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

   if -1.05e13 < j < -2.7e-116

   1. Initial program 71.9%

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

   2. Taylor expanded in c around inf 64.9%

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

   if -2.7e-116 < j < -1.2e-277 or 3.09999999999999986e-256 < j < 1.15e9

   1. Initial program 85.3%

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

   2. Taylor expanded in a around -inf 79.8%

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

   3. Taylor expanded in j around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. mul-1-neg 80.1%

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

      3. *-commutative 80.1%

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

      4. *-commutative 80.1%

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

      5. fma-neg 80.1%

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

      6. unsub-neg 80.1%

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

      7. associate-*r* 77.8%

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

      8. *-commutative 77.8%

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

      9. associate-*r* 77.9%

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

      10. fma-neg 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in c around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. *-commutative 71.0%

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

      3. *-commutative 71.0%

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

      4. sub-neg 71.0%

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

      5. distribute-lft-in 69.8%

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

      6. *-commutative 69.8%

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

      7. distribute-rgt-neg-in 69.8%

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

      8. mul-1-neg 69.8%

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

      9. associate--l- 69.8%

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

      10. sub-neg 69.8%

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

      11. mul-1-neg 69.8%

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

      12. +-commutative 69.8%

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

      13. associate-*r* 69.8%

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

      14. neg-mul-1 69.8%

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

      15. cancel-sign-sub 69.8%

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

   8. Simplified 76.3%

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

   if -1.2e-277 < j < 3.09999999999999986e-256

   1. Initial program 64.3%

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

   2. Taylor expanded in z around inf 63.8%

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

      1. *-commutative 63.8%

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

   4. Simplified 63.8%

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

   if 1.15e9 < j

   1. Initial program 69.7%

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

   2. Taylor expanded in a around -inf 71.9%

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

   3. Taylor expanded in y around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

   5. Simplified 62.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -10500000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-116}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-256}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1150000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 10: 52.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-219}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+22}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (* a i)))))
   (if (<= x -2.15e+21)
     t_1
     (if (<= x -4.4e-219)
       (* c (- (* t j) (* z b)))
       (if (<= x 4.6e-123)
         (* b (- (* a i) (* z c)))
         (if (<= x 1.05e+22) (* i (- (* a b) (* y j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * (a * i));
	double tmp;
	if (x <= -2.15e+21) {
		tmp = t_1;
	} else if (x <= -4.4e-219) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 4.6e-123) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.05e+22) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (b * (a * i))
    if (x <= (-2.15d+21)) then
        tmp = t_1
    else if (x <= (-4.4d-219)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 4.6d-123) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 1.05d+22) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * (a * i));
	double tmp;
	if (x <= -2.15e+21) {
		tmp = t_1;
	} else if (x <= -4.4e-219) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 4.6e-123) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.05e+22) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (b * (a * i))
	tmp = 0
	if x <= -2.15e+21:
		tmp = t_1
	elif x <= -4.4e-219:
		tmp = c * ((t * j) - (z * b))
	elif x <= 4.6e-123:
		tmp = b * ((a * i) - (z * c))
	elif x <= 1.05e+22:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(a * i)))
	tmp = 0.0
	if (x <= -2.15e+21)
		tmp = t_1;
	elseif (x <= -4.4e-219)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 4.6e-123)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 1.05e+22)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (b * (a * i));
	tmp = 0.0;
	if (x <= -2.15e+21)
		tmp = t_1;
	elseif (x <= -4.4e-219)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 4.6e-123)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 1.05e+22)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+21], t$95$1, If[LessEqual[x, -4.4e-219], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-123], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+22], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.15e21 or 1.0499999999999999e22 < x

   1. Initial program 79.3%

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

   2. Taylor expanded in a around -inf 74.3%

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

   3. Taylor expanded in j around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. *-commutative 74.2%

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

      4. *-commutative 74.2%

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

      5. fma-neg 74.2%

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

      6. unsub-neg 74.2%

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

      7. associate-*r* 71.9%

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

      8. *-commutative 71.9%

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

      9. associate-*r* 67.3%

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

      10. fma-neg 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in c around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. *-commutative 69.6%

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

      4. sub-neg 69.6%

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

      5. distribute-lft-in 68.0%

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

      6. *-commutative 68.0%

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

      7. distribute-rgt-neg-in 68.0%

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

      8. mul-1-neg 68.0%

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

      9. associate--l- 68.0%

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

      10. sub-neg 68.0%

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

      11. mul-1-neg 68.0%

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

      12. +-commutative 68.0%

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

      13. associate-*r* 68.0%

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

      14. neg-mul-1 68.0%

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

      15. cancel-sign-sub 68.0%

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

   8. Simplified 69.5%

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

   if -2.15e21 < x < -4.3999999999999999e-219

   1. Initial program 78.3%

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

   2. Taylor expanded in c around inf 57.4%

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

   if -4.3999999999999999e-219 < x < 4.59999999999999973e-123

   1. Initial program 67.2%

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

   2. Taylor expanded in b around inf 63.4%

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

   if 4.59999999999999973e-123 < x < 1.0499999999999999e22

   1. Initial program 68.2%

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

   2. Taylor expanded in i around inf 65.4%

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

      1. distribute-lft-out-- 65.4%

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

      2. *-commutative 65.4%

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

   4. Simplified 65.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-219}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+22}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 11: 58.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;x \leq -450000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (* a i))))
        (t_2 (- (* i (- (* a b) (* y j))) (* b (* z c)))))
   (if (<= x -450000.0)
     t_1
     (if (<= x -5.1e-98)
       t_2
       (if (<= x -2.3e-196)
         (* c (- (* t j) (* z b)))
         (if (<= x 2.6e+113) 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 = (x * ((y * z) - (t * a))) + (b * (a * i));
	double t_2 = (i * ((a * b) - (y * j))) - (b * (z * c));
	double tmp;
	if (x <= -450000.0) {
		tmp = t_1;
	} else if (x <= -5.1e-98) {
		tmp = t_2;
	} else if (x <= -2.3e-196) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 2.6e+113) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (b * (a * i))
    t_2 = (i * ((a * b) - (y * j))) - (b * (z * c))
    if (x <= (-450000.0d0)) then
        tmp = t_1
    else if (x <= (-5.1d-98)) then
        tmp = t_2
    else if (x <= (-2.3d-196)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 2.6d+113) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * (a * i));
	double t_2 = (i * ((a * b) - (y * j))) - (b * (z * c));
	double tmp;
	if (x <= -450000.0) {
		tmp = t_1;
	} else if (x <= -5.1e-98) {
		tmp = t_2;
	} else if (x <= -2.3e-196) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 2.6e+113) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (b * (a * i))
	t_2 = (i * ((a * b) - (y * j))) - (b * (z * c))
	tmp = 0
	if x <= -450000.0:
		tmp = t_1
	elif x <= -5.1e-98:
		tmp = t_2
	elif x <= -2.3e-196:
		tmp = c * ((t * j) - (z * b))
	elif x <= 2.6e+113:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(a * i)))
	t_2 = Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) - Float64(b * Float64(z * c)))
	tmp = 0.0
	if (x <= -450000.0)
		tmp = t_1;
	elseif (x <= -5.1e-98)
		tmp = t_2;
	elseif (x <= -2.3e-196)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 2.6e+113)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (b * (a * i));
	t_2 = (i * ((a * b) - (y * j))) - (b * (z * c));
	tmp = 0.0;
	if (x <= -450000.0)
		tmp = t_1;
	elseif (x <= -5.1e-98)
		tmp = t_2;
	elseif (x <= -2.3e-196)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 2.6e+113)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -450000.0], t$95$1, If[LessEqual[x, -5.1e-98], t$95$2, If[LessEqual[x, -2.3e-196], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+113], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5e5 or 2.5999999999999999e113 < x

   1. Initial program 81.3%

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

   2. Taylor expanded in a around -inf 75.9%

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

   3. Taylor expanded in j around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. *-commutative 75.9%

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

      4. *-commutative 75.9%

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

      5. fma-neg 75.9%

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

      6. unsub-neg 75.9%

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

      7. associate-*r* 73.4%

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

      8. *-commutative 73.4%

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

      9. associate-*r* 68.5%

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

      10. fma-neg 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in c around 0 70.1%

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

      1. *-commutative 70.1%

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

      2. *-commutative 70.1%

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

      3. *-commutative 70.1%

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

      4. sub-neg 70.1%

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

      5. distribute-lft-in 69.2%

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

      6. *-commutative 69.2%

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

      7. distribute-rgt-neg-in 69.2%

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

      8. mul-1-neg 69.2%

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

      9. associate--l- 69.2%

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

      10. sub-neg 69.2%

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

      11. mul-1-neg 69.2%

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

      12. +-commutative 69.2%

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

      13. associate-*r* 69.2%

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

      14. neg-mul-1 69.2%

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

      15. cancel-sign-sub 69.2%

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

   8. Simplified 71.5%

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

   if -4.5e5 < x < -5.10000000000000022e-98 or -2.3000000000000002e-196 < x < 2.5999999999999999e113

   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. Taylor expanded in a around -inf 73.8%

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

   3. Taylor expanded in i around inf 65.8%

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

   if -5.10000000000000022e-98 < x < -2.3000000000000002e-196

   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. Taylor expanded in c around inf 69.5%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -450000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-98}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+113}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 12: 60.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.62 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -3.5e+132)
     t_1
     (if (<= i 1.62e-55)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (if (<= i 1.2e+139) (* c (- (* t j) (* z b))) (- t_1 (* b (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -3.5e+132) {
		tmp = t_1;
	} else if (i <= 1.62e-55) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (i <= 1.2e+139) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-3.5d+132)) then
        tmp = t_1
    else if (i <= 1.62d-55) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (i <= 1.2d+139) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1 - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -3.5e+132) {
		tmp = t_1;
	} else if (i <= 1.62e-55) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (i <= 1.2e+139) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -3.5e+132:
		tmp = t_1
	elif i <= 1.62e-55:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif i <= 1.2e+139:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1 - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.5e+132)
		tmp = t_1;
	elseif (i <= 1.62e-55)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (i <= 1.2e+139)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.5e+132)
		tmp = t_1;
	elseif (i <= 1.62e-55)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (i <= 1.2e+139)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1 - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.5e+132], t$95$1, If[LessEqual[i, 1.62e-55], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e+139], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.5000000000000002e132

   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. Taylor expanded in i around inf 81.8%

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

      1. distribute-lft-out-- 81.8%

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

      2. *-commutative 81.8%

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

   4. Simplified 81.8%

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

   if -3.5000000000000002e132 < i < 1.62000000000000006e-55

   1. Initial program 82.9%

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

   2. Taylor expanded in j around 0 74.4%

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

      1. *-commutative 74.4%

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

      2. *-commutative 74.4%

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

      3. *-commutative 74.4%

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

   4. Simplified 74.4%

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

   if 1.62000000000000006e-55 < i < 1.20000000000000004e139

   1. Initial program 65.7%

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

   2. Taylor expanded in c around inf 65.9%

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

   if 1.20000000000000004e139 < i

   1. Initial program 63.6%

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

   2. Taylor expanded in a around -inf 67.2%

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

   3. Taylor expanded in i around inf 79.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} - b \cdot \left(c \cdot z\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.62 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 13: 28.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -b \cdot \left(z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -3.35 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* z c)))) (t_2 (* i (* a b))))
   (if (<= x -4.8e+71)
     (* a (* x (- t)))
     (if (<= x -3.35e-202)
       t_1
       (if (<= x 5e-254)
         (* a (* b i))
         (if (<= x 4.6e-123)
           t_1
           (if (<= x 3.5e-77)
             (* i (- (* y j)))
             (if (<= x 4.5e+93)
               t_2
               (if (<= x 1.4e+116)
                 (* z (- (* b c)))
                 (if (<= x 2.4e+140) t_2 (* z (* x y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -(b * (z * c));
	double t_2 = i * (a * b);
	double tmp;
	if (x <= -4.8e+71) {
		tmp = a * (x * -t);
	} else if (x <= -3.35e-202) {
		tmp = t_1;
	} else if (x <= 5e-254) {
		tmp = a * (b * i);
	} else if (x <= 4.6e-123) {
		tmp = t_1;
	} else if (x <= 3.5e-77) {
		tmp = i * -(y * j);
	} else if (x <= 4.5e+93) {
		tmp = t_2;
	} else if (x <= 1.4e+116) {
		tmp = z * -(b * c);
	} else if (x <= 2.4e+140) {
		tmp = t_2;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -(b * (z * c))
    t_2 = i * (a * b)
    if (x <= (-4.8d+71)) then
        tmp = a * (x * -t)
    else if (x <= (-3.35d-202)) then
        tmp = t_1
    else if (x <= 5d-254) then
        tmp = a * (b * i)
    else if (x <= 4.6d-123) then
        tmp = t_1
    else if (x <= 3.5d-77) then
        tmp = i * -(y * j)
    else if (x <= 4.5d+93) then
        tmp = t_2
    else if (x <= 1.4d+116) then
        tmp = z * -(b * c)
    else if (x <= 2.4d+140) then
        tmp = t_2
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -(b * (z * c));
	double t_2 = i * (a * b);
	double tmp;
	if (x <= -4.8e+71) {
		tmp = a * (x * -t);
	} else if (x <= -3.35e-202) {
		tmp = t_1;
	} else if (x <= 5e-254) {
		tmp = a * (b * i);
	} else if (x <= 4.6e-123) {
		tmp = t_1;
	} else if (x <= 3.5e-77) {
		tmp = i * -(y * j);
	} else if (x <= 4.5e+93) {
		tmp = t_2;
	} else if (x <= 1.4e+116) {
		tmp = z * -(b * c);
	} else if (x <= 2.4e+140) {
		tmp = t_2;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -(b * (z * c))
	t_2 = i * (a * b)
	tmp = 0
	if x <= -4.8e+71:
		tmp = a * (x * -t)
	elif x <= -3.35e-202:
		tmp = t_1
	elif x <= 5e-254:
		tmp = a * (b * i)
	elif x <= 4.6e-123:
		tmp = t_1
	elif x <= 3.5e-77:
		tmp = i * -(y * j)
	elif x <= 4.5e+93:
		tmp = t_2
	elif x <= 1.4e+116:
		tmp = z * -(b * c)
	elif x <= 2.4e+140:
		tmp = t_2
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(-Float64(b * Float64(z * c)))
	t_2 = Float64(i * Float64(a * b))
	tmp = 0.0
	if (x <= -4.8e+71)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= -3.35e-202)
		tmp = t_1;
	elseif (x <= 5e-254)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 4.6e-123)
		tmp = t_1;
	elseif (x <= 3.5e-77)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (x <= 4.5e+93)
		tmp = t_2;
	elseif (x <= 1.4e+116)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (x <= 2.4e+140)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -(b * (z * c));
	t_2 = i * (a * b);
	tmp = 0.0;
	if (x <= -4.8e+71)
		tmp = a * (x * -t);
	elseif (x <= -3.35e-202)
		tmp = t_1;
	elseif (x <= 5e-254)
		tmp = a * (b * i);
	elseif (x <= 4.6e-123)
		tmp = t_1;
	elseif (x <= 3.5e-77)
		tmp = i * -(y * j);
	elseif (x <= 4.5e+93)
		tmp = t_2;
	elseif (x <= 1.4e+116)
		tmp = z * -(b * c);
	elseif (x <= 2.4e+140)
		tmp = t_2;
	else
		tmp = z * (x * y);
	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])}, Block[{t$95$2 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+71], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.35e-202], t$95$1, If[LessEqual[x, 5e-254], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-123], t$95$1, If[LessEqual[x, 3.5e-77], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 4.5e+93], t$95$2, If[LessEqual[x, 1.4e+116], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 2.4e+140], t$95$2, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -4.79999999999999961e71

   1. Initial program 81.4%

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

   2. Taylor expanded in x around inf 66.3%

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

      1. *-commutative 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in z around 0 49.1%

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

      1. associate-*r* 49.1%

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

      2. neg-mul-1 49.1%

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

   7. Simplified 49.1%

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

   if -4.79999999999999961e71 < x < -3.35000000000000001e-202 or 5.0000000000000003e-254 < x < 4.59999999999999973e-123

   1. Initial program 80.0%

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

   2. Taylor expanded in b around inf 51.0%

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

   3. Taylor expanded in a around 0 37.2%

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

      1. associate-*r* 37.2%

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

      2. neg-mul-1 37.2%

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

   5. Simplified 37.2%

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

   if -3.35000000000000001e-202 < x < 5.0000000000000003e-254

   1. Initial program 62.3%

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

   2. Taylor expanded in b around inf 56.2%

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

   3. Taylor expanded in a around inf 40.8%

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

   4. Taylor expanded in b around 0 40.8%

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

   if 4.59999999999999973e-123 < x < 3.50000000000000013e-77

   1. Initial program 71.0%

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

   2. Taylor expanded in i around inf 70.7%

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

      1. distribute-lft-out-- 70.7%

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

      2. *-commutative 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in j around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-in 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

   7. Simplified 70.7%

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

   if 3.50000000000000013e-77 < x < 4.49999999999999991e93 or 1.40000000000000002e116 < x < 2.4e140

   1. Initial program 67.8%

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

   2. Taylor expanded in i around inf 54.5%

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

      1. distribute-lft-out-- 54.5%

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

      2. *-commutative 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in j around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. distribute-rgt-neg-in 44.9%

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

   7. Simplified 44.9%

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

   if 4.49999999999999991e93 < x < 1.40000000000000002e116

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

   5. Taylor expanded in y around 0 99.0%

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

      1. neg-mul-1 99.0%

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

      2. distribute-rgt-neg-in 99.0%

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

   7. Simplified 99.0%

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

   if 2.4e140 < x

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

   4. Simplified 49.7%

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

   5. Taylor expanded in y around inf 49.7%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -3.35 \cdot 10^{-202}:\\ \;\;\;\;-b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;-b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+93}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 14: 50.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.05e+23)
     t_2
     (if (<= x -6e-216)
       (* c (- (* t j) (* z b)))
       (if (<= x 4.6e-123)
         t_1
         (if (<= x 3.4e-77)
           (* j (- (* t c) (* y i)))
           (if (<= x 2.5e-35)
             t_1
             (if (<= x 8e+135) (* a (- (* b i) (* x t))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.05e+23) {
		tmp = t_2;
	} else if (x <= -6e-216) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 4.6e-123) {
		tmp = t_1;
	} else if (x <= 3.4e-77) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 2.5e-35) {
		tmp = t_1;
	} else if (x <= 8e+135) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.05d+23)) then
        tmp = t_2
    else if (x <= (-6d-216)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 4.6d-123) then
        tmp = t_1
    else if (x <= 3.4d-77) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= 2.5d-35) then
        tmp = t_1
    else if (x <= 8d+135) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.05e+23) {
		tmp = t_2;
	} else if (x <= -6e-216) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 4.6e-123) {
		tmp = t_1;
	} else if (x <= 3.4e-77) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 2.5e-35) {
		tmp = t_1;
	} else if (x <= 8e+135) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.05e+23:
		tmp = t_2
	elif x <= -6e-216:
		tmp = c * ((t * j) - (z * b))
	elif x <= 4.6e-123:
		tmp = t_1
	elif x <= 3.4e-77:
		tmp = j * ((t * c) - (y * i))
	elif x <= 2.5e-35:
		tmp = t_1
	elif x <= 8e+135:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.05e+23)
		tmp = t_2;
	elseif (x <= -6e-216)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 4.6e-123)
		tmp = t_1;
	elseif (x <= 3.4e-77)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= 2.5e-35)
		tmp = t_1;
	elseif (x <= 8e+135)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.05e+23)
		tmp = t_2;
	elseif (x <= -6e-216)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 4.6e-123)
		tmp = t_1;
	elseif (x <= 3.4e-77)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= 2.5e-35)
		tmp = t_1;
	elseif (x <= 8e+135)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+23], t$95$2, If[LessEqual[x, -6e-216], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-123], t$95$1, If[LessEqual[x, 3.4e-77], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-35], t$95$1, If[LessEqual[x, 8e+135], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.0500000000000001e23 or 7.99999999999999969e135 < x

   1. Initial program 80.4%

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

   2. Taylor expanded in x around inf 68.0%

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

      1. *-commutative 68.0%

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

   4. Simplified 68.0%

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

   if -1.0500000000000001e23 < x < -6.00000000000000025e-216

   1. Initial program 78.7%

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

   2. Taylor expanded in c around inf 56.6%

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

   if -6.00000000000000025e-216 < x < 4.59999999999999973e-123 or 3.39999999999999983e-77 < x < 2.49999999999999982e-35

   1. Initial program 69.6%

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

   2. Taylor expanded in b around inf 64.8%

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

   if 4.59999999999999973e-123 < x < 3.39999999999999983e-77

   1. Initial program 71.0%

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

   2. Taylor expanded in j around inf 81.4%

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

   if 2.49999999999999982e-35 < x < 7.99999999999999969e135

   1. Initial program 64.4%

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

   2. Taylor expanded in y around -inf 60.1%

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

   4. Simplified 60.1%

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

   5. Taylor expanded in a around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

   7. Simplified 64.2%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 15: 28.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-b \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+69}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* b c)))) (t_2 (* a (* b i))))
   (if (<= x -8.6e+69)
     (* (* t a) (- x))
     (if (<= x -2.8e-202)
       t_1
       (if (<= x 1.46e-253)
         t_2
         (if (<= x 4.2e-123)
           t_1
           (if (<= x 3.15e-77)
             (* i (- (* y j)))
             (if (<= x 2.8e+140) t_2 (* z (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * -(b * c);
	double t_2 = a * (b * i);
	double tmp;
	if (x <= -8.6e+69) {
		tmp = (t * a) * -x;
	} else if (x <= -2.8e-202) {
		tmp = t_1;
	} else if (x <= 1.46e-253) {
		tmp = t_2;
	} else if (x <= 4.2e-123) {
		tmp = t_1;
	} else if (x <= 3.15e-77) {
		tmp = i * -(y * j);
	} else if (x <= 2.8e+140) {
		tmp = t_2;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -(b * c)
    t_2 = a * (b * i)
    if (x <= (-8.6d+69)) then
        tmp = (t * a) * -x
    else if (x <= (-2.8d-202)) then
        tmp = t_1
    else if (x <= 1.46d-253) then
        tmp = t_2
    else if (x <= 4.2d-123) then
        tmp = t_1
    else if (x <= 3.15d-77) then
        tmp = i * -(y * j)
    else if (x <= 2.8d+140) then
        tmp = t_2
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * -(b * c);
	double t_2 = a * (b * i);
	double tmp;
	if (x <= -8.6e+69) {
		tmp = (t * a) * -x;
	} else if (x <= -2.8e-202) {
		tmp = t_1;
	} else if (x <= 1.46e-253) {
		tmp = t_2;
	} else if (x <= 4.2e-123) {
		tmp = t_1;
	} else if (x <= 3.15e-77) {
		tmp = i * -(y * j);
	} else if (x <= 2.8e+140) {
		tmp = t_2;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * -(b * c)
	t_2 = a * (b * i)
	tmp = 0
	if x <= -8.6e+69:
		tmp = (t * a) * -x
	elif x <= -2.8e-202:
		tmp = t_1
	elif x <= 1.46e-253:
		tmp = t_2
	elif x <= 4.2e-123:
		tmp = t_1
	elif x <= 3.15e-77:
		tmp = i * -(y * j)
	elif x <= 2.8e+140:
		tmp = t_2
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(-Float64(b * c)))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (x <= -8.6e+69)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (x <= -2.8e-202)
		tmp = t_1;
	elseif (x <= 1.46e-253)
		tmp = t_2;
	elseif (x <= 4.2e-123)
		tmp = t_1;
	elseif (x <= 3.15e-77)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (x <= 2.8e+140)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * -(b * c);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (x <= -8.6e+69)
		tmp = (t * a) * -x;
	elseif (x <= -2.8e-202)
		tmp = t_1;
	elseif (x <= 1.46e-253)
		tmp = t_2;
	elseif (x <= 4.2e-123)
		tmp = t_1;
	elseif (x <= 3.15e-77)
		tmp = i * -(y * j);
	elseif (x <= 2.8e+140)
		tmp = t_2;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+69], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[x, -2.8e-202], t$95$1, If[LessEqual[x, 1.46e-253], t$95$2, If[LessEqual[x, 4.2e-123], t$95$1, If[LessEqual[x, 3.15e-77], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 2.8e+140], t$95$2, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.59999999999999986e69

   1. Initial program 81.4%

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

   2. Taylor expanded in x around inf 66.3%

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

      1. *-commutative 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in z around 0 44.5%

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

      1. neg-mul-1 44.5%

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

      2. distribute-rgt-neg-in 44.5%

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

   7. Simplified 44.5%

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

   if -8.59999999999999986e69 < x < -2.8000000000000001e-202 or 1.45999999999999989e-253 < x < 4.1999999999999998e-123

   1. Initial program 80.0%

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

   2. Taylor expanded in z around inf 39.8%

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

      1. *-commutative 39.8%

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

   4. Simplified 39.8%

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

   5. Taylor expanded in y around 0 34.0%

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

      1. neg-mul-1 34.0%

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

      2. distribute-rgt-neg-in 34.0%

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

   7. Simplified 34.0%

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

   if -2.8000000000000001e-202 < x < 1.45999999999999989e-253 or 3.15e-77 < x < 2.79999999999999983e140

   1. Initial program 65.5%

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

   2. Taylor expanded in b around inf 52.4%

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

   3. Taylor expanded in a around inf 38.2%

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

   4. Taylor expanded in b around 0 41.2%

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

   if 4.1999999999999998e-123 < x < 3.15e-77

   1. Initial program 71.0%

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

   2. Taylor expanded in i around inf 70.7%

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

      1. distribute-lft-out-- 70.7%

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

      2. *-commutative 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in j around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-in 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

   7. Simplified 70.7%

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

   if 2.79999999999999983e140 < x

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

   4. Simplified 49.7%

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

   5. Taylor expanded in y around inf 49.7%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+69}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-202}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 16: 29.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-b \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* b c)))) (t_2 (* a (* b i))))
   (if (<= x -3.9e+69)
     (* a (* x (- t)))
     (if (<= x -1.1e-201)
       t_1
       (if (<= x 1.02e-253)
         t_2
         (if (<= x 4e-123)
           t_1
           (if (<= x 3.5e-77)
             (* i (- (* y j)))
             (if (<= x 3.9e+140) t_2 (* z (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * -(b * c);
	double t_2 = a * (b * i);
	double tmp;
	if (x <= -3.9e+69) {
		tmp = a * (x * -t);
	} else if (x <= -1.1e-201) {
		tmp = t_1;
	} else if (x <= 1.02e-253) {
		tmp = t_2;
	} else if (x <= 4e-123) {
		tmp = t_1;
	} else if (x <= 3.5e-77) {
		tmp = i * -(y * j);
	} else if (x <= 3.9e+140) {
		tmp = t_2;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -(b * c)
    t_2 = a * (b * i)
    if (x <= (-3.9d+69)) then
        tmp = a * (x * -t)
    else if (x <= (-1.1d-201)) then
        tmp = t_1
    else if (x <= 1.02d-253) then
        tmp = t_2
    else if (x <= 4d-123) then
        tmp = t_1
    else if (x <= 3.5d-77) then
        tmp = i * -(y * j)
    else if (x <= 3.9d+140) then
        tmp = t_2
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * -(b * c);
	double t_2 = a * (b * i);
	double tmp;
	if (x <= -3.9e+69) {
		tmp = a * (x * -t);
	} else if (x <= -1.1e-201) {
		tmp = t_1;
	} else if (x <= 1.02e-253) {
		tmp = t_2;
	} else if (x <= 4e-123) {
		tmp = t_1;
	} else if (x <= 3.5e-77) {
		tmp = i * -(y * j);
	} else if (x <= 3.9e+140) {
		tmp = t_2;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * -(b * c)
	t_2 = a * (b * i)
	tmp = 0
	if x <= -3.9e+69:
		tmp = a * (x * -t)
	elif x <= -1.1e-201:
		tmp = t_1
	elif x <= 1.02e-253:
		tmp = t_2
	elif x <= 4e-123:
		tmp = t_1
	elif x <= 3.5e-77:
		tmp = i * -(y * j)
	elif x <= 3.9e+140:
		tmp = t_2
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(-Float64(b * c)))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (x <= -3.9e+69)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= -1.1e-201)
		tmp = t_1;
	elseif (x <= 1.02e-253)
		tmp = t_2;
	elseif (x <= 4e-123)
		tmp = t_1;
	elseif (x <= 3.5e-77)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (x <= 3.9e+140)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * -(b * c);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (x <= -3.9e+69)
		tmp = a * (x * -t);
	elseif (x <= -1.1e-201)
		tmp = t_1;
	elseif (x <= 1.02e-253)
		tmp = t_2;
	elseif (x <= 4e-123)
		tmp = t_1;
	elseif (x <= 3.5e-77)
		tmp = i * -(y * j);
	elseif (x <= 3.9e+140)
		tmp = t_2;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+69], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.1e-201], t$95$1, If[LessEqual[x, 1.02e-253], t$95$2, If[LessEqual[x, 4e-123], t$95$1, If[LessEqual[x, 3.5e-77], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 3.9e+140], t$95$2, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.8999999999999999e69

   1. Initial program 81.4%

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

   2. Taylor expanded in x around inf 66.3%

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

      1. *-commutative 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in z around 0 49.1%

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

      1. associate-*r* 49.1%

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

      2. neg-mul-1 49.1%

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

   7. Simplified 49.1%

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

   if -3.8999999999999999e69 < x < -1.1e-201 or 1.02e-253 < x < 4.0000000000000002e-123

   1. Initial program 80.0%

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

   2. Taylor expanded in z around inf 39.8%

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

      1. *-commutative 39.8%

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

   4. Simplified 39.8%

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

   5. Taylor expanded in y around 0 34.0%

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

      1. neg-mul-1 34.0%

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

      2. distribute-rgt-neg-in 34.0%

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

   7. Simplified 34.0%

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

   if -1.1e-201 < x < 1.02e-253 or 3.50000000000000013e-77 < x < 3.89999999999999974e140

   1. Initial program 65.5%

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

   2. Taylor expanded in b around inf 52.4%

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

   3. Taylor expanded in a around inf 38.2%

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

   4. Taylor expanded in b around 0 41.2%

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

   if 4.0000000000000002e-123 < x < 3.50000000000000013e-77

   1. Initial program 71.0%

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

   2. Taylor expanded in i around inf 70.7%

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

      1. distribute-lft-out-- 70.7%

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

      2. *-commutative 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in j around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-in 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

   7. Simplified 70.7%

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

   if 3.89999999999999974e140 < x

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

   4. Simplified 49.7%

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

   5. Taylor expanded in y around inf 49.7%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-201}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 17: 28.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -b \cdot \left(z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* z c)))) (t_2 (* a (* b i))))
   (if (<= x -6.6e+63)
     (* a (* x (- t)))
     (if (<= x -6.7e-202)
       t_1
       (if (<= x 3.6e-253)
         t_2
         (if (<= x 4.6e-123)
           t_1
           (if (<= x 3.1e-77)
             (* i (- (* y j)))
             (if (<= x 2.6e+140) t_2 (* z (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -(b * (z * c));
	double t_2 = a * (b * i);
	double tmp;
	if (x <= -6.6e+63) {
		tmp = a * (x * -t);
	} else if (x <= -6.7e-202) {
		tmp = t_1;
	} else if (x <= 3.6e-253) {
		tmp = t_2;
	} else if (x <= 4.6e-123) {
		tmp = t_1;
	} else if (x <= 3.1e-77) {
		tmp = i * -(y * j);
	} else if (x <= 2.6e+140) {
		tmp = t_2;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -(b * (z * c))
    t_2 = a * (b * i)
    if (x <= (-6.6d+63)) then
        tmp = a * (x * -t)
    else if (x <= (-6.7d-202)) then
        tmp = t_1
    else if (x <= 3.6d-253) then
        tmp = t_2
    else if (x <= 4.6d-123) then
        tmp = t_1
    else if (x <= 3.1d-77) then
        tmp = i * -(y * j)
    else if (x <= 2.6d+140) then
        tmp = t_2
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -(b * (z * c));
	double t_2 = a * (b * i);
	double tmp;
	if (x <= -6.6e+63) {
		tmp = a * (x * -t);
	} else if (x <= -6.7e-202) {
		tmp = t_1;
	} else if (x <= 3.6e-253) {
		tmp = t_2;
	} else if (x <= 4.6e-123) {
		tmp = t_1;
	} else if (x <= 3.1e-77) {
		tmp = i * -(y * j);
	} else if (x <= 2.6e+140) {
		tmp = t_2;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -(b * (z * c))
	t_2 = a * (b * i)
	tmp = 0
	if x <= -6.6e+63:
		tmp = a * (x * -t)
	elif x <= -6.7e-202:
		tmp = t_1
	elif x <= 3.6e-253:
		tmp = t_2
	elif x <= 4.6e-123:
		tmp = t_1
	elif x <= 3.1e-77:
		tmp = i * -(y * j)
	elif x <= 2.6e+140:
		tmp = t_2
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(-Float64(b * Float64(z * c)))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (x <= -6.6e+63)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= -6.7e-202)
		tmp = t_1;
	elseif (x <= 3.6e-253)
		tmp = t_2;
	elseif (x <= 4.6e-123)
		tmp = t_1;
	elseif (x <= 3.1e-77)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (x <= 2.6e+140)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -(b * (z * c));
	t_2 = a * (b * i);
	tmp = 0.0;
	if (x <= -6.6e+63)
		tmp = a * (x * -t);
	elseif (x <= -6.7e-202)
		tmp = t_1;
	elseif (x <= 3.6e-253)
		tmp = t_2;
	elseif (x <= 4.6e-123)
		tmp = t_1;
	elseif (x <= 3.1e-77)
		tmp = i * -(y * j);
	elseif (x <= 2.6e+140)
		tmp = t_2;
	else
		tmp = z * (x * y);
	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])}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e+63], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.7e-202], t$95$1, If[LessEqual[x, 3.6e-253], t$95$2, If[LessEqual[x, 4.6e-123], t$95$1, If[LessEqual[x, 3.1e-77], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 2.6e+140], t$95$2, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.6000000000000003e63

   1. Initial program 81.4%

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

   2. Taylor expanded in x around inf 66.3%

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

      1. *-commutative 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in z around 0 49.1%

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

      1. associate-*r* 49.1%

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

      2. neg-mul-1 49.1%

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

   7. Simplified 49.1%

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

   if -6.6000000000000003e63 < x < -6.70000000000000002e-202 or 3.6e-253 < x < 4.59999999999999973e-123

   1. Initial program 80.0%

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

   2. Taylor expanded in b around inf 51.0%

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

   3. Taylor expanded in a around 0 37.2%

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

      1. associate-*r* 37.2%

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

      2. neg-mul-1 37.2%

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

   5. Simplified 37.2%

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

   if -6.70000000000000002e-202 < x < 3.6e-253 or 3.10000000000000008e-77 < x < 2.6000000000000001e140

   1. Initial program 65.5%

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

   2. Taylor expanded in b around inf 52.4%

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

   3. Taylor expanded in a around inf 38.2%

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

   4. Taylor expanded in b around 0 41.2%

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

   if 4.59999999999999973e-123 < x < 3.10000000000000008e-77

   1. Initial program 71.0%

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

   2. Taylor expanded in i around inf 70.7%

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

      1. distribute-lft-out-- 70.7%

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

      2. *-commutative 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in j around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-in 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

   7. Simplified 70.7%

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

   if 2.6000000000000001e140 < x

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

   4. Simplified 49.7%

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

   5. Taylor expanded in y around inf 49.7%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-202}:\\ \;\;\;\;-b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-123}:\\ \;\;\;\;-b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 18: 51.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+116} \lor \neg \left(c \leq 2.2 \cdot 10^{+223}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -3200.0)
     t_1
     (if (<= c 4.9e+65)
       (* a (- (* b i) (* x t)))
       (if (or (<= c 7.4e+116) (not (<= c 2.2e+223)))
         t_1
         (* b (- (* a i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3200.0) {
		tmp = t_1;
	} else if (c <= 4.9e+65) {
		tmp = a * ((b * i) - (x * t));
	} else if ((c <= 7.4e+116) || !(c <= 2.2e+223)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-3200.0d0)) then
        tmp = t_1
    else if (c <= 4.9d+65) then
        tmp = a * ((b * i) - (x * t))
    else if ((c <= 7.4d+116) .or. (.not. (c <= 2.2d+223))) then
        tmp = t_1
    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 t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3200.0) {
		tmp = t_1;
	} else if (c <= 4.9e+65) {
		tmp = a * ((b * i) - (x * t));
	} else if ((c <= 7.4e+116) || !(c <= 2.2e+223)) {
		tmp = t_1;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3200.0:
		tmp = t_1
	elif c <= 4.9e+65:
		tmp = a * ((b * i) - (x * t))
	elif (c <= 7.4e+116) or not (c <= 2.2e+223):
		tmp = t_1
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3200.0)
		tmp = t_1;
	elseif (c <= 4.9e+65)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif ((c <= 7.4e+116) || !(c <= 2.2e+223))
		tmp = t_1;
	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)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3200.0)
		tmp = t_1;
	elseif (c <= 4.9e+65)
		tmp = a * ((b * i) - (x * t));
	elseif ((c <= 7.4e+116) || ~((c <= 2.2e+223)))
		tmp = t_1;
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3200.0], t$95$1, If[LessEqual[c, 4.9e+65], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 7.4e+116], N[Not[LessEqual[c, 2.2e+223]], $MachinePrecision]], t$95$1, N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3200 or 4.89999999999999956e65 < c < 7.4000000000000003e116 or 2.2e223 < c

   1. Initial program 68.7%

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

   2. Taylor expanded in c around inf 68.2%

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

   if -3200 < c < 4.89999999999999956e65

   1. Initial program 82.4%

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

   2. Taylor expanded in y around -inf 75.1%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in a around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

   7. Simplified 52.7%

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

   if 7.4000000000000003e116 < c < 2.2e223

   1. Initial program 70.5%

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

   2. Taylor expanded in b around inf 53.2%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3200:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+116} \lor \neg \left(c \leq 2.2 \cdot 10^{+223}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 19: 44.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-227}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.8e-71)
     t_1
     (if (<= b -2.6e-227)
       (* i (- (* y j)))
       (if (<= b 1.5e-298)
         (* z (* x y))
         (if (<= b 9.6e+26) (* a (- (* b i) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.8e-71) {
		tmp = t_1;
	} else if (b <= -2.6e-227) {
		tmp = i * -(y * j);
	} else if (b <= 1.5e-298) {
		tmp = z * (x * y);
	} else if (b <= 9.6e+26) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.8d-71)) then
        tmp = t_1
    else if (b <= (-2.6d-227)) then
        tmp = i * -(y * j)
    else if (b <= 1.5d-298) then
        tmp = z * (x * y)
    else if (b <= 9.6d+26) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.8e-71) {
		tmp = t_1;
	} else if (b <= -2.6e-227) {
		tmp = i * -(y * j);
	} else if (b <= 1.5e-298) {
		tmp = z * (x * y);
	} else if (b <= 9.6e+26) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.8e-71:
		tmp = t_1
	elif b <= -2.6e-227:
		tmp = i * -(y * j)
	elif b <= 1.5e-298:
		tmp = z * (x * y)
	elif b <= 9.6e+26:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.8e-71)
		tmp = t_1;
	elseif (b <= -2.6e-227)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (b <= 1.5e-298)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 9.6e+26)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.8e-71)
		tmp = t_1;
	elseif (b <= -2.6e-227)
		tmp = i * -(y * j);
	elseif (b <= 1.5e-298)
		tmp = z * (x * y);
	elseif (b <= 9.6e+26)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e-71], t$95$1, If[LessEqual[b, -2.6e-227], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 1.5e-298], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.6e+26], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.8e-71 or 9.60000000000000018e26 < b

   1. Initial program 78.2%

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

   2. Taylor expanded in b around inf 61.7%

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

   if -1.8e-71 < b < -2.60000000000000011e-227

   1. Initial program 61.2%

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

   2. Taylor expanded in i around inf 51.2%

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

      1. distribute-lft-out-- 51.2%

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

      2. *-commutative 51.2%

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

   4. Simplified 51.2%

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

   5. Taylor expanded in j around inf 47.5%

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

      1. mul-1-neg 47.5%

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

      2. distribute-rgt-neg-in 47.5%

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

      3. distribute-rgt-neg-in 47.5%

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

   7. Simplified 47.5%

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

   if -2.60000000000000011e-227 < b < 1.5e-298

   1. Initial program 60.8%

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

   2. Taylor expanded in z around inf 50.3%

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

      1. *-commutative 50.3%

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

   4. Simplified 50.3%

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

   5. Taylor expanded in y around inf 50.1%

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

   if 1.5e-298 < b < 9.60000000000000018e26

   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. Taylor expanded in y around -inf 73.3%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

   7. Simplified 49.7%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-227}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 20: 49.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -0.00105:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -0.00105)
     t_1
     (if (<= b 3.5e-252)
       (* j (- (* t c) (* y i)))
       (if (<= b 3.4e+27) (* a (- (* b i) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -0.00105) {
		tmp = t_1;
	} else if (b <= 3.5e-252) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 3.4e+27) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-0.00105d0)) then
        tmp = t_1
    else if (b <= 3.5d-252) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 3.4d+27) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -0.00105) {
		tmp = t_1;
	} else if (b <= 3.5e-252) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 3.4e+27) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -0.00105:
		tmp = t_1
	elif b <= 3.5e-252:
		tmp = j * ((t * c) - (y * i))
	elif b <= 3.4e+27:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -0.00105)
		tmp = t_1;
	elseif (b <= 3.5e-252)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 3.4e+27)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -0.00105)
		tmp = t_1;
	elseif (b <= 3.5e-252)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 3.4e+27)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.00105], t$95$1, If[LessEqual[b, 3.5e-252], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+27], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.00104999999999999994 or 3.4e27 < b

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf 67.6%

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

   if -0.00104999999999999994 < b < 3.49999999999999986e-252

   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. Taylor expanded in j around inf 56.3%

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

   if 3.49999999999999986e-252 < b < 3.4e27

   1. Initial program 85.6%

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

   2. Taylor expanded in y around -inf 74.8%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in a around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

   7. Simplified 53.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00105:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 21: 51.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -0.00135:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-298}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -0.00135)
     t_1
     (if (<= b 6.8e-298)
       (* j (- (* t c) (* y i)))
       (if (<= b 2.05e+33) (* t (- (* c j) (* x 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -0.00135) {
		tmp = t_1;
	} else if (b <= 6.8e-298) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.05e+33) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-0.00135d0)) then
        tmp = t_1
    else if (b <= 6.8d-298) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 2.05d+33) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -0.00135) {
		tmp = t_1;
	} else if (b <= 6.8e-298) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.05e+33) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -0.00135:
		tmp = t_1
	elif b <= 6.8e-298:
		tmp = j * ((t * c) - (y * i))
	elif b <= 2.05e+33:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -0.00135)
		tmp = t_1;
	elseif (b <= 6.8e-298)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 2.05e+33)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -0.00135)
		tmp = t_1;
	elseif (b <= 6.8e-298)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 2.05e+33)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.00135], t$95$1, If[LessEqual[b, 6.8e-298], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+33], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.0013500000000000001 or 2.04999999999999997e33 < b

   1. Initial program 79.2%

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

   2. Taylor expanded in b around inf 68.4%

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

   if -0.0013500000000000001 < b < 6.8e-298

   1. Initial program 63.2%

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

   2. Taylor expanded in j around inf 56.9%

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

   if 6.8e-298 < b < 2.04999999999999997e33

   1. Initial program 83.4%

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

   2. Taylor expanded in t around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

   4. Simplified 55.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00135:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-298}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 22: 42.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+161} \lor \neg \left(c \leq 3.4 \cdot 10^{+142}\right):\\ \;\;\;\;-b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.5e+161) (not (<= c 3.4e+142)))
   (- (* b (* z c)))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.5e+161) || !(c <= 3.4e+142)) {
		tmp = -(b * (z * c));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2.5d+161)) .or. (.not. (c <= 3.4d+142))) then
        tmp = -(b * (z * c))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.5e+161) || !(c <= 3.4e+142)) {
		tmp = -(b * (z * c));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.5e+161) or not (c <= 3.4e+142):
		tmp = -(b * (z * c))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.5e+161) || !(c <= 3.4e+142))
		tmp = Float64(-Float64(b * Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.5e+161) || ~((c <= 3.4e+142)))
		tmp = -(b * (z * c));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.5e+161], N[Not[LessEqual[c, 3.4e+142]], $MachinePrecision]], (-N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.4999999999999998e161 or 3.3999999999999998e142 < c

   1. Initial program 59.7%

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

   2. Taylor expanded in b around inf 62.2%

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

   3. Taylor expanded in a around 0 58.4%

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

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

   5. Simplified 58.4%

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

   if -2.4999999999999998e161 < c < 3.3999999999999998e142

   1. Initial program 81.3%

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

   2. Taylor expanded in y around -inf 72.3%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in a around inf 48.5%

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

      1. +-commutative 48.5%

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

      2. mul-1-neg 48.5%

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

      3. unsub-neg 48.5%

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

   7. Simplified 48.5%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+161} \lor \neg \left(c \leq 3.4 \cdot 10^{+142}\right):\\ \;\;\;\;-b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 23: 27.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+140} \lor \neg \left(x \leq 4.2 \cdot 10^{+140}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -5e+140) (not (<= x 4.2e+140))) (* x (* y z)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -5e+140) || !(x <= 4.2e+140)) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-5d+140)) .or. (.not. (x <= 4.2d+140))) then
        tmp = x * (y * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -5e+140) || !(x <= 4.2e+140)) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -5e+140) or not (x <= 4.2e+140):
		tmp = x * (y * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -5e+140) || !(x <= 4.2e+140))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -5e+140) || ~((x <= 4.2e+140)))
		tmp = x * (y * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -5e+140], N[Not[LessEqual[x, 4.2e+140]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000008e140 or 4.2000000000000004e140 < x

   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. Taylor expanded in x around inf 71.7%

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

      1. *-commutative 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in z around inf 45.9%

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

   if -5.00000000000000008e140 < x < 4.2000000000000004e140

   1. Initial program 75.2%

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

   2. Taylor expanded in b around inf 48.8%

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

   3. Taylor expanded in a around inf 28.4%

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

   4. Taylor expanded in b around 0 28.9%

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

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+140} \lor \neg \left(x \leq 4.2 \cdot 10^{+140}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 24: 27.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+141}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -4.8e+140)
   (* x (* y z))
   (if (<= x 1.95e+141) (* a (* b i)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -4.8e+140) {
		tmp = x * (y * z);
	} else if (x <= 1.95e+141) {
		tmp = a * (b * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-4.8d+140)) then
        tmp = x * (y * z)
    else if (x <= 1.95d+141) then
        tmp = a * (b * i)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -4.8e+140) {
		tmp = x * (y * z);
	} else if (x <= 1.95e+141) {
		tmp = a * (b * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -4.8e+140:
		tmp = x * (y * z)
	elif x <= 1.95e+141:
		tmp = a * (b * i)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -4.8e+140)
		tmp = Float64(x * Float64(y * z));
	elseif (x <= 1.95e+141)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -4.8e+140)
		tmp = x * (y * z);
	elseif (x <= 1.95e+141)
		tmp = a * (b * i);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -4.8e+140], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+141], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.7999999999999999e140

   1. Initial program 79.4%

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

   2. Taylor expanded in x around inf 75.0%

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

      1. *-commutative 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in z around inf 45.1%

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

   if -4.7999999999999999e140 < x < 1.94999999999999996e141

   1. Initial program 75.2%

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

   2. Taylor expanded in b around inf 48.8%

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

   3. Taylor expanded in a around inf 28.4%

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

   4. Taylor expanded in b around 0 28.9%

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

   if 1.94999999999999996e141 < x

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

   4. Simplified 49.7%

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

   5. Taylor expanded in y around inf 49.7%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+141}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 25: 28.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-27}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.7e-27)
   (* (* t a) (- x))
   (if (<= x 4e+140) (* a (* b i)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.7e-27) {
		tmp = (t * a) * -x;
	} else if (x <= 4e+140) {
		tmp = a * (b * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-1.7d-27)) then
        tmp = (t * a) * -x
    else if (x <= 4d+140) then
        tmp = a * (b * i)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.7e-27) {
		tmp = (t * a) * -x;
	} else if (x <= 4e+140) {
		tmp = a * (b * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.7e-27:
		tmp = (t * a) * -x
	elif x <= 4e+140:
		tmp = a * (b * i)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.7e-27)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (x <= 4e+140)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.7e-27)
		tmp = (t * a) * -x;
	elseif (x <= 4e+140)
		tmp = a * (b * i);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.7e-27], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[x, 4e+140], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999985e-27

   1. Initial program 79.9%

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

   2. Taylor expanded in x around inf 60.4%

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

      1. *-commutative 60.4%

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

   4. Simplified 60.4%

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

   5. Taylor expanded in z around 0 38.5%

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

      1. neg-mul-1 38.5%

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

      2. distribute-rgt-neg-in 38.5%

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

   7. Simplified 38.5%

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

   if -1.69999999999999985e-27 < x < 4.00000000000000024e140

   1. Initial program 73.4%

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

   2. Taylor expanded in b around inf 51.4%

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

   3. Taylor expanded in a around inf 30.6%

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

   4. Taylor expanded in b around 0 32.0%

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

   if 4.00000000000000024e140 < x

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

   4. Simplified 49.7%

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

   5. Taylor expanded in y around inf 49.7%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-27}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 26: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.9%

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

2. Taylor expanded in b around inf 42.6%

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

3. Taylor expanded in a around inf 22.8%

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

4. Taylor expanded in b around 0 21.8%

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

5. Final simplification 21.8%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Alternative 27: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.9%

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

2. Taylor expanded in b around inf 42.6%

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

3. Taylor expanded in a around inf 22.8%

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

4. Final simplification 22.8%

   \[\leadsto b \cdot \left(a \cdot i\right) \]

Developer target: 69.1% 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 2023275 
(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)))))