Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Percentage Accurate: 99.5% → 99.7%

Time: 11.7s

Alternatives: 15

Speedup: 1.2×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (+ 4.0 (* z -6.0)) x))

C

double code(double x, double y, double z) {
	return fma((y - x), (4.0 + (z * -6.0)), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(4.0 + Float64(z * -6.0)), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.5%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

   5. distribute-rgt-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

   7. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

   8. distribute-lft-neg-out 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

   9. distribute-rgt-neg-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

   10. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right) \]
6. Add Preprocessing

Alternative 2: 51.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x + y \cdot 4\\ t_2 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+121}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -18000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-111}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-270}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (+ x (* y 4.0))) (t_2 (* x (* z 6.0))))
   (if (<= z -2.4e+121)
     t_0
     (if (<= z -7.6e+74)
       t_2
       (if (<= z -18000000.0)
         t_0
         (if (<= z -1.3e-111)
           (* x -3.0)
           (if (<= z -8e-181)
             t_1
             (if (<= z -2.9e-270)
               (* x -3.0)
               (if (<= z 2e-217) t_1 (if (<= z 0.065) (* x -3.0) t_2))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x + (y * 4.0);
	double t_2 = x * (z * 6.0);
	double tmp;
	if (z <= -2.4e+121) {
		tmp = t_0;
	} else if (z <= -7.6e+74) {
		tmp = t_2;
	} else if (z <= -18000000.0) {
		tmp = t_0;
	} else if (z <= -1.3e-111) {
		tmp = x * -3.0;
	} else if (z <= -8e-181) {
		tmp = t_1;
	} else if (z <= -2.9e-270) {
		tmp = x * -3.0;
	} else if (z <= 2e-217) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x * -3.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x + (y * 4.0d0)
    t_2 = x * (z * 6.0d0)
    if (z <= (-2.4d+121)) then
        tmp = t_0
    else if (z <= (-7.6d+74)) then
        tmp = t_2
    else if (z <= (-18000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.3d-111)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8d-181)) then
        tmp = t_1
    else if (z <= (-2.9d-270)) then
        tmp = x * (-3.0d0)
    else if (z <= 2d-217) then
        tmp = t_1
    else if (z <= 0.065d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x + (y * 4.0);
	double t_2 = x * (z * 6.0);
	double tmp;
	if (z <= -2.4e+121) {
		tmp = t_0;
	} else if (z <= -7.6e+74) {
		tmp = t_2;
	} else if (z <= -18000000.0) {
		tmp = t_0;
	} else if (z <= -1.3e-111) {
		tmp = x * -3.0;
	} else if (z <= -8e-181) {
		tmp = t_1;
	} else if (z <= -2.9e-270) {
		tmp = x * -3.0;
	} else if (z <= 2e-217) {
		tmp = t_1;
	} else if (z <= 0.065) {
		tmp = x * -3.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x + (y * 4.0)
	t_2 = x * (z * 6.0)
	tmp = 0
	if z <= -2.4e+121:
		tmp = t_0
	elif z <= -7.6e+74:
		tmp = t_2
	elif z <= -18000000.0:
		tmp = t_0
	elif z <= -1.3e-111:
		tmp = x * -3.0
	elif z <= -8e-181:
		tmp = t_1
	elif z <= -2.9e-270:
		tmp = x * -3.0
	elif z <= 2e-217:
		tmp = t_1
	elif z <= 0.065:
		tmp = x * -3.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(x + Float64(y * 4.0))
	t_2 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -2.4e+121)
		tmp = t_0;
	elseif (z <= -7.6e+74)
		tmp = t_2;
	elseif (z <= -18000000.0)
		tmp = t_0;
	elseif (z <= -1.3e-111)
		tmp = Float64(x * -3.0);
	elseif (z <= -8e-181)
		tmp = t_1;
	elseif (z <= -2.9e-270)
		tmp = Float64(x * -3.0);
	elseif (z <= 2e-217)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = Float64(x * -3.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = x + (y * 4.0);
	t_2 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -2.4e+121)
		tmp = t_0;
	elseif (z <= -7.6e+74)
		tmp = t_2;
	elseif (z <= -18000000.0)
		tmp = t_0;
	elseif (z <= -1.3e-111)
		tmp = x * -3.0;
	elseif (z <= -8e-181)
		tmp = t_1;
	elseif (z <= -2.9e-270)
		tmp = x * -3.0;
	elseif (z <= 2e-217)
		tmp = t_1;
	elseif (z <= 0.065)
		tmp = x * -3.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+121], t$95$0, If[LessEqual[z, -7.6e+74], t$95$2, If[LessEqual[z, -18000000.0], t$95$0, If[LessEqual[z, -1.3e-111], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8e-181], t$95$1, If[LessEqual[z, -2.9e-270], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2e-217], t$95$1, If[LessEqual[z, 0.065], N[(x * -3.0), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4e121 or -7.5999999999999997e74 < z < -1.8e7

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 62.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]

   if -2.4e121 < z < -7.5999999999999997e74 or 0.065000000000000002 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 59.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 59.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 59.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 59.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 59.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 59.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 59.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 59.7%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 59.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around inf 59.5%

      \[\leadsto x \cdot \color{blue}{\left(6 \cdot z\right)} \]

   if -1.8e7 < z < -1.29999999999999991e-111 or -8.00000000000000038e-181 < z < -2.89999999999999983e-270 or 2.00000000000000016e-217 < z < 0.065000000000000002

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.2%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 63.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 63.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 63.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 63.3%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 63.3%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 63.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 63.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 63.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 63.3%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 61.1%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 61.1%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 61.1%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -1.29999999999999991e-111 < z < -8.00000000000000038e-181 or -2.89999999999999983e-270 < z < 2.00000000000000016e-217

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.9%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

   7. Simplified 68.8%

      \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

   8. Taylor expanded in z around 0 69.2%

      \[\leadsto x + \color{blue}{4 \cdot y} \]
   9. Step-by-step derivation

      1. *-commutative 69.2%

         \[\leadsto x + \color{blue}{y \cdot 4} \]

   10. Simplified 69.2%

       \[\leadsto x + \color{blue}{y \cdot 4} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+121}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -18000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-111}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-181}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-270}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-217}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0146:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-111}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-181}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-271}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-216}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0146)
     t_1
     (if (<= z -1.45e-111)
       (* x -3.0)
       (if (<= z -7.8e-181)
         t_0
         (if (<= z -5.5e-271)
           (* x -3.0)
           (if (<= z 2.2e-216) t_0 (if (<= z 0.5) (* x -3.0) t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0146) {
		tmp = t_1;
	} else if (z <= -1.45e-111) {
		tmp = x * -3.0;
	} else if (z <= -7.8e-181) {
		tmp = t_0;
	} else if (z <= -5.5e-271) {
		tmp = x * -3.0;
	} else if (z <= 2.2e-216) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y * 4.0d0)
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.0146d0)) then
        tmp = t_1
    else if (z <= (-1.45d-111)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7.8d-181)) then
        tmp = t_0
    else if (z <= (-5.5d-271)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.2d-216) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0146) {
		tmp = t_1;
	} else if (z <= -1.45e-111) {
		tmp = x * -3.0;
	} else if (z <= -7.8e-181) {
		tmp = t_0;
	} else if (z <= -5.5e-271) {
		tmp = x * -3.0;
	} else if (z <= 2.2e-216) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0146:
		tmp = t_1
	elif z <= -1.45e-111:
		tmp = x * -3.0
	elif z <= -7.8e-181:
		tmp = t_0
	elif z <= -5.5e-271:
		tmp = x * -3.0
	elif z <= 2.2e-216:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0146)
		tmp = t_1;
	elseif (z <= -1.45e-111)
		tmp = Float64(x * -3.0);
	elseif (z <= -7.8e-181)
		tmp = t_0;
	elseif (z <= -5.5e-271)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.2e-216)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.0146)
		tmp = t_1;
	elseif (z <= -1.45e-111)
		tmp = x * -3.0;
	elseif (z <= -7.8e-181)
		tmp = t_0;
	elseif (z <= -5.5e-271)
		tmp = x * -3.0;
	elseif (z <= 2.2e-216)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0146], t$95$1, If[LessEqual[z, -1.45e-111], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7.8e-181], t$95$0, If[LessEqual[z, -5.5e-271], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.2e-216], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0146000000000000001 or 0.5 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.6%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.0146000000000000001 < z < -1.45000000000000001e-111 or -7.800000000000001e-181 < z < -5.4999999999999996e-271 or 2.1999999999999999e-216 < z < 0.5

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.2%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 62.2%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 62.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 62.2%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 62.2%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 62.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 62.2%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 62.2%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 62.2%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 62.2%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 61.0%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 61.0%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 61.0%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -1.45000000000000001e-111 < z < -7.800000000000001e-181 or -5.4999999999999996e-271 < z < 2.1999999999999999e-216

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.9%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

   7. Simplified 68.8%

      \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

   8. Taylor expanded in z around 0 69.2%

      \[\leadsto x + \color{blue}{4 \cdot y} \]
   9. Step-by-step derivation

      1. *-commutative 69.2%

         \[\leadsto x + \color{blue}{y \cdot 4} \]

   10. Simplified 69.2%

       \[\leadsto x + \color{blue}{y \cdot 4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0146:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-111}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-181}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-271}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-216}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0096:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-111}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-180}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-240}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-216}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0096)
     t_1
     (if (<= z -3e-111)
       (* x -3.0)
       (if (<= z -1.2e-180)
         t_0
         (if (<= z -2.25e-240)
           (* x -3.0)
           (if (<= z 3.6e-216) t_0 (if (<= z 0.5) (* x -3.0) t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0096) {
		tmp = t_1;
	} else if (z <= -3e-111) {
		tmp = x * -3.0;
	} else if (z <= -1.2e-180) {
		tmp = t_0;
	} else if (z <= -2.25e-240) {
		tmp = x * -3.0;
	} else if (z <= 3.6e-216) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.0096d0)) then
        tmp = t_1
    else if (z <= (-3d-111)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.2d-180)) then
        tmp = t_0
    else if (z <= (-2.25d-240)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.6d-216) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0096) {
		tmp = t_1;
	} else if (z <= -3e-111) {
		tmp = x * -3.0;
	} else if (z <= -1.2e-180) {
		tmp = t_0;
	} else if (z <= -2.25e-240) {
		tmp = x * -3.0;
	} else if (z <= 3.6e-216) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0096:
		tmp = t_1
	elif z <= -3e-111:
		tmp = x * -3.0
	elif z <= -1.2e-180:
		tmp = t_0
	elif z <= -2.25e-240:
		tmp = x * -3.0
	elif z <= 3.6e-216:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0096)
		tmp = t_1;
	elseif (z <= -3e-111)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.2e-180)
		tmp = t_0;
	elseif (z <= -2.25e-240)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.6e-216)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.0096)
		tmp = t_1;
	elseif (z <= -3e-111)
		tmp = x * -3.0;
	elseif (z <= -1.2e-180)
		tmp = t_0;
	elseif (z <= -2.25e-240)
		tmp = x * -3.0;
	elseif (z <= 3.6e-216)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0096], t$95$1, If[LessEqual[z, -3e-111], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.2e-180], t$95$0, If[LessEqual[z, -2.25e-240], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.6e-216], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00959999999999999916 or 0.5 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.6%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.00959999999999999916 < z < -3.00000000000000008e-111 or -1.1999999999999999e-180 < z < -2.2500000000000001e-240 or 3.5999999999999999e-216 < z < 0.5

   1. Initial program 99.1%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.1%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 63.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 63.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 63.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 63.6%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 63.6%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 63.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 63.6%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 63.6%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 63.6%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 63.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 62.2%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 62.2%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 62.2%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -3.00000000000000008e-111 < z < -1.1999999999999999e-180 or -2.2500000000000001e-240 < z < 3.5999999999999999e-216

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 93.7%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot \frac{x \cdot \left(0.6666666666666666 - z\right)}{y} + \left(6 \cdot \left(0.6666666666666666 - z\right) + \frac{x}{y}\right)\right)} \]

   6. Taylor expanded in y around inf 66.0%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 66.0%

         \[\leadsto 6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot y\right)} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{6 \cdot \left(\left(0.6666666666666666 - z\right) \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0096:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-111}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-180}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-240}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-216}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-9}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-108} \lor \neg \left(x \leq 3 \cdot 10^{-5}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -1e+73)
     t_0
     (if (<= x -7.6e-9)
       (* -6.0 (* (- y x) z))
       (if (or (<= x -5.3e-108) (not (<= x 3e-5)))
         t_0
         (* 6.0 (* y (- 0.6666666666666666 z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1e+73) {
		tmp = t_0;
	} else if (x <= -7.6e-9) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((x <= -5.3e-108) || !(x <= 3e-5)) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-1d+73)) then
        tmp = t_0
    else if (x <= (-7.6d-9)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if ((x <= (-5.3d-108)) .or. (.not. (x <= 3d-5))) then
        tmp = t_0
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1e+73) {
		tmp = t_0;
	} else if (x <= -7.6e-9) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((x <= -5.3e-108) || !(x <= 3e-5)) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -1e+73:
		tmp = t_0
	elif x <= -7.6e-9:
		tmp = -6.0 * ((y - x) * z)
	elif (x <= -5.3e-108) or not (x <= 3e-5):
		tmp = t_0
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -1e+73)
		tmp = t_0;
	elseif (x <= -7.6e-9)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif ((x <= -5.3e-108) || !(x <= 3e-5))
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -1e+73)
		tmp = t_0;
	elseif (x <= -7.6e-9)
		tmp = -6.0 * ((y - x) * z);
	elseif ((x <= -5.3e-108) || ~((x <= 3e-5)))
		tmp = t_0;
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+73], t$95$0, If[LessEqual[x, -7.6e-9], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.3e-108], N[Not[LessEqual[x, 3e-5]], $MachinePrecision]], t$95$0, N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999983e72 or -7.60000000000000023e-9 < x < -5.29999999999999989e-108 or 3.00000000000000008e-5 < x

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 77.8%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 77.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 77.8%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 77.8%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 77.8%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 77.8%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 77.8%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 77.8%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   if -9.99999999999999983e72 < x < -7.60000000000000023e-9

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 76.5%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -5.29999999999999989e-108 < x < 3.00000000000000008e-5

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 97.7%

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot \frac{x \cdot \left(0.6666666666666666 - z\right)}{y} + \left(6 \cdot \left(0.6666666666666666 - z\right) + \frac{x}{y}\right)\right)} \]

   6. Taylor expanded in y around inf 84.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto 6 \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot y\right)} \]

   8. Simplified 84.7%

      \[\leadsto \color{blue}{6 \cdot \left(\left(0.6666666666666666 - z\right) \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-9}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-108} \lor \neg \left(x \leq 3 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-37} \lor \neg \left(x \leq 3.8 \cdot 10^{-5}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -1.4e+74)
     t_0
     (if (<= x -9e-10)
       (* -6.0 (* (- y x) z))
       (if (or (<= x -3.1e-37) (not (<= x 3.8e-5)))
         t_0
         (* y (+ 4.0 (* z -6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1.4e+74) {
		tmp = t_0;
	} else if (x <= -9e-10) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((x <= -3.1e-37) || !(x <= 3.8e-5)) {
		tmp = t_0;
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-1.4d+74)) then
        tmp = t_0
    else if (x <= (-9d-10)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if ((x <= (-3.1d-37)) .or. (.not. (x <= 3.8d-5))) then
        tmp = t_0
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1.4e+74) {
		tmp = t_0;
	} else if (x <= -9e-10) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((x <= -3.1e-37) || !(x <= 3.8e-5)) {
		tmp = t_0;
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -1.4e+74:
		tmp = t_0
	elif x <= -9e-10:
		tmp = -6.0 * ((y - x) * z)
	elif (x <= -3.1e-37) or not (x <= 3.8e-5):
		tmp = t_0
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -1.4e+74)
		tmp = t_0;
	elseif (x <= -9e-10)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif ((x <= -3.1e-37) || !(x <= 3.8e-5))
		tmp = t_0;
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -1.4e+74)
		tmp = t_0;
	elseif (x <= -9e-10)
		tmp = -6.0 * ((y - x) * z);
	elseif ((x <= -3.1e-37) || ~((x <= 3.8e-5)))
		tmp = t_0;
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+74], t$95$0, If[LessEqual[x, -9e-10], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.1e-37], N[Not[LessEqual[x, 3.8e-5]], $MachinePrecision]], t$95$0, N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.40000000000000001e74 or -8.9999999999999999e-10 < x < -3.09999999999999993e-37 or 3.8000000000000002e-5 < x

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 81.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 81.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 81.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 81.3%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 81.3%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 81.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 81.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 81.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 81.3%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 81.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   if -1.40000000000000001e74 < x < -8.9999999999999999e-10

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 76.5%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -3.09999999999999993e-37 < x < 3.8000000000000002e-5

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.3%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-37} \lor \neg \left(x \leq 3.8 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -18000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -7.2e+118)
     t_0
     (if (<= z -9.5e+74)
       t_1
       (if (<= z -18000000.0) t_0 (if (<= z 0.065) (* x -3.0) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -7.2e+118) {
		tmp = t_0;
	} else if (z <= -9.5e+74) {
		tmp = t_1;
	} else if (z <= -18000000.0) {
		tmp = t_0;
	} else if (z <= 0.065) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-7.2d+118)) then
        tmp = t_0
    else if (z <= (-9.5d+74)) then
        tmp = t_1
    else if (z <= (-18000000.0d0)) then
        tmp = t_0
    else if (z <= 0.065d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -7.2e+118) {
		tmp = t_0;
	} else if (z <= -9.5e+74) {
		tmp = t_1;
	} else if (z <= -18000000.0) {
		tmp = t_0;
	} else if (z <= 0.065) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -7.2e+118:
		tmp = t_0
	elif z <= -9.5e+74:
		tmp = t_1
	elif z <= -18000000.0:
		tmp = t_0
	elif z <= 0.065:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -7.2e+118)
		tmp = t_0;
	elseif (z <= -9.5e+74)
		tmp = t_1;
	elseif (z <= -18000000.0)
		tmp = t_0;
	elseif (z <= 0.065)
		tmp = Float64(x * -3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -7.2e+118)
		tmp = t_0;
	elseif (z <= -9.5e+74)
		tmp = t_1;
	elseif (z <= -18000000.0)
		tmp = t_0;
	elseif (z <= 0.065)
		tmp = x * -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+118], t$95$0, If[LessEqual[z, -9.5e+74], t$95$1, If[LessEqual[z, -18000000.0], t$95$0, If[LessEqual[z, 0.065], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e118 or -9.5000000000000006e74 < z < -1.8e7

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 62.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]

   if -7.2e118 < z < -9.5000000000000006e74 or 0.065000000000000002 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 97.2%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around 0 59.4%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   if -1.8e7 < z < 0.065000000000000002

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 53.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 53.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 53.6%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 53.6%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 53.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 53.6%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 53.6%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 53.6%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 53.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 52.1%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 52.1%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+118}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+74}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -18000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+123}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -18000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* x (* z 6.0))))
   (if (<= z -7.2e+123)
     t_0
     (if (<= z -8.5e+74)
       t_1
       (if (<= z -18000000.0) t_0 (if (<= z 0.065) (* x -3.0) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -7.2e+123) {
		tmp = t_0;
	} else if (z <= -8.5e+74) {
		tmp = t_1;
	} else if (z <= -18000000.0) {
		tmp = t_0;
	} else if (z <= 0.065) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x * (z * 6.0d0)
    if (z <= (-7.2d+123)) then
        tmp = t_0
    else if (z <= (-8.5d+74)) then
        tmp = t_1
    else if (z <= (-18000000.0d0)) then
        tmp = t_0
    else if (z <= 0.065d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -7.2e+123) {
		tmp = t_0;
	} else if (z <= -8.5e+74) {
		tmp = t_1;
	} else if (z <= -18000000.0) {
		tmp = t_0;
	} else if (z <= 0.065) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -7.2e+123:
		tmp = t_0
	elif z <= -8.5e+74:
		tmp = t_1
	elif z <= -18000000.0:
		tmp = t_0
	elif z <= 0.065:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -7.2e+123)
		tmp = t_0;
	elseif (z <= -8.5e+74)
		tmp = t_1;
	elseif (z <= -18000000.0)
		tmp = t_0;
	elseif (z <= 0.065)
		tmp = Float64(x * -3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -7.2e+123)
		tmp = t_0;
	elseif (z <= -8.5e+74)
		tmp = t_1;
	elseif (z <= -18000000.0)
		tmp = t_0;
	elseif (z <= 0.065)
		tmp = x * -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+123], t$95$0, If[LessEqual[z, -8.5e+74], t$95$1, If[LessEqual[z, -18000000.0], t$95$0, If[LessEqual[z, 0.065], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999996e123 or -8.50000000000000028e74 < z < -1.8e7

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 62.7%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]

   if -7.19999999999999996e123 < z < -8.50000000000000028e74 or 0.065000000000000002 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 59.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 59.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 59.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 59.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 59.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 59.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 59.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 59.7%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 59.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around inf 59.5%

      \[\leadsto x \cdot \color{blue}{\left(6 \cdot z\right)} \]

   if -1.8e7 < z < 0.065000000000000002

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 53.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 53.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 53.6%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 53.6%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 53.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 53.6%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 53.6%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 53.6%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 53.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 52.1%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 52.1%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+123}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -18000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x - 4 \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.56)
   (* (- y x) (* z -6.0))
   (if (<= z 0.6) (- x (* 4.0 (- x y))) (+ x (* z (* 6.0 (- x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.56) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.6) {
		tmp = x - (4.0 * (x - y));
	} else {
		tmp = x + (z * (6.0 * (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.56d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.6d0) then
        tmp = x - (4.0d0 * (x - y))
    else
        tmp = x + (z * (6.0d0 * (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.56) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.6) {
		tmp = x - (4.0 * (x - y));
	} else {
		tmp = x + (z * (6.0 * (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.56:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.6:
		tmp = x - (4.0 * (x - y))
	else:
		tmp = x + (z * (6.0 * (x - y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.56)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.6)
		tmp = Float64(x - Float64(4.0 * Float64(x - y)));
	else
		tmp = Float64(x + Float64(z * Float64(6.0 * Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.56)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.6)
		tmp = x - (4.0 * (x - y));
	else
		tmp = x + (z * (6.0 * (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.56], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.6], N[(x - N[(4.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.56000000000000005

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.6%

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

      1. associate-*r* 98.9%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.9%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(y - x\right)} \]

   if -0.56000000000000005 < z < 0.599999999999999978

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 97.9%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   if 0.599999999999999978 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 98.8%

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

      1. neg-mul-1 98.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(-z\right)} \]

   7. Simplified 98.8%

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

      1. *-commutative 98.8%

         \[\leadsto x + \color{blue}{\left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} \]

      2. add-sqr-sqrt 0.0%

         \[\leadsto x + \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      3. sqrt-unprod 0.6%

         \[\leadsto x + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      4. sqr-neg 0.6%

         \[\leadsto x + \sqrt{\color{blue}{z \cdot z}} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      5. sqrt-unprod 0.6%

         \[\leadsto x + \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      6. add-sqr-sqrt 0.6%

         \[\leadsto x + \color{blue}{z} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      7. cancel-sign-sub 0.6%

         \[\leadsto \color{blue}{x - \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} \]

      8. add-sqr-sqrt 0.0%

         \[\leadsto x - \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      9. sqrt-unprod 89.4%

         \[\leadsto x - \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      10. sqr-neg 89.4%

          \[\leadsto x - \sqrt{\color{blue}{z \cdot z}} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      11. sqrt-unprod 98.3%

          \[\leadsto x - \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      12. add-sqr-sqrt 98.8%

          \[\leadsto x - \color{blue}{z} \cdot \left(\left(y - x\right) \cdot 6\right) \]

      13. *-commutative 98.8%

          \[\leadsto x - z \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} \]

   9. Applied egg-rr 98.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x - 4 \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.54\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x - 4 \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.54)))
   (* (- y x) (* z -6.0))
   (- x (* 4.0 (- x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.54)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x - (4.0 * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.6d0)) .or. (.not. (z <= 0.54d0))) then
        tmp = (y - x) * (z * (-6.0d0))
    else
        tmp = x - (4.0d0 * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.54)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x - (4.0 * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.54):
		tmp = (y - x) * (z * -6.0)
	else:
		tmp = x - (4.0 * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.54))
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	else
		tmp = Float64(x - Float64(4.0 * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.54)))
		tmp = (y - x) * (z * -6.0);
	else
		tmp = x - (4.0 * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.54]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(4.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.54000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.6%

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

      1. associate-*r* 98.8%

         \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.8%

         \[\leadsto \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

   8. Simplified 98.8%

      \[\leadsto \color{blue}{\left(z \cdot -6\right) \cdot \left(y - x\right)} \]

   if -0.599999999999999978 < z < 0.54000000000000004

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 97.9%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.54\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x - 4 \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -18000000 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -18000000.0) (not (<= z 0.65))) (* -6.0 (* y z)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -18000000.0) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-18000000.0d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -18000000.0) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -18000000.0) or not (z <= 0.65):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -18000000.0) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -18000000.0) || ~((z <= 0.65)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -18000000.0], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e7 or 0.650000000000000022 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.9%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 52.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]

   if -1.8e7 < z < 0.650000000000000022

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. sub-neg 53.2%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 53.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 53.2%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. distribute-lft-neg-in 53.2%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      5. associate-+r+ 53.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

      6. metadata-eval 53.2%

         \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

      7. distribute-rgt-neg-in 53.2%

         \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

      8. metadata-eval 53.2%

         \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   7. Simplified 53.2%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   8. Taylor expanded in z around 0 51.7%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 51.7%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 51.7%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18000000 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ x + \left(-6 \cdot \left(\left(y - x\right) \cdot z\right) + \left(y - x\right) \cdot 4\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (+ (* -6.0 (* (- y x) z)) (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	return x + ((-6.0 * ((y - x) * z)) + ((y - x) * 4.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((-6.0d0) * ((y - x) * z)) + ((y - x) * 4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((-6.0 * ((y - x) * z)) + ((y - x) * 4.0));
}

Python

def code(x, y, z):
	return x + ((-6.0 * ((y - x) * z)) + ((y - x) * 4.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(-6.0 * Float64(Float64(y - x) * z)) + Float64(Float64(y - x) * 4.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((-6.0 * ((y - x) * z)) + ((y - x) * 4.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 99.7%

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

6. Final simplification 99.7%

   \[\leadsto x + \left(-6 \cdot \left(\left(y - x\right) \cdot z\right) + \left(y - x\right) \cdot 4\right) \]
7. Add Preprocessing

Alternative 13: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(6 \cdot \left(x - y\right)\right) \cdot \left(z - 0.6666666666666666\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* 6.0 (- x y)) (- z 0.6666666666666666))))

C

double code(double x, double y, double z) {
	return x + ((6.0 * (x - y)) * (z - 0.6666666666666666));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((6.0d0 * (x - y)) * (z - 0.6666666666666666d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((6.0 * (x - y)) * (z - 0.6666666666666666));
}

Python

def code(x, y, z):
	return x + ((6.0 * (x - y)) * (z - 0.6666666666666666))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(6.0 * Float64(x - y)) * Float64(z - 0.6666666666666666)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((6.0 * (x - y)) * (z - 0.6666666666666666));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] * N[(z - 0.6666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Final simplification 99.5%

   \[\leadsto x + \left(6 \cdot \left(x - y\right)\right) \cdot \left(z - 0.6666666666666666\right) \]
6. Add Preprocessing

Alternative 14: 26.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 52.1%

   \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
6. Step-by-step derivation

   1. sub-neg 52.1%

      \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

   2. distribute-rgt-in 52.2%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

   3. metadata-eval 52.2%

      \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

   4. distribute-lft-neg-in 52.2%

      \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

   5. associate-+r+ 52.2%

      \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   6. metadata-eval 52.2%

      \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-z \cdot -6\right)\right) \]

   7. distribute-rgt-neg-in 52.2%

      \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(--6\right)}\right) \]

   8. metadata-eval 52.2%

      \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

7. Simplified 52.2%

   \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

8. Taylor expanded in z around 0 28.3%

   \[\leadsto \color{blue}{-3 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 28.3%

      \[\leadsto \color{blue}{x \cdot -3} \]

10. Simplified 28.3%

    \[\leadsto \color{blue}{x \cdot -3} \]

11. Final simplification 28.3%

    \[\leadsto x \cdot -3 \]
12. Add Preprocessing

Alternative 15: 2.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 50.2%

   \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
6. Step-by-step derivation

   1. associate-*r* 50.3%

      \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

7. Simplified 50.3%

   \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

8. Taylor expanded in x around inf 2.6%

   \[\leadsto \color{blue}{x} \]

9. Final simplification 2.6%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))