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

Percentage Accurate: 99.6% → 99.8%

Time: 12.5s

Alternatives: 14

Speedup: 1.2×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = -1.3417401723754592e+99
  2. y = -2.1239460443447692e-285
  3. z = 1.1742434926332434e-293

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: 99.6% 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: 99.8% 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 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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-def 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: 51.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ t_1 := 6 \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+89}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1040000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-250}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-283}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-98}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))) (t_1 (* 6.0 (* z (- y)))))
   (if (<= z -2.6e+89)
     t_0
     (if (<= z -2e+65)
       t_1
       (if (<= z -1040000000.0)
         t_0
         (if (<= z -7.2e-184)
           (* y 4.0)
           (if (<= z -8.2e-250)
             (* x -3.0)
             (if (<= z -8.8e-296)
               (* y 4.0)
               (if (<= z 9.5e-283)
                 (* x -3.0)
                 (if (<= z 5.8e-98)
                   (* y 4.0)
                   (if (<= z 0.65) (* x -3.0) t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = 6.0 * (z * -y);
	double tmp;
	if (z <= -2.6e+89) {
		tmp = t_0;
	} else if (z <= -2e+65) {
		tmp = t_1;
	} else if (z <= -1040000000.0) {
		tmp = t_0;
	} else if (z <= -7.2e-184) {
		tmp = y * 4.0;
	} else if (z <= -8.2e-250) {
		tmp = x * -3.0;
	} else if (z <= -8.8e-296) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-283) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-98) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		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 * (z * 6.0d0)
    t_1 = 6.0d0 * (z * -y)
    if (z <= (-2.6d+89)) then
        tmp = t_0
    else if (z <= (-2d+65)) then
        tmp = t_1
    else if (z <= (-1040000000.0d0)) then
        tmp = t_0
    else if (z <= (-7.2d-184)) then
        tmp = y * 4.0d0
    else if (z <= (-8.2d-250)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8.8d-296)) then
        tmp = y * 4.0d0
    else if (z <= 9.5d-283) then
        tmp = x * (-3.0d0)
    else if (z <= 5.8d-98) then
        tmp = y * 4.0d0
    else if (z <= 0.65d0) 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 * (z * 6.0);
	double t_1 = 6.0 * (z * -y);
	double tmp;
	if (z <= -2.6e+89) {
		tmp = t_0;
	} else if (z <= -2e+65) {
		tmp = t_1;
	} else if (z <= -1040000000.0) {
		tmp = t_0;
	} else if (z <= -7.2e-184) {
		tmp = y * 4.0;
	} else if (z <= -8.2e-250) {
		tmp = x * -3.0;
	} else if (z <= -8.8e-296) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-283) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-98) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	t_1 = 6.0 * (z * -y)
	tmp = 0
	if z <= -2.6e+89:
		tmp = t_0
	elif z <= -2e+65:
		tmp = t_1
	elif z <= -1040000000.0:
		tmp = t_0
	elif z <= -7.2e-184:
		tmp = y * 4.0
	elif z <= -8.2e-250:
		tmp = x * -3.0
	elif z <= -8.8e-296:
		tmp = y * 4.0
	elif z <= 9.5e-283:
		tmp = x * -3.0
	elif z <= 5.8e-98:
		tmp = y * 4.0
	elif z <= 0.65:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	t_1 = Float64(6.0 * Float64(z * Float64(-y)))
	tmp = 0.0
	if (z <= -2.6e+89)
		tmp = t_0;
	elseif (z <= -2e+65)
		tmp = t_1;
	elseif (z <= -1040000000.0)
		tmp = t_0;
	elseif (z <= -7.2e-184)
		tmp = Float64(y * 4.0);
	elseif (z <= -8.2e-250)
		tmp = Float64(x * -3.0);
	elseif (z <= -8.8e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.5e-283)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.8e-98)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.65)
		tmp = Float64(x * -3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	t_1 = 6.0 * (z * -y);
	tmp = 0.0;
	if (z <= -2.6e+89)
		tmp = t_0;
	elseif (z <= -2e+65)
		tmp = t_1;
	elseif (z <= -1040000000.0)
		tmp = t_0;
	elseif (z <= -7.2e-184)
		tmp = y * 4.0;
	elseif (z <= -8.2e-250)
		tmp = x * -3.0;
	elseif (z <= -8.8e-296)
		tmp = y * 4.0;
	elseif (z <= 9.5e-283)
		tmp = x * -3.0;
	elseif (z <= 5.8e-98)
		tmp = y * 4.0;
	elseif (z <= 0.65)
		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[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+89], t$95$0, If[LessEqual[z, -2e+65], t$95$1, If[LessEqual[z, -1040000000.0], t$95$0, If[LessEqual[z, -7.2e-184], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -8.2e-250], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8.8e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.5e-283], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.8e-98], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000001e89 or -2e65 < z < -1.04e9

   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 67.0%

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

      1. sub-neg 67.0%

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

      2. distribute-rgt-in 67.0%

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

      3. metadata-eval 67.0%

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

      4. metadata-eval 67.0%

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

      5. distribute-lft-neg-in 67.0%

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

      6. associate-+r+ 67.0%

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

      7. metadata-eval 67.0%

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

      8. metadata-eval 67.0%

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

      9. distribute-rgt-neg-in 67.0%

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

      10. metadata-eval 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in z around inf 66.2%

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

      1. *-commutative 66.2%

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

   10. Simplified 66.2%

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

   if -2.6000000000000001e89 < z < -2e65 or 0.650000000000000022 < z

   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 x around 0 96.9%

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

      1. fma-def 96.9%

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

      2. *-commutative 96.9%

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

   7. Simplified 96.9%

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

   8. Taylor expanded in y around inf 66.5%

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

   9. Taylor expanded in z around inf 66.2%

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

       1. neg-mul-1 66.2%

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

   11. Simplified 66.2%

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

   if -1.04e9 < z < -7.2000000000000002e-184 or -8.20000000000000032e-250 < z < -8.80000000000000048e-296 or 9.49999999999999979e-283 < z < 5.8e-98

   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 0 99.6%

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

      1. fma-def 99.7%

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

      2. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*l* 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in z around 0 63.4%

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

   if -7.2000000000000002e-184 < z < -8.20000000000000032e-250 or -8.80000000000000048e-296 < z < 9.49999999999999979e-283 or 5.8e-98 < z < 0.650000000000000022

   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 x around inf 80.1%

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

      1. sub-neg 80.1%

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

      2. distribute-rgt-in 80.1%

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

      3. metadata-eval 80.1%

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

      4. metadata-eval 80.1%

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

      5. distribute-lft-neg-in 80.1%

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

      6. associate-+r+ 80.1%

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

      7. metadata-eval 80.1%

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

      8. metadata-eval 80.1%

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

      9. distribute-rgt-neg-in 80.1%

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

      10. metadata-eval 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around 0 78.8%

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

      1. *-commutative 78.8%

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

   10. Simplified 78.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+65}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{elif}\;z \leq -1040000000:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-250}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-283}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-98}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1040000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-251}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -1040000000.0)
     t_0
     (if (<= z -5.8e-189)
       (* y 4.0)
       (if (<= z -1.9e-251)
         (* x -3.0)
         (if (<= z -3.6e-296)
           (* y 4.0)
           (if (<= z 3e-283)
             (* x -3.0)
             (if (<= z 1.6e-97)
               (* y 4.0)
               (if (<= z 0.5) (* x -3.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -1040000000.0) {
		tmp = t_0;
	} else if (z <= -5.8e-189) {
		tmp = y * 4.0;
	} else if (z <= -1.9e-251) {
		tmp = x * -3.0;
	} else if (z <= -3.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 3e-283) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-97) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_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 = 6.0d0 * (x * z)
    if (z <= (-1040000000.0d0)) then
        tmp = t_0
    else if (z <= (-5.8d-189)) then
        tmp = y * 4.0d0
    else if (z <= (-1.9d-251)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.6d-296)) then
        tmp = y * 4.0d0
    else if (z <= 3d-283) then
        tmp = x * (-3.0d0)
    else if (z <= 1.6d-97) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -1040000000.0) {
		tmp = t_0;
	} else if (z <= -5.8e-189) {
		tmp = y * 4.0;
	} else if (z <= -1.9e-251) {
		tmp = x * -3.0;
	} else if (z <= -3.6e-296) {
		tmp = y * 4.0;
	} else if (z <= 3e-283) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-97) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -1040000000.0:
		tmp = t_0
	elif z <= -5.8e-189:
		tmp = y * 4.0
	elif z <= -1.9e-251:
		tmp = x * -3.0
	elif z <= -3.6e-296:
		tmp = y * 4.0
	elif z <= 3e-283:
		tmp = x * -3.0
	elif z <= 1.6e-97:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1040000000.0)
		tmp = t_0;
	elseif (z <= -5.8e-189)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.9e-251)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.6e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 3e-283)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.6e-97)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1040000000.0)
		tmp = t_0;
	elseif (z <= -5.8e-189)
		tmp = y * 4.0;
	elseif (z <= -1.9e-251)
		tmp = x * -3.0;
	elseif (z <= -3.6e-296)
		tmp = y * 4.0;
	elseif (z <= 3e-283)
		tmp = x * -3.0;
	elseif (z <= 1.6e-97)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1040000000.0], t$95$0, If[LessEqual[z, -5.8e-189], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.9e-251], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.6e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3e-283], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.6e-97], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04e9 or 0.5 < z

   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 x around inf 51.1%

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

      1. sub-neg 51.1%

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

      2. distribute-rgt-in 51.1%

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

      3. metadata-eval 51.1%

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

      4. metadata-eval 51.1%

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

      5. distribute-lft-neg-in 51.1%

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

      6. associate-+r+ 51.1%

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

      7. metadata-eval 51.1%

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

      8. metadata-eval 51.1%

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

      9. distribute-rgt-neg-in 51.1%

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

      10. metadata-eval 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in z around inf 50.6%

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

   if -1.04e9 < z < -5.8e-189 or -1.8999999999999999e-251 < z < -3.5999999999999998e-296 or 2.99999999999999996e-283 < z < 1.5999999999999999e-97

   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 0 99.6%

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

      1. fma-def 99.7%

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

      2. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*l* 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in z around 0 63.4%

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

   if -5.8e-189 < z < -1.8999999999999999e-251 or -3.5999999999999998e-296 < z < 2.99999999999999996e-283 or 1.5999999999999999e-97 < z < 0.5

   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. 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 x around inf 80.1%

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

      1. sub-neg 80.1%

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

      2. distribute-rgt-in 80.1%

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

      3. metadata-eval 80.1%

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

      4. metadata-eval 80.1%

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

      5. distribute-lft-neg-in 80.1%

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

      6. associate-+r+ 80.1%

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

      7. metadata-eval 80.1%

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

      8. metadata-eval 80.1%

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

      9. distribute-rgt-neg-in 80.1%

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

      10. metadata-eval 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around 0 78.8%

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

      1. *-commutative 78.8%

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

   10. Simplified 78.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1040000000:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-251}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-283}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1040000000:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-193}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-239}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-284}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-98}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1040000000.0)
   (* x (* z 6.0))
   (if (<= z -1.85e-193)
     (* y 4.0)
     (if (<= z -4.4e-239)
       (* x -3.0)
       (if (<= z -8.5e-298)
         (* y 4.0)
         (if (<= z 2.8e-284)
           (* x -3.0)
           (if (<= z 5.5e-98)
             (* y 4.0)
             (if (<= z 0.5) (* x -3.0) (* 6.0 (* x z))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1040000000.0) {
		tmp = x * (z * 6.0);
	} else if (z <= -1.85e-193) {
		tmp = y * 4.0;
	} else if (z <= -4.4e-239) {
		tmp = x * -3.0;
	} else if (z <= -8.5e-298) {
		tmp = y * 4.0;
	} else if (z <= 2.8e-284) {
		tmp = x * -3.0;
	} else if (z <= 5.5e-98) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (x * 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) :: tmp
    if (z <= (-1040000000.0d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-1.85d-193)) then
        tmp = y * 4.0d0
    else if (z <= (-4.4d-239)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8.5d-298)) then
        tmp = y * 4.0d0
    else if (z <= 2.8d-284) then
        tmp = x * (-3.0d0)
    else if (z <= 5.5d-98) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1040000000.0) {
		tmp = x * (z * 6.0);
	} else if (z <= -1.85e-193) {
		tmp = y * 4.0;
	} else if (z <= -4.4e-239) {
		tmp = x * -3.0;
	} else if (z <= -8.5e-298) {
		tmp = y * 4.0;
	} else if (z <= 2.8e-284) {
		tmp = x * -3.0;
	} else if (z <= 5.5e-98) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1040000000.0:
		tmp = x * (z * 6.0)
	elif z <= -1.85e-193:
		tmp = y * 4.0
	elif z <= -4.4e-239:
		tmp = x * -3.0
	elif z <= -8.5e-298:
		tmp = y * 4.0
	elif z <= 2.8e-284:
		tmp = x * -3.0
	elif z <= 5.5e-98:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1040000000.0)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -1.85e-193)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.4e-239)
		tmp = Float64(x * -3.0);
	elseif (z <= -8.5e-298)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.8e-284)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.5e-98)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1040000000.0)
		tmp = x * (z * 6.0);
	elseif (z <= -1.85e-193)
		tmp = y * 4.0;
	elseif (z <= -4.4e-239)
		tmp = x * -3.0;
	elseif (z <= -8.5e-298)
		tmp = y * 4.0;
	elseif (z <= 2.8e-284)
		tmp = x * -3.0;
	elseif (z <= 5.5e-98)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1040000000.0], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-193], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.4e-239], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8.5e-298], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.8e-284], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.5e-98], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.04e9

   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 61.3%

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

      1. sub-neg 61.3%

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

      2. distribute-rgt-in 61.3%

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

      3. metadata-eval 61.3%

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

      4. metadata-eval 61.3%

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

      5. distribute-lft-neg-in 61.3%

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

      6. associate-+r+ 61.3%

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

      7. metadata-eval 61.3%

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

      8. metadata-eval 61.3%

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

      9. distribute-rgt-neg-in 61.3%

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

      10. metadata-eval 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in z around inf 60.6%

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

      1. *-commutative 60.6%

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

   10. Simplified 60.6%

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

   if -1.04e9 < z < -1.8500000000000001e-193 or -4.39999999999999965e-239 < z < -8.49999999999999957e-298 or 2.8000000000000003e-284 < z < 5.4999999999999997e-98

   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 0 99.6%

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

      1. fma-def 99.7%

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

      2. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*l* 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in z around 0 63.4%

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

   if -1.8500000000000001e-193 < z < -4.39999999999999965e-239 or -8.49999999999999957e-298 < z < 2.8000000000000003e-284 or 5.4999999999999997e-98 < z < 0.5

   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. 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 x around inf 80.1%

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

      1. sub-neg 80.1%

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

      2. distribute-rgt-in 80.1%

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

      3. metadata-eval 80.1%

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

      4. metadata-eval 80.1%

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

      5. distribute-lft-neg-in 80.1%

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

      6. associate-+r+ 80.1%

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

      7. metadata-eval 80.1%

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

      8. metadata-eval 80.1%

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

      9. distribute-rgt-neg-in 80.1%

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

      10. metadata-eval 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around 0 78.8%

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

      1. *-commutative 78.8%

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

   10. Simplified 78.8%

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

   if 0.5 < z

   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 x around inf 41.0%

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

      1. sub-neg 41.0%

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

      2. distribute-rgt-in 41.0%

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

      3. metadata-eval 41.0%

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

      4. metadata-eval 41.0%

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

      5. distribute-lft-neg-in 41.0%

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

      6. associate-+r+ 41.0%

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

      7. metadata-eval 41.0%

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

      8. metadata-eval 41.0%

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

      9. distribute-rgt-neg-in 41.0%

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

      10. metadata-eval 41.0%

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

   7. Simplified 41.0%

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

   8. Taylor expanded in z around inf 40.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1040000000:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-193}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-239}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-284}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-98}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1040000000:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-195}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-243}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-284}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-98}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1040000000.0)
   (* x (* z 6.0))
   (if (<= z -3.35e-195)
     (* y 4.0)
     (if (<= z -3.9e-243)
       (* x -3.0)
       (if (<= z -5.8e-298)
         (* y 4.0)
         (if (<= z 5.5e-284)
           (* x -3.0)
           (if (<= z 1.85e-98)
             (* y 4.0)
             (if (<= z 0.5) (* x -3.0) (* z (* x 6.0))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1040000000.0) {
		tmp = x * (z * 6.0);
	} else if (z <= -3.35e-195) {
		tmp = y * 4.0;
	} else if (z <= -3.9e-243) {
		tmp = x * -3.0;
	} else if (z <= -5.8e-298) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-284) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-98) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = z * (x * 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) :: tmp
    if (z <= (-1040000000.0d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-3.35d-195)) then
        tmp = y * 4.0d0
    else if (z <= (-3.9d-243)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.8d-298)) then
        tmp = y * 4.0d0
    else if (z <= 5.5d-284) then
        tmp = x * (-3.0d0)
    else if (z <= 1.85d-98) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = z * (x * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1040000000.0) {
		tmp = x * (z * 6.0);
	} else if (z <= -3.35e-195) {
		tmp = y * 4.0;
	} else if (z <= -3.9e-243) {
		tmp = x * -3.0;
	} else if (z <= -5.8e-298) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-284) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-98) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1040000000.0:
		tmp = x * (z * 6.0)
	elif z <= -3.35e-195:
		tmp = y * 4.0
	elif z <= -3.9e-243:
		tmp = x * -3.0
	elif z <= -5.8e-298:
		tmp = y * 4.0
	elif z <= 5.5e-284:
		tmp = x * -3.0
	elif z <= 1.85e-98:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = z * (x * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1040000000.0)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -3.35e-195)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.9e-243)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.8e-298)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.5e-284)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.85e-98)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(z * Float64(x * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1040000000.0)
		tmp = x * (z * 6.0);
	elseif (z <= -3.35e-195)
		tmp = y * 4.0;
	elseif (z <= -3.9e-243)
		tmp = x * -3.0;
	elseif (z <= -5.8e-298)
		tmp = y * 4.0;
	elseif (z <= 5.5e-284)
		tmp = x * -3.0;
	elseif (z <= 1.85e-98)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = z * (x * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1040000000.0], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.35e-195], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.9e-243], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.8e-298], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.5e-284], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.85e-98], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.04e9

   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 61.3%

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

      1. sub-neg 61.3%

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

      2. distribute-rgt-in 61.3%

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

      3. metadata-eval 61.3%

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

      4. metadata-eval 61.3%

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

      5. distribute-lft-neg-in 61.3%

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

      6. associate-+r+ 61.3%

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

      7. metadata-eval 61.3%

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

      8. metadata-eval 61.3%

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

      9. distribute-rgt-neg-in 61.3%

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

      10. metadata-eval 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in z around inf 60.6%

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

      1. *-commutative 60.6%

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

   10. Simplified 60.6%

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

   if -1.04e9 < z < -3.3500000000000001e-195 or -3.90000000000000015e-243 < z < -5.8000000000000003e-298 or 5.4999999999999995e-284 < z < 1.85e-98

   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 0 99.6%

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

      1. fma-def 99.7%

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

      2. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*l* 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in z around 0 63.4%

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

   if -3.3500000000000001e-195 < z < -3.90000000000000015e-243 or -5.8000000000000003e-298 < z < 5.4999999999999995e-284 or 1.85e-98 < z < 0.5

   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. 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 x around inf 80.1%

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

      1. sub-neg 80.1%

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

      2. distribute-rgt-in 80.1%

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

      3. metadata-eval 80.1%

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

      4. metadata-eval 80.1%

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

      5. distribute-lft-neg-in 80.1%

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

      6. associate-+r+ 80.1%

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

      7. metadata-eval 80.1%

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

      8. metadata-eval 80.1%

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

      9. distribute-rgt-neg-in 80.1%

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

      10. metadata-eval 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in z around 0 78.8%

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

      1. *-commutative 78.8%

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

   10. Simplified 78.8%

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

   if 0.5 < z

   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 x around inf 41.0%

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

      1. sub-neg 41.0%

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

      2. distribute-rgt-in 41.0%

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

      3. metadata-eval 41.0%

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

      4. metadata-eval 41.0%

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

      5. distribute-lft-neg-in 41.0%

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

      6. associate-+r+ 41.0%

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

      7. metadata-eval 41.0%

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

      8. metadata-eval 41.0%

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

      9. distribute-rgt-neg-in 41.0%

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

      10. metadata-eval 41.0%

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

   7. Simplified 41.0%

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

   8. Taylor expanded in z around inf 40.7%

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

      1. associate-*r* 40.8%

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

      2. *-commutative 40.8%

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

   10. Simplified 40.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1040000000:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-195}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-243}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-284}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-98}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{-62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq 26000000:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+36}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -5.8e-62)
     t_0
     (if (<= x 1.05e-76)
       (* y (+ 4.0 (* z -6.0)))
       (if (<= x 26000000.0)
         (+ x (* (- y x) 4.0))
         (if (<= x 2.6e+36) (* 6.0 (* y (- 0.6666666666666666 z))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -5.8e-62) {
		tmp = t_0;
	} else if (x <= 1.05e-76) {
		tmp = y * (4.0 + (z * -6.0));
	} else if (x <= 26000000.0) {
		tmp = x + ((y - x) * 4.0);
	} else if (x <= 2.6e+36) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_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 <= (-5.8d-62)) then
        tmp = t_0
    else if (x <= 1.05d-76) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else if (x <= 26000000.0d0) then
        tmp = x + ((y - x) * 4.0d0)
    else if (x <= 2.6d+36) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = t_0
    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 <= -5.8e-62) {
		tmp = t_0;
	} else if (x <= 1.05e-76) {
		tmp = y * (4.0 + (z * -6.0));
	} else if (x <= 26000000.0) {
		tmp = x + ((y - x) * 4.0);
	} else if (x <= 2.6e+36) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -5.8e-62:
		tmp = t_0
	elif x <= 1.05e-76:
		tmp = y * (4.0 + (z * -6.0))
	elif x <= 26000000.0:
		tmp = x + ((y - x) * 4.0)
	elif x <= 2.6e+36:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_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 <= -5.8e-62)
		tmp = t_0;
	elseif (x <= 1.05e-76)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	elseif (x <= 26000000.0)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	elseif (x <= 2.6e+36)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = t_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 <= -5.8e-62)
		tmp = t_0;
	elseif (x <= 1.05e-76)
		tmp = y * (4.0 + (z * -6.0));
	elseif (x <= 26000000.0)
		tmp = x + ((y - x) * 4.0);
	elseif (x <= 2.6e+36)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = t_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, -5.8e-62], t$95$0, If[LessEqual[x, 1.05e-76], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 26000000.0], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+36], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.79999999999999971e-62 or 2.6000000000000001e36 < x

   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 x around inf 80.8%

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

      1. sub-neg 80.8%

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

      2. distribute-rgt-in 80.8%

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

      3. metadata-eval 80.8%

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

      4. metadata-eval 80.8%

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

      5. distribute-lft-neg-in 80.8%

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

      6. associate-+r+ 80.8%

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

      7. metadata-eval 80.8%

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

      8. metadata-eval 80.8%

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

      9. distribute-rgt-neg-in 80.8%

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

      10. metadata-eval 80.8%

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

   7. Simplified 80.8%

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

   if -5.79999999999999971e-62 < x < 1.04999999999999996e-76

   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-def 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 83.8%

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

   if 1.04999999999999996e-76 < x < 2.6e7

   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 z around 0 79.3%

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

   if 2.6e7 < x < 2.6000000000000001e36

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 97.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq 26000000:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+36}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq 195000000:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+35}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -1.7e-62)
     t_0
     (if (<= x 1.05e-76)
       (* y (+ 4.0 (* z -6.0)))
       (if (<= x 195000000.0)
         (+ (* y 4.0) (* x -3.0))
         (if (<= x 9.8e+35) (* 6.0 (* y (- 0.6666666666666666 z))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1.7e-62) {
		tmp = t_0;
	} else if (x <= 1.05e-76) {
		tmp = y * (4.0 + (z * -6.0));
	} else if (x <= 195000000.0) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (x <= 9.8e+35) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_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 <= (-1.7d-62)) then
        tmp = t_0
    else if (x <= 1.05d-76) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else if (x <= 195000000.0d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else if (x <= 9.8d+35) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = t_0
    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 <= -1.7e-62) {
		tmp = t_0;
	} else if (x <= 1.05e-76) {
		tmp = y * (4.0 + (z * -6.0));
	} else if (x <= 195000000.0) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (x <= 9.8e+35) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -1.7e-62:
		tmp = t_0
	elif x <= 1.05e-76:
		tmp = y * (4.0 + (z * -6.0))
	elif x <= 195000000.0:
		tmp = (y * 4.0) + (x * -3.0)
	elif x <= 9.8e+35:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_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 <= -1.7e-62)
		tmp = t_0;
	elseif (x <= 1.05e-76)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	elseif (x <= 195000000.0)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	elseif (x <= 9.8e+35)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = t_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 <= -1.7e-62)
		tmp = t_0;
	elseif (x <= 1.05e-76)
		tmp = y * (4.0 + (z * -6.0));
	elseif (x <= 195000000.0)
		tmp = (y * 4.0) + (x * -3.0);
	elseif (x <= 9.8e+35)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = t_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, -1.7e-62], t$95$0, If[LessEqual[x, 1.05e-76], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 195000000.0], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+35], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.69999999999999994e-62 or 9.8000000000000005e35 < x

   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 x around inf 80.8%

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

      1. sub-neg 80.8%

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

      2. distribute-rgt-in 80.8%

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

      3. metadata-eval 80.8%

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

      4. metadata-eval 80.8%

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

      5. distribute-lft-neg-in 80.8%

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

      6. associate-+r+ 80.8%

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

      7. metadata-eval 80.8%

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

      8. metadata-eval 80.8%

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

      9. distribute-rgt-neg-in 80.8%

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

      10. metadata-eval 80.8%

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

   7. Simplified 80.8%

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

   if -1.69999999999999994e-62 < x < 1.04999999999999996e-76

   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-def 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 83.8%

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

   if 1.04999999999999996e-76 < x < 1.95e8

   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. +-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around -inf 99.8%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]

   6. Taylor expanded in z around 0 79.4%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 1.95e8 < x < 9.8000000000000005e35

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 97.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq 195000000:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+35}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{-74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq 1.68 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z)))))
   (if (<= y -6.2e-74)
     t_0
     (if (<= y 1.18e-295)
       (* x -3.0)
       (if (<= y 1.68e-122) (* x (* z 6.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -6.2e-74) {
		tmp = t_0;
	} else if (y <= 1.18e-295) {
		tmp = x * -3.0;
	} else if (y <= 1.68e-122) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_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 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    if (y <= (-6.2d-74)) then
        tmp = t_0
    else if (y <= 1.18d-295) then
        tmp = x * (-3.0d0)
    else if (y <= 1.68d-122) then
        tmp = x * (z * 6.0d0)
    else
        tmp = t_0
    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 tmp;
	if (y <= -6.2e-74) {
		tmp = t_0;
	} else if (y <= 1.18e-295) {
		tmp = x * -3.0;
	} else if (y <= 1.68e-122) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	tmp = 0
	if y <= -6.2e-74:
		tmp = t_0
	elif y <= 1.18e-295:
		tmp = x * -3.0
	elif y <= 1.68e-122:
		tmp = x * (z * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	tmp = 0.0
	if (y <= -6.2e-74)
		tmp = t_0;
	elseif (y <= 1.18e-295)
		tmp = Float64(x * -3.0);
	elseif (y <= 1.68e-122)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	tmp = 0.0;
	if (y <= -6.2e-74)
		tmp = t_0;
	elseif (y <= 1.18e-295)
		tmp = x * -3.0;
	elseif (y <= 1.68e-122)
		tmp = x * (z * 6.0);
	else
		tmp = t_0;
	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]}, If[LessEqual[y, -6.2e-74], t$95$0, If[LessEqual[y, 1.18e-295], N[(x * -3.0), $MachinePrecision], If[LessEqual[y, 1.68e-122], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2000000000000003e-74 or 1.6799999999999999e-122 < y

   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 x around 0 96.7%

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

      1. fma-def 96.7%

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

      2. *-commutative 96.7%

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

   7. Simplified 96.7%

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

   8. Taylor expanded in y around inf 70.0%

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

   if -6.2000000000000003e-74 < y < 1.18e-295

   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 84.9%

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

      1. sub-neg 84.9%

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

      2. distribute-rgt-in 84.9%

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

      3. metadata-eval 84.9%

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

      4. metadata-eval 84.9%

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

      5. distribute-lft-neg-in 84.9%

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

      6. associate-+r+ 84.9%

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

      7. metadata-eval 84.9%

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

      8. metadata-eval 84.9%

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

      9. distribute-rgt-neg-in 84.9%

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

      10. metadata-eval 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in z around 0 57.6%

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

      1. *-commutative 57.6%

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

   10. Simplified 57.6%

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

   if 1.18e-295 < y < 1.6799999999999999e-122

   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 75.5%

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

      1. sub-neg 75.5%

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

      2. distribute-rgt-in 75.5%

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

      3. metadata-eval 75.5%

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

      4. metadata-eval 75.5%

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

      5. distribute-lft-neg-in 75.5%

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

      6. associate-+r+ 75.5%

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

      7. metadata-eval 75.5%

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

      8. metadata-eval 75.5%

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

      9. distribute-rgt-neg-in 75.5%

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

      10. metadata-eval 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in z around inf 51.3%

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

      1. *-commutative 51.3%

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

   10. Simplified 51.3%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-74}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq 1.68 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.68 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.68) (not (<= z 0.5)))
   (+ x (* -6.0 (* (- y x) z)))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.68) || !(z <= 0.5)) {
		tmp = x + (-6.0 * ((y - x) * z));
	} else {
		tmp = (y * 4.0) + (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 <= (-0.68d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = x + ((-6.0d0) * ((y - x) * z))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.68) || !(z <= 0.5)) {
		tmp = x + (-6.0 * ((y - x) * z));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.68) or not (z <= 0.5):
		tmp = x + (-6.0 * ((y - x) * z))
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.68) || !(z <= 0.5))
		tmp = Float64(x + Float64(-6.0 * Float64(Float64(y - x) * z)));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.68) || ~((z <= 0.5)))
		tmp = x + (-6.0 * ((y - x) * z));
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.68], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.680000000000000049 or 0.5 < z

   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 z around inf 98.3%

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

   if -0.680000000000000049 < z < 0.5

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]

   6. Taylor expanded in z around 0 98.8%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-62} \lor \neg \left(x \leq 5.8 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.9e-62) (not (<= x 5.8e+35)))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.9e-62) || !(x <= 5.8e+35)) {
		tmp = x * (-3.0 + (z * 6.0));
	} 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) :: tmp
    if ((x <= (-2.9d-62)) .or. (.not. (x <= 5.8d+35))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    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 tmp;
	if ((x <= -2.9e-62) || !(x <= 5.8e+35)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.9e-62) or not (x <= 5.8e+35):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.9e-62) || !(x <= 5.8e+35))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.9e-62) || ~((x <= 5.8e+35)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.9e-62], N[Not[LessEqual[x, 5.8e+35]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.89999999999999986e-62 or 5.79999999999999989e35 < x

   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 x around inf 80.8%

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

      1. sub-neg 80.8%

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

      2. distribute-rgt-in 80.8%

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

      3. metadata-eval 80.8%

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

      4. metadata-eval 80.8%

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

      5. distribute-lft-neg-in 80.8%

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

      6. associate-+r+ 80.8%

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

      7. metadata-eval 80.8%

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

      8. metadata-eval 80.8%

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

      9. distribute-rgt-neg-in 80.8%

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

      10. metadata-eval 80.8%

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

   7. Simplified 80.8%

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

   if -2.89999999999999986e-62 < x < 5.79999999999999989e35

   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 0 99.6%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 80.1%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-62} \lor \neg \left(x \leq 5.8 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-62} \lor \neg \left(x \leq 2.5 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e-62) (not (<= x 2.5e+35)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e-62) || !(x <= 2.5e+35)) {
		tmp = x * (-3.0 + (z * 6.0));
	} 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) :: tmp
    if ((x <= (-3.3d-62)) .or. (.not. (x <= 2.5d+35))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    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 tmp;
	if ((x <= -3.3e-62) || !(x <= 2.5e+35)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e-62) or not (x <= 2.5e+35):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e-62) || !(x <= 2.5e+35))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.3e-62) || ~((x <= 2.5e+35)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e-62], N[Not[LessEqual[x, 2.5e+35]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.30000000000000004e-62 or 2.50000000000000011e35 < x

   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 x around inf 80.8%

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

      1. sub-neg 80.8%

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

      2. distribute-rgt-in 80.8%

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

      3. metadata-eval 80.8%

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

      4. metadata-eval 80.8%

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

      5. distribute-lft-neg-in 80.8%

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

      6. associate-+r+ 80.8%

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

      7. metadata-eval 80.8%

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

      8. metadata-eval 80.8%

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

      9. distribute-rgt-neg-in 80.8%

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

      10. metadata-eval 80.8%

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

   7. Simplified 80.8%

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

   if -3.30000000000000004e-62 < x < 2.50000000000000011e35

   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-def 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 80.2%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-62} \lor \neg \left(x \leq 2.5 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-55} \lor \neg \left(x \leq 1.12 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e-55) (not (<= x 1.12e-7))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-55) || !(x <= 1.12e-7)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	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 ((x <= (-1.5d-55)) .or. (.not. (x <= 1.12d-7))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-55) || !(x <= 1.12e-7)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e-55) or not (x <= 1.12e-7):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e-55) || !(x <= 1.12e-7))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.5e-55) || ~((x <= 1.12e-7)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e-55], N[Not[LessEqual[x, 1.12e-7]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000008e-55 or 1.12e-7 < x

   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 x around inf 78.1%

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

      1. sub-neg 78.1%

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

      2. distribute-rgt-in 78.1%

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

      3. metadata-eval 78.1%

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

      4. metadata-eval 78.1%

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

      5. distribute-lft-neg-in 78.1%

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

      6. associate-+r+ 78.1%

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

      7. metadata-eval 78.1%

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

      8. metadata-eval 78.1%

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

      9. distribute-rgt-neg-in 78.1%

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

      10. metadata-eval 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in z around 0 39.8%

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

      1. *-commutative 39.8%

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

   10. Simplified 39.8%

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

   if -1.50000000000000008e-55 < x < 1.12e-7

   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 0 99.6%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around inf 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*l* 90.5%

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

   10. Simplified 90.5%

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

   11. Taylor expanded in z around 0 42.2%

       \[\leadsto \color{blue}{4 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-55} \lor \neg \left(x \leq 1.12 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.6% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - 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) * (0.6666666666666666d0 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 99.6%

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

Alternative 14: 26.9% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y \cdot 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 4.0))

C

double code(double x, double y, double z) {
	return y * 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 = y * 4.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * 4.0), $MachinePrecision]

Derivation

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 x around 0 97.8%

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

   1. fma-def 97.8%

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

   2. *-commutative 97.8%

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

7. Simplified 97.8%

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

8. Taylor expanded in z around inf 73.5%

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

   1. *-commutative 73.5%

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

   2. associate-*l* 73.5%

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

10. Simplified 73.5%

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

11. Taylor expanded in z around 0 25.6%

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

12. Final simplification 25.6%

    \[\leadsto y \cdot 4 \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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))))