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

Percentage Accurate: 99.5% → 99.8%

Time: 9.5s

Alternatives: 16

Speedup: 1.2×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% 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 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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. Final simplification 99.8%

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

Alternative 2: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+245}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-293}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-184}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+136}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))) (t_1 (* -6.0 (* y z))))
   (if (<= z -6.8e+245)
     t_0
     (if (<= z -2.2e+57)
       t_1
       (if (<= z -0.5)
         t_0
         (if (<= z -9e-186)
           (* x -3.0)
           (if (<= z 4.4e-293)
             (* y 4.0)
             (if (<= z 6e-184)
               (* x -3.0)
               (if (<= z 0.5) (* y 4.0) (if (<= z 5.8e+136) t_0 t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -6.8e+245) {
		tmp = t_0;
	} else if (z <= -2.2e+57) {
		tmp = t_1;
	} else if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -9e-186) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-293) {
		tmp = y * 4.0;
	} else if (z <= 6e-184) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else if (z <= 5.8e+136) {
		tmp = t_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) * (y * z)
    if (z <= (-6.8d+245)) then
        tmp = t_0
    else if (z <= (-2.2d+57)) then
        tmp = t_1
    else if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-9d-186)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.4d-293) then
        tmp = y * 4.0d0
    else if (z <= 6d-184) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else if (z <= 5.8d+136) then
        tmp = t_0
    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 * (y * z);
	double tmp;
	if (z <= -6.8e+245) {
		tmp = t_0;
	} else if (z <= -2.2e+57) {
		tmp = t_1;
	} else if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -9e-186) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-293) {
		tmp = y * 4.0;
	} else if (z <= 6e-184) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else if (z <= 5.8e+136) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -6.8e+245:
		tmp = t_0
	elif z <= -2.2e+57:
		tmp = t_1
	elif z <= -0.5:
		tmp = t_0
	elif z <= -9e-186:
		tmp = x * -3.0
	elif z <= 4.4e-293:
		tmp = y * 4.0
	elif z <= 6e-184:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	elif z <= 5.8e+136:
		tmp = t_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(y * z))
	tmp = 0.0
	if (z <= -6.8e+245)
		tmp = t_0;
	elseif (z <= -2.2e+57)
		tmp = t_1;
	elseif (z <= -0.5)
		tmp = t_0;
	elseif (z <= -9e-186)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.4e-293)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e-184)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.8e+136)
		tmp = t_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 * (y * z);
	tmp = 0.0;
	if (z <= -6.8e+245)
		tmp = t_0;
	elseif (z <= -2.2e+57)
		tmp = t_1;
	elseif (z <= -0.5)
		tmp = t_0;
	elseif (z <= -9e-186)
		tmp = x * -3.0;
	elseif (z <= 4.4e-293)
		tmp = y * 4.0;
	elseif (z <= 6e-184)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	elseif (z <= 5.8e+136)
		tmp = t_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[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+245], t$95$0, If[LessEqual[z, -2.2e+57], t$95$1, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -9e-186], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.4e-293], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e-184], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.8e+136], t$95$0, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999996e245 or -2.2000000000000001e57 < z < -0.5 or 0.5 < z < 5.79999999999999949e136

   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. Taylor expanded in x around inf 65.1%

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

      1. sub-neg 65.1%

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

      2. distribute-rgt-in 65.1%

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

      3. metadata-eval 65.1%

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

      4. metadata-eval 65.1%

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

      5. neg-mul-1 65.1%

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

      6. associate-*r* 65.1%

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

      7. *-commutative 65.1%

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

      8. associate-+r+ 65.1%

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

      9. metadata-eval 65.1%

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

      10. metadata-eval 65.1%

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

      11. associate-*r* 65.1%

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

      12. metadata-eval 65.1%

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

      13. *-commutative 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in z around inf 64.2%

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

   if -6.79999999999999996e245 < z < -2.2000000000000001e57 or 5.79999999999999949e136 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      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. Taylor expanded in y around inf 61.5%

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

   5. Taylor expanded in z around inf 61.5%

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

   if -0.5 < z < -8.9999999999999996e-186 or 4.4e-293 < z < 5.99999999999999982e-184

   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. Taylor expanded in x around inf 63.8%

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

      1. sub-neg 63.8%

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

      2. distribute-rgt-in 63.9%

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

      3. metadata-eval 63.9%

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

      4. metadata-eval 63.9%

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

      5. neg-mul-1 63.9%

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

      6. associate-*r* 63.9%

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

      7. *-commutative 63.9%

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

      8. associate-+r+ 63.9%

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

      9. metadata-eval 63.9%

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

      10. metadata-eval 63.9%

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

      11. associate-*r* 63.9%

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

      12. metadata-eval 63.9%

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

      13. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in z around 0 62.4%

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

      1. *-commutative 62.4%

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

   9. Simplified 62.4%

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

   if -8.9999999999999996e-186 < z < 4.4e-293 or 5.99999999999999982e-184 < z < 0.5

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      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. Taylor expanded in y around inf 64.1%

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

   5. Taylor expanded in z around 0 60.8%

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

      1. *-commutative 60.8%

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

   7. Simplified 60.8%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+57}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-293}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-184}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 3: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+246}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+134}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -7.2e+246)
     t_0
     (if (<= z -9.5e+55)
       (* y (* z -6.0))
       (if (<= z -0.5)
         t_0
         (if (<= z -5.6e-186)
           (* x -3.0)
           (if (<= z 8.5e-296)
             (* y 4.0)
             (if (<= z 1.42e-185)
               (* x -3.0)
               (if (<= z 0.6)
                 (* y 4.0)
                 (if (<= z 3.35e+134) t_0 (* -6.0 (* y z))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -7.2e+246) {
		tmp = t_0;
	} else if (z <= -9.5e+55) {
		tmp = y * (z * -6.0);
	} else if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -5.6e-186) {
		tmp = x * -3.0;
	} else if (z <= 8.5e-296) {
		tmp = y * 4.0;
	} else if (z <= 1.42e-185) {
		tmp = x * -3.0;
	} else if (z <= 0.6) {
		tmp = y * 4.0;
	} else if (z <= 3.35e+134) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-7.2d+246)) then
        tmp = t_0
    else if (z <= (-9.5d+55)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-5.6d-186)) then
        tmp = x * (-3.0d0)
    else if (z <= 8.5d-296) then
        tmp = y * 4.0d0
    else if (z <= 1.42d-185) then
        tmp = x * (-3.0d0)
    else if (z <= 0.6d0) then
        tmp = y * 4.0d0
    else if (z <= 3.35d+134) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (y * z)
    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 tmp;
	if (z <= -7.2e+246) {
		tmp = t_0;
	} else if (z <= -9.5e+55) {
		tmp = y * (z * -6.0);
	} else if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -5.6e-186) {
		tmp = x * -3.0;
	} else if (z <= 8.5e-296) {
		tmp = y * 4.0;
	} else if (z <= 1.42e-185) {
		tmp = x * -3.0;
	} else if (z <= 0.6) {
		tmp = y * 4.0;
	} else if (z <= 3.35e+134) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -7.2e+246:
		tmp = t_0
	elif z <= -9.5e+55:
		tmp = y * (z * -6.0)
	elif z <= -0.5:
		tmp = t_0
	elif z <= -5.6e-186:
		tmp = x * -3.0
	elif z <= 8.5e-296:
		tmp = y * 4.0
	elif z <= 1.42e-185:
		tmp = x * -3.0
	elif z <= 0.6:
		tmp = y * 4.0
	elif z <= 3.35e+134:
		tmp = t_0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -7.2e+246)
		tmp = t_0;
	elseif (z <= -9.5e+55)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -0.5)
		tmp = t_0;
	elseif (z <= -5.6e-186)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.5e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.42e-185)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.6)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.35e+134)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -7.2e+246)
		tmp = t_0;
	elseif (z <= -9.5e+55)
		tmp = y * (z * -6.0);
	elseif (z <= -0.5)
		tmp = t_0;
	elseif (z <= -5.6e-186)
		tmp = x * -3.0;
	elseif (z <= 8.5e-296)
		tmp = y * 4.0;
	elseif (z <= 1.42e-185)
		tmp = x * -3.0;
	elseif (z <= 0.6)
		tmp = y * 4.0;
	elseif (z <= 3.35e+134)
		tmp = t_0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+246], t$95$0, If[LessEqual[z, -9.5e+55], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -5.6e-186], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.5e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.42e-185], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.6], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.35e+134], t$95$0, N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.2e246 or -9.49999999999999989e55 < z < -0.5 or 0.599999999999999978 < z < 3.3499999999999998e134

   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. Taylor expanded in x around inf 65.1%

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

      1. sub-neg 65.1%

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

      2. distribute-rgt-in 65.1%

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

      3. metadata-eval 65.1%

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

      4. metadata-eval 65.1%

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

      5. neg-mul-1 65.1%

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

      6. associate-*r* 65.1%

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

      7. *-commutative 65.1%

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

      8. associate-+r+ 65.1%

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

      9. metadata-eval 65.1%

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

      10. metadata-eval 65.1%

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

      11. associate-*r* 65.1%

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

      12. metadata-eval 65.1%

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

      13. *-commutative 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in z around inf 64.2%

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

   if -7.2e246 < z < -9.49999999999999989e55

   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* 99.8%

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

      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. Taylor expanded in y around inf 61.3%

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

   5. Taylor expanded in z around inf 61.3%

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

      1. associate-*r* 61.3%

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

      2. *-commutative 61.3%

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

      3. associate-*r* 61.3%

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

   7. Simplified 61.3%

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

   if -0.5 < z < -5.59999999999999966e-186 or 8.50000000000000018e-296 < z < 1.42000000000000003e-185

   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. Taylor expanded in x around inf 63.8%

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

      1. sub-neg 63.8%

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

      2. distribute-rgt-in 63.9%

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

      3. metadata-eval 63.9%

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

      4. metadata-eval 63.9%

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

      5. neg-mul-1 63.9%

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

      6. associate-*r* 63.9%

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

      7. *-commutative 63.9%

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

      8. associate-+r+ 63.9%

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

      9. metadata-eval 63.9%

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

      10. metadata-eval 63.9%

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

      11. associate-*r* 63.9%

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

      12. metadata-eval 63.9%

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

      13. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in z around 0 62.4%

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

      1. *-commutative 62.4%

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

   9. Simplified 62.4%

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

   if -5.59999999999999966e-186 < z < 8.50000000000000018e-296 or 1.42000000000000003e-185 < z < 0.599999999999999978

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      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. Taylor expanded in y around inf 64.1%

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

   5. Taylor expanded in z around 0 60.8%

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

      1. *-commutative 60.8%

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

   7. Simplified 60.8%

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

   if 3.3499999999999998e134 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      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. Taylor expanded in y around inf 61.7%

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

   5. Taylor expanded in z around inf 61.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.036:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-295}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.036)
     t_0
     (if (<= z -1.05e-185)
       (* x -3.0)
       (if (<= z 1.25e-295)
         (* y 4.0)
         (if (<= z 5e-186) (* x -3.0) (if (<= z 0.56) (* y 4.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.036) {
		tmp = t_0;
	} else if (z <= -1.05e-185) {
		tmp = x * -3.0;
	} else if (z <= 1.25e-295) {
		tmp = y * 4.0;
	} else if (z <= 5e-186) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} 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 - x) * z)
    if (z <= (-0.036d0)) then
        tmp = t_0
    else if (z <= (-1.05d-185)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.25d-295) then
        tmp = y * 4.0d0
    else if (z <= 5d-186) then
        tmp = x * (-3.0d0)
    else if (z <= 0.56d0) then
        tmp = y * 4.0d0
    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 - x) * z);
	double tmp;
	if (z <= -0.036) {
		tmp = t_0;
	} else if (z <= -1.05e-185) {
		tmp = x * -3.0;
	} else if (z <= 1.25e-295) {
		tmp = y * 4.0;
	} else if (z <= 5e-186) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.036:
		tmp = t_0
	elif z <= -1.05e-185:
		tmp = x * -3.0
	elif z <= 1.25e-295:
		tmp = y * 4.0
	elif z <= 5e-186:
		tmp = x * -3.0
	elif z <= 0.56:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.036)
		tmp = t_0;
	elseif (z <= -1.05e-185)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.25e-295)
		tmp = Float64(y * 4.0);
	elseif (z <= 5e-186)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.56)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.036)
		tmp = t_0;
	elseif (z <= -1.05e-185)
		tmp = x * -3.0;
	elseif (z <= 1.25e-295)
		tmp = y * 4.0;
	elseif (z <= 5e-186)
		tmp = x * -3.0;
	elseif (z <= 0.56)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.036], t$95$0, If[LessEqual[z, -1.05e-185], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.25e-295], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5e-186], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0359999999999999973 or 0.56000000000000005 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.4%

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

   if -0.0359999999999999973 < z < -1.05e-185 or 1.25000000000000002e-295 < z < 5e-186

   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. Taylor expanded in x around inf 63.8%

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

      1. sub-neg 63.8%

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

      2. distribute-rgt-in 63.9%

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

      3. metadata-eval 63.9%

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

      4. metadata-eval 63.9%

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

      5. neg-mul-1 63.9%

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

      6. associate-*r* 63.9%

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

      7. *-commutative 63.9%

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

      8. associate-+r+ 63.9%

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

      9. metadata-eval 63.9%

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

      10. metadata-eval 63.9%

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

      11. associate-*r* 63.9%

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

      12. metadata-eval 63.9%

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

      13. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in z around 0 62.4%

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

      1. *-commutative 62.4%

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

   9. Simplified 62.4%

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

   if -1.05e-185 < z < 1.25000000000000002e-295 or 5e-186 < z < 0.56000000000000005

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      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. Taylor expanded in y around inf 64.1%

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

   5. Taylor expanded in z around 0 60.8%

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

      1. *-commutative 60.8%

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

   7. Simplified 60.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.036:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-295}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 5: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-295}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -2.6e+14)
     t_0
     (if (<= z -8.5e-186)
       (* x (+ -3.0 (* z 6.0)))
       (if (<= z 6e-295)
         (* y 4.0)
         (if (<= z 9.2e-185) (* x -3.0) (if (<= z 0.68) (* y 4.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2.6e+14) {
		tmp = t_0;
	} else if (z <= -8.5e-186) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 6e-295) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-185) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} 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 - x) * z)
    if (z <= (-2.6d+14)) then
        tmp = t_0
    else if (z <= (-8.5d-186)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 6d-295) then
        tmp = y * 4.0d0
    else if (z <= 9.2d-185) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    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 - x) * z);
	double tmp;
	if (z <= -2.6e+14) {
		tmp = t_0;
	} else if (z <= -8.5e-186) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 6e-295) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-185) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -2.6e+14:
		tmp = t_0
	elif z <= -8.5e-186:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 6e-295:
		tmp = y * 4.0
	elif z <= 9.2e-185:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -2.6e+14)
		tmp = t_0;
	elseif (z <= -8.5e-186)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 6e-295)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.2e-185)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -2.6e+14)
		tmp = t_0;
	elseif (z <= -8.5e-186)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 6e-295)
		tmp = y * 4.0;
	elseif (z <= 9.2e-185)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+14], t$95$0, If[LessEqual[z, -8.5e-186], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-295], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.2e-185], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e14 or 0.680000000000000049 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.6%

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

   if -2.6e14 < z < -8.4999999999999994e-186

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. distribute-rgt-in 64.5%

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

      3. metadata-eval 64.5%

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

      4. metadata-eval 64.5%

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

      5. neg-mul-1 64.5%

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

      6. associate-*r* 64.5%

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

      7. *-commutative 64.5%

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

      8. associate-+r+ 64.5%

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

      9. metadata-eval 64.5%

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

      10. metadata-eval 64.5%

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

      11. associate-*r* 64.5%

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

      12. metadata-eval 64.5%

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

      13. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   if -8.4999999999999994e-186 < z < 5.99999999999999993e-295 or 9.2000000000000003e-185 < z < 0.680000000000000049

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      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. Taylor expanded in y around inf 64.1%

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

   5. Taylor expanded in z around 0 60.8%

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

      1. *-commutative 60.8%

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

   7. Simplified 60.8%

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

   if 5.99999999999999993e-295 < z < 9.2000000000000003e-185

   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. Taylor expanded in x around inf 67.5%

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

      1. sub-neg 67.5%

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

      2. distribute-rgt-in 67.5%

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

      3. metadata-eval 67.5%

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

      4. metadata-eval 67.5%

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

      5. neg-mul-1 67.5%

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

      6. associate-*r* 67.5%

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

      7. *-commutative 67.5%

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

      8. associate-+r+ 67.5%

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

      9. metadata-eval 67.5%

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

      10. metadata-eval 67.5%

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

      11. associate-*r* 67.5%

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

      12. metadata-eval 67.5%

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

      13. *-commutative 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in z around 0 67.5%

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

      1. *-commutative 67.5%

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

   9. Simplified 67.5%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-295}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-293}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 23000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -2.6e+14)
     t_0
     (if (<= z -5.5e-186)
       (* x (+ -3.0 (* z 6.0)))
       (if (<= z 4.4e-293)
         (* y 4.0)
         (if (<= z 2.6e-186)
           (* x -3.0)
           (if (<= z 23000.0) (* y (+ 4.0 (* z -6.0))) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2.6e+14) {
		tmp = t_0;
	} else if (z <= -5.5e-186) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4.4e-293) {
		tmp = y * 4.0;
	} else if (z <= 2.6e-186) {
		tmp = x * -3.0;
	} else if (z <= 23000.0) {
		tmp = y * (4.0 + (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 - x) * z)
    if (z <= (-2.6d+14)) then
        tmp = t_0
    else if (z <= (-5.5d-186)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 4.4d-293) then
        tmp = y * 4.0d0
    else if (z <= 2.6d-186) then
        tmp = x * (-3.0d0)
    else if (z <= 23000.0d0) then
        tmp = y * (4.0d0 + (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 - x) * z);
	double tmp;
	if (z <= -2.6e+14) {
		tmp = t_0;
	} else if (z <= -5.5e-186) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4.4e-293) {
		tmp = y * 4.0;
	} else if (z <= 2.6e-186) {
		tmp = x * -3.0;
	} else if (z <= 23000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -2.6e+14:
		tmp = t_0
	elif z <= -5.5e-186:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 4.4e-293:
		tmp = y * 4.0
	elif z <= 2.6e-186:
		tmp = x * -3.0
	elif z <= 23000.0:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -2.6e+14)
		tmp = t_0;
	elseif (z <= -5.5e-186)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 4.4e-293)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.6e-186)
		tmp = Float64(x * -3.0);
	elseif (z <= 23000.0)
		tmp = Float64(y * Float64(4.0 + 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 - x) * z);
	tmp = 0.0;
	if (z <= -2.6e+14)
		tmp = t_0;
	elseif (z <= -5.5e-186)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 4.4e-293)
		tmp = y * 4.0;
	elseif (z <= 2.6e-186)
		tmp = x * -3.0;
	elseif (z <= 23000.0)
		tmp = y * (4.0 + (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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+14], t$95$0, If[LessEqual[z, -5.5e-186], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-293], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.6e-186], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 23000.0], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.6e14 or 23000 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 99.5%

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

   if -2.6e14 < z < -5.5000000000000001e-186

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. distribute-rgt-in 64.5%

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

      3. metadata-eval 64.5%

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

      4. metadata-eval 64.5%

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

      5. neg-mul-1 64.5%

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

      6. associate-*r* 64.5%

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

      7. *-commutative 64.5%

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

      8. associate-+r+ 64.5%

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

      9. metadata-eval 64.5%

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

      10. metadata-eval 64.5%

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

      11. associate-*r* 64.5%

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

      12. metadata-eval 64.5%

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

      13. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   if -5.5000000000000001e-186 < z < 4.4e-293

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      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. Taylor expanded in y around inf 67.5%

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

   5. Taylor expanded in z around 0 67.5%

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

      1. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   if 4.4e-293 < z < 2.59999999999999993e-186

   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. Taylor expanded in x around inf 67.5%

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

      1. sub-neg 67.5%

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

      2. distribute-rgt-in 67.5%

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

      3. metadata-eval 67.5%

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

      4. metadata-eval 67.5%

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

      5. neg-mul-1 67.5%

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

      6. associate-*r* 67.5%

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

      7. *-commutative 67.5%

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

      8. associate-+r+ 67.5%

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

      9. metadata-eval 67.5%

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

      10. metadata-eval 67.5%

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

      11. associate-*r* 67.5%

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

      12. metadata-eval 67.5%

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

      13. *-commutative 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in z around 0 67.5%

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

      1. *-commutative 67.5%

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

   9. Simplified 67.5%

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

   if 2.59999999999999993e-186 < z < 23000

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate-*l* 99.6%

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

      3. fma-def 99.6%

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

      4. sub-neg 99.6%

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

      5. distribute-rgt-in 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 63.8%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-293}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 23000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-293}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2800000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.6e+14)
   (* z (* (- y x) -6.0))
   (if (<= z -4.5e-186)
     (* x (+ -3.0 (* z 6.0)))
     (if (<= z 1.55e-293)
       (* y 4.0)
       (if (<= z 3.5e-187)
         (* x -3.0)
         (if (<= z 2800000.0)
           (* y (+ 4.0 (* z -6.0)))
           (* -6.0 (* (- y x) z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.6e+14) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= -4.5e-186) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 1.55e-293) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-187) {
		tmp = x * -3.0;
	} else if (z <= 2800000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = -6.0 * ((y - 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 <= (-2.6d+14)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= (-4.5d-186)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 1.55d-293) then
        tmp = y * 4.0d0
    else if (z <= 3.5d-187) then
        tmp = x * (-3.0d0)
    else if (z <= 2800000.0d0) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.6e+14) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= -4.5e-186) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 1.55e-293) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-187) {
		tmp = x * -3.0;
	} else if (z <= 2800000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.6e+14:
		tmp = z * ((y - x) * -6.0)
	elif z <= -4.5e-186:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 1.55e-293:
		tmp = y * 4.0
	elif z <= 3.5e-187:
		tmp = x * -3.0
	elif z <= 2800000.0:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.6e+14)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= -4.5e-186)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 1.55e-293)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.5e-187)
		tmp = Float64(x * -3.0);
	elseif (z <= 2800000.0)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.6e+14)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= -4.5e-186)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 1.55e-293)
		tmp = y * 4.0;
	elseif (z <= 3.5e-187)
		tmp = x * -3.0;
	elseif (z <= 2800000.0)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.6e+14], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e-186], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-293], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.5e-187], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2800000.0], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.6e14

   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* 99.8%

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

      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. Taylor expanded in x around -inf 90.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]
   5. Step-by-step derivation

      1. flip-+ 71.3%

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

      2. associate-*r/ 60.2%

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

      3. metadata-eval 60.2%

         \[\leadsto -1 \cdot \frac{x \cdot \left(\color{blue}{9} - \left(-6 \cdot z\right) \cdot \left(-6 \cdot z\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      4. *-commutative 60.2%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot -6\right)} \cdot \left(-6 \cdot z\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      5. *-commutative 60.2%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \left(z \cdot -6\right) \cdot \color{blue}{\left(z \cdot -6\right)}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      6. swap-sqr 60.2%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(-6 \cdot -6\right)}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      7. pow2 60.2%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      8. metadata-eval 60.2%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      9. cancel-sign-sub-inv 60.2%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{3 + \left(--6\right) \cdot z}} + y \cdot \left(4 + -6 \cdot z\right) \]

      10. metadata-eval 60.2%

          \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{3 + \color{blue}{6} \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

   6. Applied egg-rr 60.2%

      \[\leadsto -1 \cdot \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{3 + 6 \cdot z}} + y \cdot \left(4 + -6 \cdot z\right) \]
   7. Step-by-step derivation

      1. associate-/l* 71.2%

         \[\leadsto -1 \cdot \color{blue}{\frac{x}{\frac{3 + 6 \cdot z}{9 - {z}^{2} \cdot 36}}} + y \cdot \left(4 + -6 \cdot z\right) \]

      2. *-commutative 71.2%

         \[\leadsto -1 \cdot \frac{x}{\frac{3 + \color{blue}{z \cdot 6}}{9 - {z}^{2} \cdot 36}} + y \cdot \left(4 + -6 \cdot z\right) \]

   8. Simplified 71.2%

      \[\leadsto -1 \cdot \color{blue}{\frac{x}{\frac{3 + z \cdot 6}{9 - {z}^{2} \cdot 36}}} + y \cdot \left(4 + -6 \cdot z\right) \]

   9. Taylor expanded in z around -inf 99.7%

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

       1. mul-1-neg 99.7%

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

       2. +-commutative 99.7%

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

       3. metadata-eval 99.7%

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

       4. associate-*r* 99.7%

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

       5. neg-mul-1 99.7%

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

       6. distribute-lft-in 99.7%

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

       7. sub-neg 99.7%

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

       8. associate-*l* 99.7%

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

       9. distribute-lft-neg-in 99.7%

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

       10. distribute-rgt-neg-in 99.7%

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

       11. metadata-eval 99.7%

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

       12. associate-*r* 99.7%

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

   11. Simplified 99.7%

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

   if -2.6e14 < z < -4.4999999999999998e-186

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. distribute-rgt-in 64.5%

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

      3. metadata-eval 64.5%

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

      4. metadata-eval 64.5%

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

      5. neg-mul-1 64.5%

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

      6. associate-*r* 64.5%

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

      7. *-commutative 64.5%

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

      8. associate-+r+ 64.5%

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

      9. metadata-eval 64.5%

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

      10. metadata-eval 64.5%

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

      11. associate-*r* 64.5%

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

      12. metadata-eval 64.5%

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

      13. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   if -4.4999999999999998e-186 < z < 1.54999999999999991e-293

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      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. Taylor expanded in y around inf 67.5%

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

   5. Taylor expanded in z around 0 67.5%

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

      1. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   if 1.54999999999999991e-293 < z < 3.49999999999999979e-187

   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. Taylor expanded in x around inf 67.5%

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

      1. sub-neg 67.5%

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

      2. distribute-rgt-in 67.5%

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

      3. metadata-eval 67.5%

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

      4. metadata-eval 67.5%

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

      5. neg-mul-1 67.5%

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

      6. associate-*r* 67.5%

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

      7. *-commutative 67.5%

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

      8. associate-+r+ 67.5%

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

      9. metadata-eval 67.5%

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

      10. metadata-eval 67.5%

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

      11. associate-*r* 67.5%

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

      12. metadata-eval 67.5%

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

      13. *-commutative 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in z around 0 67.5%

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

      1. *-commutative 67.5%

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

   9. Simplified 67.5%

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

   if 3.49999999999999979e-187 < z < 2.8e6

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate-*l* 99.6%

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

      3. fma-def 99.6%

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

      4. sub-neg 99.6%

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

      5. distribute-rgt-in 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 63.8%

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

   if 2.8e6 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 99.4%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-293}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2800000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 8: 51.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2.6e+14)
     t_0
     (if (<= z -6.5e-186)
       (* x -3.0)
       (if (<= z 9.8e-296)
         (* y 4.0)
         (if (<= z 4.2e-188) (* x -3.0) (if (<= z 0.68) (* y 4.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.6e+14) {
		tmp = t_0;
	} else if (z <= -6.5e-186) {
		tmp = x * -3.0;
	} else if (z <= 9.8e-296) {
		tmp = y * 4.0;
	} else if (z <= 4.2e-188) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} 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 * z)
    if (z <= (-2.6d+14)) then
        tmp = t_0
    else if (z <= (-6.5d-186)) then
        tmp = x * (-3.0d0)
    else if (z <= 9.8d-296) then
        tmp = y * 4.0d0
    else if (z <= 4.2d-188) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    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 * z);
	double tmp;
	if (z <= -2.6e+14) {
		tmp = t_0;
	} else if (z <= -6.5e-186) {
		tmp = x * -3.0;
	} else if (z <= 9.8e-296) {
		tmp = y * 4.0;
	} else if (z <= 4.2e-188) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.6e+14:
		tmp = t_0
	elif z <= -6.5e-186:
		tmp = x * -3.0
	elif z <= 9.8e-296:
		tmp = y * 4.0
	elif z <= 4.2e-188:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.6e+14)
		tmp = t_0;
	elseif (z <= -6.5e-186)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.8e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.2e-188)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.6e+14)
		tmp = t_0;
	elseif (z <= -6.5e-186)
		tmp = x * -3.0;
	elseif (z <= 9.8e-296)
		tmp = y * 4.0;
	elseif (z <= 4.2e-188)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+14], t$95$0, If[LessEqual[z, -6.5e-186], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.8e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.2e-188], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e14 or 0.680000000000000049 < 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. +-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* 99.8%

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

      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. Taylor expanded in y around inf 50.3%

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

   5. Taylor expanded in z around inf 49.4%

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

   if -2.6e14 < z < -6.49999999999999962e-186 or 9.7999999999999997e-296 < z < 4.1999999999999998e-188

   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. Taylor expanded in x around inf 65.7%

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

      1. sub-neg 65.7%

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

      2. distribute-rgt-in 65.7%

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

      3. metadata-eval 65.7%

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

      4. metadata-eval 65.7%

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

      5. neg-mul-1 65.7%

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

      6. associate-*r* 65.7%

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

      7. *-commutative 65.7%

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

      8. associate-+r+ 65.7%

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

      9. metadata-eval 65.7%

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

      10. metadata-eval 65.7%

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

      11. associate-*r* 65.7%

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

      12. metadata-eval 65.7%

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

      13. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in z around 0 59.8%

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

      1. *-commutative 59.8%

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

   9. Simplified 59.8%

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

   if -6.49999999999999962e-186 < z < 9.7999999999999997e-296 or 4.1999999999999998e-188 < z < 0.680000000000000049

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      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. Taylor expanded in y around inf 64.1%

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

   5. Taylor expanded in z around 0 60.8%

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

      1. *-commutative 60.8%

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

   7. Simplified 60.8%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 9: 99.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in z around 0 99.7%

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

5. Final simplification 99.7%

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

Alternative 10: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.44:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.44)
   (* z (* (- y x) -6.0))
   (if (<= z 0.56) (+ (* y 4.0) (* x -3.0)) (+ x (* (- y x) (* z -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.44) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.56) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = x + ((y - x) * (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 (z <= (-0.44d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.56d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = x + ((y - x) * (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.44) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.56) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = x + ((y - x) * (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.44:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.56:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = x + ((y - x) * (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.44)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.56)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.44)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.56)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = x + ((y - x) * (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.44], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.56], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.440000000000000002

   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* 99.8%

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

      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. Taylor expanded in x around -inf 91.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]
   5. Step-by-step derivation

      1. flip-+ 72.5%

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

      2. associate-*r/ 61.8%

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

      3. metadata-eval 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(\color{blue}{9} - \left(-6 \cdot z\right) \cdot \left(-6 \cdot z\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      4. *-commutative 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot -6\right)} \cdot \left(-6 \cdot z\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      5. *-commutative 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \left(z \cdot -6\right) \cdot \color{blue}{\left(z \cdot -6\right)}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      6. swap-sqr 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(-6 \cdot -6\right)}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      7. pow2 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      8. metadata-eval 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      9. cancel-sign-sub-inv 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{3 + \left(--6\right) \cdot z}} + y \cdot \left(4 + -6 \cdot z\right) \]

      10. metadata-eval 61.8%

          \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{3 + \color{blue}{6} \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

   6. Applied egg-rr 61.8%

      \[\leadsto -1 \cdot \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{3 + 6 \cdot z}} + y \cdot \left(4 + -6 \cdot z\right) \]
   7. Step-by-step derivation

      1. associate-/l* 72.4%

         \[\leadsto -1 \cdot \color{blue}{\frac{x}{\frac{3 + 6 \cdot z}{9 - {z}^{2} \cdot 36}}} + y \cdot \left(4 + -6 \cdot z\right) \]

      2. *-commutative 72.4%

         \[\leadsto -1 \cdot \frac{x}{\frac{3 + \color{blue}{z \cdot 6}}{9 - {z}^{2} \cdot 36}} + y \cdot \left(4 + -6 \cdot z\right) \]

   8. Simplified 72.4%

      \[\leadsto -1 \cdot \color{blue}{\frac{x}{\frac{3 + z \cdot 6}{9 - {z}^{2} \cdot 36}}} + y \cdot \left(4 + -6 \cdot z\right) \]

   9. Taylor expanded in z around -inf 99.1%

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

       1. mul-1-neg 99.1%

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

       2. +-commutative 99.1%

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

       3. metadata-eval 99.1%

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

       4. associate-*r* 99.1%

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

       5. neg-mul-1 99.1%

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

       6. distribute-lft-in 99.1%

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

       7. sub-neg 99.1%

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

       8. associate-*l* 99.1%

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

       9. distribute-lft-neg-in 99.1%

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

       10. distribute-rgt-neg-in 99.1%

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

       11. metadata-eval 99.1%

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

       12. associate-*r* 99.1%

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

   11. Simplified 99.1%

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

   if -0.440000000000000002 < z < 0.56000000000000005

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      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 99.8%

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

      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. Taylor expanded in x around -inf 99.8%

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

   5. Taylor expanded in z around 0 96.8%

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

   if 0.56000000000000005 < 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. Taylor expanded in z around inf 97.6%

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

   5. Taylor expanded in y around 0 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*l* 96.1%

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

      3. associate-*r* 96.2%

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

      4. metadata-eval 96.2%

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

      5. distribute-lft-neg-in 96.2%

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

      6. *-commutative 96.2%

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

      7. distribute-lft-neg-in 96.2%

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

      8. associate-*r* 96.3%

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

      9. *-commutative 96.3%

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

      10. distribute-lft-out 97.7%

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

      11. sub-neg 97.7%

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

      12. *-commutative 97.7%

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

   7. Simplified 97.7%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.44:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 11: 97.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.62:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.62)
   (* z (* (- y x) -6.0))
   (if (<= z 0.5) (+ x (* (- y x) 4.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.62) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = -6.0 * ((y - 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 <= (-0.62d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.5d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.62) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.62:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.5:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.62)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.5)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.62)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.5)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.62], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.619999999999999996

   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* 99.8%

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

      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. Taylor expanded in x around -inf 91.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]
   5. Step-by-step derivation

      1. flip-+ 72.5%

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

      2. associate-*r/ 61.8%

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

      3. metadata-eval 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(\color{blue}{9} - \left(-6 \cdot z\right) \cdot \left(-6 \cdot z\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      4. *-commutative 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot -6\right)} \cdot \left(-6 \cdot z\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      5. *-commutative 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \left(z \cdot -6\right) \cdot \color{blue}{\left(z \cdot -6\right)}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      6. swap-sqr 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(-6 \cdot -6\right)}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      7. pow2 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      8. metadata-eval 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      9. cancel-sign-sub-inv 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{3 + \left(--6\right) \cdot z}} + y \cdot \left(4 + -6 \cdot z\right) \]

      10. metadata-eval 61.8%

          \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{3 + \color{blue}{6} \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

   6. Applied egg-rr 61.8%

      \[\leadsto -1 \cdot \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{3 + 6 \cdot z}} + y \cdot \left(4 + -6 \cdot z\right) \]
   7. Step-by-step derivation

      1. associate-/l* 72.4%

         \[\leadsto -1 \cdot \color{blue}{\frac{x}{\frac{3 + 6 \cdot z}{9 - {z}^{2} \cdot 36}}} + y \cdot \left(4 + -6 \cdot z\right) \]

      2. *-commutative 72.4%

         \[\leadsto -1 \cdot \frac{x}{\frac{3 + \color{blue}{z \cdot 6}}{9 - {z}^{2} \cdot 36}} + y \cdot \left(4 + -6 \cdot z\right) \]

   8. Simplified 72.4%

      \[\leadsto -1 \cdot \color{blue}{\frac{x}{\frac{3 + z \cdot 6}{9 - {z}^{2} \cdot 36}}} + y \cdot \left(4 + -6 \cdot z\right) \]

   9. Taylor expanded in z around -inf 99.1%

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

       1. mul-1-neg 99.1%

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

       2. +-commutative 99.1%

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

       3. metadata-eval 99.1%

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

       4. associate-*r* 99.1%

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

       5. neg-mul-1 99.1%

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

       6. distribute-lft-in 99.1%

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

       7. sub-neg 99.1%

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

       8. associate-*l* 99.1%

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

       9. distribute-lft-neg-in 99.1%

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

       10. distribute-rgt-neg-in 99.1%

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

       11. metadata-eval 99.1%

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

       12. associate-*r* 99.1%

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

   11. Simplified 99.1%

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

   if -0.619999999999999996 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 96.8%

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

   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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 97.6%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.62:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 12: 97.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* z (* (- y x) -6.0))
   (if (<= z 0.6) (+ (* y 4.0) (* x -3.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.6) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -6.0 * ((y - 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 <= (-0.55d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.6d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.6) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.6:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.6)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.6)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.6], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   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* 99.8%

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

      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. Taylor expanded in x around -inf 91.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]
   5. Step-by-step derivation

      1. flip-+ 72.5%

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

      2. associate-*r/ 61.8%

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

      3. metadata-eval 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(\color{blue}{9} - \left(-6 \cdot z\right) \cdot \left(-6 \cdot z\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      4. *-commutative 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot -6\right)} \cdot \left(-6 \cdot z\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      5. *-commutative 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \left(z \cdot -6\right) \cdot \color{blue}{\left(z \cdot -6\right)}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      6. swap-sqr 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(-6 \cdot -6\right)}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      7. pow2 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      8. metadata-eval 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{3 - -6 \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

      9. cancel-sign-sub-inv 61.8%

         \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{3 + \left(--6\right) \cdot z}} + y \cdot \left(4 + -6 \cdot z\right) \]

      10. metadata-eval 61.8%

          \[\leadsto -1 \cdot \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{3 + \color{blue}{6} \cdot z} + y \cdot \left(4 + -6 \cdot z\right) \]

   6. Applied egg-rr 61.8%

      \[\leadsto -1 \cdot \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{3 + 6 \cdot z}} + y \cdot \left(4 + -6 \cdot z\right) \]
   7. Step-by-step derivation

      1. associate-/l* 72.4%

         \[\leadsto -1 \cdot \color{blue}{\frac{x}{\frac{3 + 6 \cdot z}{9 - {z}^{2} \cdot 36}}} + y \cdot \left(4 + -6 \cdot z\right) \]

      2. *-commutative 72.4%

         \[\leadsto -1 \cdot \frac{x}{\frac{3 + \color{blue}{z \cdot 6}}{9 - {z}^{2} \cdot 36}} + y \cdot \left(4 + -6 \cdot z\right) \]

   8. Simplified 72.4%

      \[\leadsto -1 \cdot \color{blue}{\frac{x}{\frac{3 + z \cdot 6}{9 - {z}^{2} \cdot 36}}} + y \cdot \left(4 + -6 \cdot z\right) \]

   9. Taylor expanded in z around -inf 99.1%

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

       1. mul-1-neg 99.1%

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

       2. +-commutative 99.1%

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

       3. metadata-eval 99.1%

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

       4. associate-*r* 99.1%

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

       5. neg-mul-1 99.1%

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

       6. distribute-lft-in 99.1%

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

       7. sub-neg 99.1%

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

       8. associate-*l* 99.1%

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

       9. distribute-lft-neg-in 99.1%

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

       10. distribute-rgt-neg-in 99.1%

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

       11. metadata-eval 99.1%

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

       12. associate-*r* 99.1%

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

   11. Simplified 99.1%

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

   if -0.55000000000000004 < z < 0.599999999999999978

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      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 99.8%

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

      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. Taylor expanded in x around -inf 99.8%

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

   5. Taylor expanded in z around 0 96.8%

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

   if 0.599999999999999978 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 97.6%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 13: 99.5% 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 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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. Final simplification 99.5%

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

Alternative 14: 37.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+79} \lor \neg \left(y \leq 4.5 \cdot 10^{-55}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.6e+79) (not (<= y 4.5e-55))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e+79) || !(y <= 4.5e-55)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.6d+79)) .or. (.not. (y <= 4.5d-55))) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e+79) || !(y <= 4.5e-55)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.6e+79) or not (y <= 4.5e-55):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.6e+79) || !(y <= 4.5e-55))
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.6e+79) || ~((y <= 4.5e-55)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.6e+79], N[Not[LessEqual[y, 4.5e-55]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6000000000000003e79 or 4.4999999999999997e-55 < y

   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* 99.9%

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

      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 99.8%

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

      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. Taylor expanded in y around inf 76.9%

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

   5. Taylor expanded in z around 0 39.4%

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

      1. *-commutative 39.4%

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

   7. Simplified 39.4%

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

   if -6.6000000000000003e79 < y < 4.4999999999999997e-55

   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. Taylor expanded in x around inf 70.9%

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

      1. sub-neg 70.9%

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

      2. distribute-rgt-in 71.0%

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

      3. metadata-eval 71.0%

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

      4. metadata-eval 71.0%

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

      5. neg-mul-1 71.0%

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

      6. associate-*r* 71.0%

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

      7. *-commutative 71.0%

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

      8. associate-+r+ 71.0%

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

      9. metadata-eval 71.0%

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

      10. metadata-eval 71.0%

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

      11. associate-*r* 71.0%

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

      12. metadata-eval 71.0%

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

      13. *-commutative 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in z around 0 34.2%

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

      1. *-commutative 34.2%

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

   9. Simplified 34.2%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+79} \lor \neg \left(y \leq 4.5 \cdot 10^{-55}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 15: 25.9% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around inf 50.8%

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

   1. sub-neg 50.8%

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

   2. distribute-rgt-in 50.8%

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

   3. metadata-eval 50.8%

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

   4. metadata-eval 50.8%

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

   5. neg-mul-1 50.8%

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

   6. associate-*r* 50.8%

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

   7. *-commutative 50.8%

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

   8. associate-+r+ 50.8%

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

   9. metadata-eval 50.8%

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

   10. metadata-eval 50.8%

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

   11. associate-*r* 50.8%

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

   12. metadata-eval 50.8%

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

   13. *-commutative 50.8%

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

6. Simplified 50.8%

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

7. Taylor expanded in z around 0 23.4%

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

   1. *-commutative 23.4%

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

9. Simplified 23.4%

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

10. Final simplification 23.4%

    \[\leadsto x \cdot -3 \]

Alternative 16: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in z around inf 55.0%

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

5. Taylor expanded in z around 0 2.9%

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

6. Final simplification 2.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023332 
(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))))