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

Percentage Accurate: 99.5% → 99.8%

Time: 11.3s

Alternatives: 14

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% 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-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(y - x), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision] * 6.0 + 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. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. +-commutative 99.5%

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

   2. *-commutative 99.5%

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

   3. associate-*r* 99.5%

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

   4. fma-define 99.5%

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

6. Applied egg-rr 99.5%

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

7. Final simplification 99.5%

   \[\leadsto \mathsf{fma}\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right), 6, x\right) \]
8. Add Preprocessing

Alternative 3: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -0.44:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-302}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-226}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.025:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+194} \lor \neg \left(z \leq 1.55 \cdot 10^{+223}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -0.44)
     t_0
     (if (<= z -6.2e-280)
       (* y 4.0)
       (if (<= z 9.2e-302)
         (* x -3.0)
         (if (<= z 7.4e-253)
           (* y 4.0)
           (if (<= z 3.6e-226)
             (* x -3.0)
             (if (<= z 0.025)
               (* y 4.0)
               (if (or (<= z 8.8e+194) (not (<= z 1.55e+223)))
                 (* -6.0 (* y z))
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.44) {
		tmp = t_0;
	} else if (z <= -6.2e-280) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-302) {
		tmp = x * -3.0;
	} else if (z <= 7.4e-253) {
		tmp = y * 4.0;
	} else if (z <= 3.6e-226) {
		tmp = x * -3.0;
	} else if (z <= 0.025) {
		tmp = y * 4.0;
	} else if ((z <= 8.8e+194) || !(z <= 1.55e+223)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-0.44d0)) then
        tmp = t_0
    else if (z <= (-6.2d-280)) then
        tmp = y * 4.0d0
    else if (z <= 9.2d-302) then
        tmp = x * (-3.0d0)
    else if (z <= 7.4d-253) then
        tmp = y * 4.0d0
    else if (z <= 3.6d-226) then
        tmp = x * (-3.0d0)
    else if (z <= 0.025d0) then
        tmp = y * 4.0d0
    else if ((z <= 8.8d+194) .or. (.not. (z <= 1.55d+223))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.44) {
		tmp = t_0;
	} else if (z <= -6.2e-280) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-302) {
		tmp = x * -3.0;
	} else if (z <= 7.4e-253) {
		tmp = y * 4.0;
	} else if (z <= 3.6e-226) {
		tmp = x * -3.0;
	} else if (z <= 0.025) {
		tmp = y * 4.0;
	} else if ((z <= 8.8e+194) || !(z <= 1.55e+223)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -0.44:
		tmp = t_0
	elif z <= -6.2e-280:
		tmp = y * 4.0
	elif z <= 9.2e-302:
		tmp = x * -3.0
	elif z <= 7.4e-253:
		tmp = y * 4.0
	elif z <= 3.6e-226:
		tmp = x * -3.0
	elif z <= 0.025:
		tmp = y * 4.0
	elif (z <= 8.8e+194) or not (z <= 1.55e+223):
		tmp = -6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -0.44)
		tmp = t_0;
	elseif (z <= -6.2e-280)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.2e-302)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.4e-253)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.6e-226)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.025)
		tmp = Float64(y * 4.0);
	elseif ((z <= 8.8e+194) || !(z <= 1.55e+223))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -0.44)
		tmp = t_0;
	elseif (z <= -6.2e-280)
		tmp = y * 4.0;
	elseif (z <= 9.2e-302)
		tmp = x * -3.0;
	elseif (z <= 7.4e-253)
		tmp = y * 4.0;
	elseif (z <= 3.6e-226)
		tmp = x * -3.0;
	elseif (z <= 0.025)
		tmp = y * 4.0;
	elseif ((z <= 8.8e+194) || ~((z <= 1.55e+223)))
		tmp = -6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.44], t$95$0, If[LessEqual[z, -6.2e-280], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.2e-302], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.4e-253], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.6e-226], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.025], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 8.8e+194], N[Not[LessEqual[z, 1.55e+223]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.440000000000000002 or 8.8000000000000004e194 < z < 1.54999999999999991e223

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 61.0%

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

      1. sub-neg 61.0%

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

      2. distribute-rgt-in 61.0%

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

      3. metadata-eval 61.0%

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

      4. neg-mul-1 61.0%

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

      5. associate-*r* 61.0%

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

      6. *-commutative 61.0%

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

      7. associate-+r+ 61.0%

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

      8. metadata-eval 61.0%

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

      9. associate-*r* 61.0%

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

      10. metadata-eval 61.0%

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

      11. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in z around inf 59.3%

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

   if -0.440000000000000002 < z < -6.20000000000000042e-280 or 9.20000000000000007e-302 < z < 7.3999999999999995e-253 or 3.59999999999999994e-226 < z < 0.025000000000000001

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 59.3%

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

   6. Taylor expanded in z around 0 58.8%

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

   if -6.20000000000000042e-280 < z < 9.20000000000000007e-302 or 7.3999999999999995e-253 < z < 3.59999999999999994e-226

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-rgt-in 80.2%

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

      3. metadata-eval 80.2%

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

      4. neg-mul-1 80.2%

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

      5. associate-*r* 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-+r+ 80.2%

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

      8. metadata-eval 80.2%

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

      9. associate-*r* 80.2%

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

      10. metadata-eval 80.2%

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

      11. *-commutative 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in z around 0 80.2%

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

      1. *-commutative 80.2%

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

   10. Simplified 80.2%

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

   if 0.025000000000000001 < z < 8.8000000000000004e194 or 1.54999999999999991e223 < 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* 99.5%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in y around inf 66.7%

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

   6. Taylor expanded in z around inf 65.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.44:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-302}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-226}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.025:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+194} \lor \neg \left(z \leq 1.55 \cdot 10^{+223}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -0.29:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-278}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-302}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-251}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-226}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.025:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+193} \lor \neg \left(z \leq 1.42 \cdot 10^{+223}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -0.29)
     t_0
     (if (<= z -3.5e-278)
       (* y 4.0)
       (if (<= z 5.2e-302)
         (* x -3.0)
         (if (<= z 6e-251)
           (* y 4.0)
           (if (<= z 1.4e-226)
             (* x -3.0)
             (if (<= z 0.025)
               (* y 4.0)
               (if (or (<= z 5.2e+193) (not (<= z 1.42e+223)))
                 (* -6.0 (* y z))
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.29) {
		tmp = t_0;
	} else if (z <= -3.5e-278) {
		tmp = y * 4.0;
	} else if (z <= 5.2e-302) {
		tmp = x * -3.0;
	} else if (z <= 6e-251) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-226) {
		tmp = x * -3.0;
	} else if (z <= 0.025) {
		tmp = y * 4.0;
	} else if ((z <= 5.2e+193) || !(z <= 1.42e+223)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-0.29d0)) then
        tmp = t_0
    else if (z <= (-3.5d-278)) then
        tmp = y * 4.0d0
    else if (z <= 5.2d-302) then
        tmp = x * (-3.0d0)
    else if (z <= 6d-251) then
        tmp = y * 4.0d0
    else if (z <= 1.4d-226) then
        tmp = x * (-3.0d0)
    else if (z <= 0.025d0) then
        tmp = y * 4.0d0
    else if ((z <= 5.2d+193) .or. (.not. (z <= 1.42d+223))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.29) {
		tmp = t_0;
	} else if (z <= -3.5e-278) {
		tmp = y * 4.0;
	} else if (z <= 5.2e-302) {
		tmp = x * -3.0;
	} else if (z <= 6e-251) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-226) {
		tmp = x * -3.0;
	} else if (z <= 0.025) {
		tmp = y * 4.0;
	} else if ((z <= 5.2e+193) || !(z <= 1.42e+223)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -0.29:
		tmp = t_0
	elif z <= -3.5e-278:
		tmp = y * 4.0
	elif z <= 5.2e-302:
		tmp = x * -3.0
	elif z <= 6e-251:
		tmp = y * 4.0
	elif z <= 1.4e-226:
		tmp = x * -3.0
	elif z <= 0.025:
		tmp = y * 4.0
	elif (z <= 5.2e+193) or not (z <= 1.42e+223):
		tmp = -6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -0.29)
		tmp = t_0;
	elseif (z <= -3.5e-278)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.2e-302)
		tmp = Float64(x * -3.0);
	elseif (z <= 6e-251)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.4e-226)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.025)
		tmp = Float64(y * 4.0);
	elseif ((z <= 5.2e+193) || !(z <= 1.42e+223))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -0.29)
		tmp = t_0;
	elseif (z <= -3.5e-278)
		tmp = y * 4.0;
	elseif (z <= 5.2e-302)
		tmp = x * -3.0;
	elseif (z <= 6e-251)
		tmp = y * 4.0;
	elseif (z <= 1.4e-226)
		tmp = x * -3.0;
	elseif (z <= 0.025)
		tmp = y * 4.0;
	elseif ((z <= 5.2e+193) || ~((z <= 1.42e+223)))
		tmp = -6.0 * (y * z);
	else
		tmp = t_0;
	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, -0.29], t$95$0, If[LessEqual[z, -3.5e-278], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.2e-302], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6e-251], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.4e-226], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.025], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 5.2e+193], N[Not[LessEqual[z, 1.42e+223]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.28999999999999998 or 5.20000000000000026e193 < z < 1.42e223

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 61.0%

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

      1. sub-neg 61.0%

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

      2. distribute-rgt-in 61.0%

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

      3. metadata-eval 61.0%

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

      4. neg-mul-1 61.0%

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

      5. associate-*r* 61.0%

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

      6. *-commutative 61.0%

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

      7. associate-+r+ 61.0%

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

      8. metadata-eval 61.0%

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

      9. associate-*r* 61.0%

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

      10. metadata-eval 61.0%

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

      11. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in z around inf 59.3%

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

      1. associate-*r* 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*r* 59.4%

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

      4. *-commutative 59.4%

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

   10. Simplified 59.4%

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

   if -0.28999999999999998 < z < -3.4999999999999997e-278 or 5.20000000000000022e-302 < z < 5.9999999999999997e-251 or 1.40000000000000004e-226 < z < 0.025000000000000001

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 59.3%

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

   6. Taylor expanded in z around 0 58.8%

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

   if -3.4999999999999997e-278 < z < 5.20000000000000022e-302 or 5.9999999999999997e-251 < z < 1.40000000000000004e-226

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-rgt-in 80.2%

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

      3. metadata-eval 80.2%

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

      4. neg-mul-1 80.2%

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

      5. associate-*r* 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-+r+ 80.2%

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

      8. metadata-eval 80.2%

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

      9. associate-*r* 80.2%

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

      10. metadata-eval 80.2%

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

      11. *-commutative 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in z around 0 80.2%

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

      1. *-commutative 80.2%

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

   10. Simplified 80.2%

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

   if 0.025000000000000001 < z < 5.20000000000000026e193 or 1.42e223 < 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* 99.5%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in y around inf 66.7%

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

   6. Taylor expanded in z around inf 65.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.29:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-278}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-302}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-251}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-226}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.025:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+193} \lor \neg \left(z \leq 1.42 \cdot 10^{+223}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0136:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-278}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-251}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-227}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-122}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 49000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0136)
     t_1
     (if (<= z -3.9e-278)
       (* y 4.0)
       (if (<= z 9.5e-302)
         t_0
         (if (<= z 2.9e-251)
           (* y 4.0)
           (if (<= z 2.7e-227)
             (* x -3.0)
             (if (<= z 3.1e-122) (* y 4.0) (if (<= z 49000.0) t_0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0136) {
		tmp = t_1;
	} else if (z <= -3.9e-278) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-302) {
		tmp = t_0;
	} else if (z <= 2.9e-251) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-227) {
		tmp = x * -3.0;
	} else if (z <= 3.1e-122) {
		tmp = y * 4.0;
	} else if (z <= 49000.0) {
		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 * ((-3.0d0) + (z * 6.0d0))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.0136d0)) then
        tmp = t_1
    else if (z <= (-3.9d-278)) then
        tmp = y * 4.0d0
    else if (z <= 9.5d-302) then
        tmp = t_0
    else if (z <= 2.9d-251) then
        tmp = y * 4.0d0
    else if (z <= 2.7d-227) then
        tmp = x * (-3.0d0)
    else if (z <= 3.1d-122) then
        tmp = y * 4.0d0
    else if (z <= 49000.0d0) 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 * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0136) {
		tmp = t_1;
	} else if (z <= -3.9e-278) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-302) {
		tmp = t_0;
	} else if (z <= 2.9e-251) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-227) {
		tmp = x * -3.0;
	} else if (z <= 3.1e-122) {
		tmp = y * 4.0;
	} else if (z <= 49000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0136:
		tmp = t_1
	elif z <= -3.9e-278:
		tmp = y * 4.0
	elif z <= 9.5e-302:
		tmp = t_0
	elif z <= 2.9e-251:
		tmp = y * 4.0
	elif z <= 2.7e-227:
		tmp = x * -3.0
	elif z <= 3.1e-122:
		tmp = y * 4.0
	elif z <= 49000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0136)
		tmp = t_1;
	elseif (z <= -3.9e-278)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.5e-302)
		tmp = t_0;
	elseif (z <= 2.9e-251)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.7e-227)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.1e-122)
		tmp = Float64(y * 4.0);
	elseif (z <= 49000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.0136)
		tmp = t_1;
	elseif (z <= -3.9e-278)
		tmp = y * 4.0;
	elseif (z <= 9.5e-302)
		tmp = t_0;
	elseif (z <= 2.9e-251)
		tmp = y * 4.0;
	elseif (z <= 2.7e-227)
		tmp = x * -3.0;
	elseif (z <= 3.1e-122)
		tmp = y * 4.0;
	elseif (z <= 49000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0136], t$95$1, If[LessEqual[z, -3.9e-278], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.5e-302], t$95$0, If[LessEqual[z, 2.9e-251], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.7e-227], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.1e-122], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 49000.0], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0135999999999999992 or 49000 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 97.4%

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

   6. Taylor expanded in z around inf 97.4%

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

   if -0.0135999999999999992 < z < -3.9000000000000001e-278 or 9.49999999999999991e-302 < z < 2.9000000000000001e-251 or 2.7e-227 < z < 3.0999999999999998e-122

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 62.4%

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

   6. Taylor expanded in z around 0 62.4%

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

   if -3.9000000000000001e-278 < z < 9.49999999999999991e-302 or 3.0999999999999998e-122 < z < 49000

   1. Initial program 99.0%

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

      1. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around inf 66.9%

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

      1. sub-neg 66.9%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. neg-mul-1 67.2%

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

      5. associate-*r* 67.2%

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

      6. *-commutative 67.2%

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

      7. associate-+r+ 67.2%

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

      8. metadata-eval 67.2%

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

      9. associate-*r* 67.2%

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

      10. metadata-eval 67.2%

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

      11. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 2.9000000000000001e-251 < z < 2.7e-227

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 88.4%

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

      1. sub-neg 88.4%

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

      2. distribute-rgt-in 88.4%

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

      3. metadata-eval 88.4%

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

      4. neg-mul-1 88.4%

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

      5. associate-*r* 88.4%

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

      6. *-commutative 88.4%

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

      7. associate-+r+ 88.4%

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

      8. metadata-eval 88.4%

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

      9. associate-*r* 88.4%

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

      10. metadata-eval 88.4%

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

      11. *-commutative 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in z around 0 88.4%

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

      1. *-commutative 88.4%

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

   10. Simplified 88.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0136:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-278}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-251}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-227}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-122}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 49000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0115:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-302}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-251}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-227}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.51:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0115)
     t_0
     (if (<= z -1.25e-280)
       (* y 4.0)
       (if (<= z 4.6e-302)
         (* x -3.0)
         (if (<= z 6.6e-251)
           (* y 4.0)
           (if (<= z 4.8e-227) (* x -3.0) (if (<= z 0.51) (* 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 <= -0.0115) {
		tmp = t_0;
	} else if (z <= -1.25e-280) {
		tmp = y * 4.0;
	} else if (z <= 4.6e-302) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-251) {
		tmp = y * 4.0;
	} else if (z <= 4.8e-227) {
		tmp = x * -3.0;
	} else if (z <= 0.51) {
		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 <= (-0.0115d0)) then
        tmp = t_0
    else if (z <= (-1.25d-280)) then
        tmp = y * 4.0d0
    else if (z <= 4.6d-302) then
        tmp = x * (-3.0d0)
    else if (z <= 6.6d-251) then
        tmp = y * 4.0d0
    else if (z <= 4.8d-227) then
        tmp = x * (-3.0d0)
    else if (z <= 0.51d0) 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 <= -0.0115) {
		tmp = t_0;
	} else if (z <= -1.25e-280) {
		tmp = y * 4.0;
	} else if (z <= 4.6e-302) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-251) {
		tmp = y * 4.0;
	} else if (z <= 4.8e-227) {
		tmp = x * -3.0;
	} else if (z <= 0.51) {
		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 <= -0.0115:
		tmp = t_0
	elif z <= -1.25e-280:
		tmp = y * 4.0
	elif z <= 4.6e-302:
		tmp = x * -3.0
	elif z <= 6.6e-251:
		tmp = y * 4.0
	elif z <= 4.8e-227:
		tmp = x * -3.0
	elif z <= 0.51:
		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 <= -0.0115)
		tmp = t_0;
	elseif (z <= -1.25e-280)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.6e-302)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.6e-251)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.8e-227)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.51)
		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 <= -0.0115)
		tmp = t_0;
	elseif (z <= -1.25e-280)
		tmp = y * 4.0;
	elseif (z <= 4.6e-302)
		tmp = x * -3.0;
	elseif (z <= 6.6e-251)
		tmp = y * 4.0;
	elseif (z <= 4.8e-227)
		tmp = x * -3.0;
	elseif (z <= 0.51)
		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, -0.0115], t$95$0, If[LessEqual[z, -1.25e-280], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.6e-302], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.6e-251], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.8e-227], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.51], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0115 or 0.51000000000000001 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.8%

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

   6. Taylor expanded in z around inf 96.8%

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

   if -0.0115 < z < -1.25000000000000007e-280 or 4.60000000000000004e-302 < z < 6.6e-251 or 4.7999999999999999e-227 < z < 0.51000000000000001

   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* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 58.4%

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

   6. Taylor expanded in z around 0 57.8%

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

   if -1.25000000000000007e-280 < z < 4.60000000000000004e-302 or 6.6e-251 < z < 4.7999999999999999e-227

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-rgt-in 80.2%

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

      3. metadata-eval 80.2%

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

      4. neg-mul-1 80.2%

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

      5. associate-*r* 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-+r+ 80.2%

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

      8. metadata-eval 80.2%

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

      9. associate-*r* 80.2%

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

      10. metadata-eval 80.2%

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

      11. *-commutative 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in z around 0 80.2%

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

      1. *-commutative 80.2%

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

   10. Simplified 80.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0115:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-302}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-251}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-227}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.51:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.45:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-302}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-226}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.025:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.45)
     t_0
     (if (<= z -8.5e-280)
       (* y 4.0)
       (if (<= z 6.4e-302)
         (* x -3.0)
         (if (<= z 5.4e-250)
           (* y 4.0)
           (if (<= z 6e-226) (* x -3.0) (if (<= z 0.025) (* 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 <= -0.45) {
		tmp = t_0;
	} else if (z <= -8.5e-280) {
		tmp = y * 4.0;
	} else if (z <= 6.4e-302) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-250) {
		tmp = y * 4.0;
	} else if (z <= 6e-226) {
		tmp = x * -3.0;
	} else if (z <= 0.025) {
		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 <= (-0.45d0)) then
        tmp = t_0
    else if (z <= (-8.5d-280)) then
        tmp = y * 4.0d0
    else if (z <= 6.4d-302) then
        tmp = x * (-3.0d0)
    else if (z <= 5.4d-250) then
        tmp = y * 4.0d0
    else if (z <= 6d-226) then
        tmp = x * (-3.0d0)
    else if (z <= 0.025d0) 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 <= -0.45) {
		tmp = t_0;
	} else if (z <= -8.5e-280) {
		tmp = y * 4.0;
	} else if (z <= 6.4e-302) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-250) {
		tmp = y * 4.0;
	} else if (z <= 6e-226) {
		tmp = x * -3.0;
	} else if (z <= 0.025) {
		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 <= -0.45:
		tmp = t_0
	elif z <= -8.5e-280:
		tmp = y * 4.0
	elif z <= 6.4e-302:
		tmp = x * -3.0
	elif z <= 5.4e-250:
		tmp = y * 4.0
	elif z <= 6e-226:
		tmp = x * -3.0
	elif z <= 0.025:
		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 <= -0.45)
		tmp = t_0;
	elseif (z <= -8.5e-280)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.4e-302)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.4e-250)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e-226)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.025)
		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 <= -0.45)
		tmp = t_0;
	elseif (z <= -8.5e-280)
		tmp = y * 4.0;
	elseif (z <= 6.4e-302)
		tmp = x * -3.0;
	elseif (z <= 5.4e-250)
		tmp = y * 4.0;
	elseif (z <= 6e-226)
		tmp = x * -3.0;
	elseif (z <= 0.025)
		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, -0.45], t$95$0, If[LessEqual[z, -8.5e-280], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.4e-302], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.4e-250], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e-226], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.025], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.450000000000000011 or 0.025000000000000001 < 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* 99.6%

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

      3. fma-define 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 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 54.8%

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

   6. Taylor expanded in z around inf 53.8%

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

   if -0.450000000000000011 < z < -8.50000000000000037e-280 or 6.39999999999999956e-302 < z < 5.40000000000000004e-250 or 5.9999999999999999e-226 < z < 0.025000000000000001

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 59.3%

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

   6. Taylor expanded in z around 0 58.8%

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

   if -8.50000000000000037e-280 < z < 6.39999999999999956e-302 or 5.40000000000000004e-250 < z < 5.9999999999999999e-226

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-rgt-in 80.2%

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

      3. metadata-eval 80.2%

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

      4. neg-mul-1 80.2%

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

      5. associate-*r* 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-+r+ 80.2%

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

      8. metadata-eval 80.2%

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

      9. associate-*r* 80.2%

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

      10. metadata-eval 80.2%

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

      11. *-commutative 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in z around 0 80.2%

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

      1. *-commutative 80.2%

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

   10. Simplified 80.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.45:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-302}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-226}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.025:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-8} \lor \neg \left(x \leq 1150000000\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e-8) (not (<= x 1150000000.0)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-8) || !(x <= 1150000000.0)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.9d-8)) .or. (.not. (x <= 1150000000.0d0))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-8) || !(x <= 1150000000.0)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e-8) or not (x <= 1150000000.0):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e-8) || !(x <= 1150000000.0))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.9e-8) || ~((x <= 1150000000.0)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e-8], N[Not[LessEqual[x, 1150000000.0]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000014e-8 or 1.15e9 < x

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 77.6%

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

      1. sub-neg 77.6%

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

      2. distribute-rgt-in 77.6%

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

      3. metadata-eval 77.6%

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

      4. neg-mul-1 77.6%

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

      5. associate-*r* 77.6%

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

      6. *-commutative 77.6%

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

      7. associate-+r+ 77.6%

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

      8. metadata-eval 77.6%

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

      9. associate-*r* 77.6%

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

      10. metadata-eval 77.6%

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

      11. *-commutative 77.6%

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

   7. Simplified 77.6%

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

   if -1.90000000000000014e-8 < x < 1.15e9

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 78.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-8} \lor \neg \left(x \leq 1150000000\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* (- y x) (* z -6.0))
   (if (<= z 0.66) (+ x (* (- y x) 4.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.66) {
		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 <= (-0.6d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.66d0) 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 <= -0.6) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.66) {
		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 <= -0.6:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.66:
		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 <= -0.6)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.66)
		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 <= -0.6)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.66)
		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, -0.6], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], 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 < -0.599999999999999978

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.6%

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

   6. Taylor expanded in z around inf 98.6%

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

      1. associate-*r* 98.7%

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

   8. Simplified 98.7%

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

   if -0.599999999999999978 < z < 0.660000000000000031

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 97.2%

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

   if 0.660000000000000031 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.7%

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

   6. Taylor expanded in z around inf 96.7%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* (- y x) (* z -6.0))
   (if (<= z 0.68) (+ (* y 4.0) (* x -3.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.68) {
		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 <= (-0.58d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.68d0) 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 <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.68) {
		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 <= -0.58:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.68:
		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 <= -0.58)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.68)
		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 <= -0.58)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.68)
		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, -0.58], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.68], 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 < -0.57999999999999996

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.6%

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

   6. Taylor expanded in z around inf 98.6%

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

      1. associate-*r* 98.7%

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

   8. Simplified 98.7%

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

   if -0.57999999999999996 < 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. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

      1. *-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. distribute-rgt-in 99.2%

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

      4. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in x around 0 99.5%

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

      1. +-commutative 99.5%

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

      2. fma-define 99.5%

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

      3. +-commutative 99.5%

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

      4. fma-define 99.5%

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

      5. associate-*r* 99.4%

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

   9. Simplified 99.4%

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

   10. Taylor expanded in z around 0 97.3%

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

   if 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.7%

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

   6. Taylor expanded in z around inf 96.7%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00165 \lor \neg \left(x \leq 7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.00165) (not (<= x 7e-7))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.00165) || !(x <= 7e-7)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.00165d0)) .or. (.not. (x <= 7d-7))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.00165) || !(x <= 7e-7)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.00165) or not (x <= 7e-7):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.00165) || !(x <= 7e-7))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.00165) || ~((x <= 7e-7)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.00165], N[Not[LessEqual[x, 7e-7]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00165 or 6.99999999999999968e-7 < x

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 75.0%

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

      1. sub-neg 75.0%

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

      2. distribute-rgt-in 75.0%

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

      3. metadata-eval 75.0%

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

      4. neg-mul-1 75.0%

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

      5. associate-*r* 75.0%

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

      6. *-commutative 75.0%

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

      7. associate-+r+ 75.0%

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

      8. metadata-eval 75.0%

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

      9. associate-*r* 75.0%

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

      10. metadata-eval 75.0%

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

      11. *-commutative 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in z around 0 40.5%

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

      1. *-commutative 40.5%

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

   10. Simplified 40.5%

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

   if -0.00165 < x < 6.99999999999999968e-7

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 78.7%

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

   6. Taylor expanded in z around 0 45.8%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00165 \lor \neg \left(x \leq 7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 13: 26.4% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around inf 49.1%

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

   1. sub-neg 49.1%

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

   2. distribute-rgt-in 49.1%

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

   3. metadata-eval 49.1%

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

   4. neg-mul-1 49.1%

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

   5. associate-*r* 49.1%

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

   6. *-commutative 49.1%

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

   7. associate-+r+ 49.1%

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

   8. metadata-eval 49.1%

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

   9. associate-*r* 49.1%

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

   10. metadata-eval 49.1%

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

   11. *-commutative 49.1%

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

7. Simplified 49.1%

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

8. Taylor expanded in z around 0 26.1%

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

   1. *-commutative 26.1%

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

10. Simplified 26.1%

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

11. Final simplification 26.1%

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

Alternative 14: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in z around inf 46.8%

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

6. Taylor expanded in z around 0 2.6%

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

7. Final simplification 2.6%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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))))