Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 87.9% → 99.8%

Time: 8.2s

Alternatives: 14

Speedup: 0.6×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / 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 - z) + 1.0d0)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}

Python

def code(x, y, z):
	return (x * ((y - z) + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * ((y - z) + 1.0)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 87.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / 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 - z) + 1.0d0)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}

Python

def code(x, y, z):
	return (x * ((y - z) + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * ((y - z) + 1.0)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-38}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+26)
   (- (* x (/ y z)) x)
   (if (<= z 5e-38)
     (* (+ (- y z) 1.0) (/ x z))
     (* x (+ (/ (+ y 1.0) z) -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+26) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 5e-38) {
		tmp = ((y - z) + 1.0) * (x / z);
	} else {
		tmp = x * (((y + 1.0) / z) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9d+26)) then
        tmp = (x * (y / z)) - x
    else if (z <= 5d-38) then
        tmp = ((y - z) + 1.0d0) * (x / z)
    else
        tmp = x * (((y + 1.0d0) / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+26) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 5e-38) {
		tmp = ((y - z) + 1.0) * (x / z);
	} else {
		tmp = x * (((y + 1.0) / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+26:
		tmp = (x * (y / z)) - x
	elif z <= 5e-38:
		tmp = ((y - z) + 1.0) * (x / z)
	else:
		tmp = x * (((y + 1.0) / z) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+26)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (z <= 5e-38)
		tmp = Float64(Float64(Float64(y - z) + 1.0) * Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+26)
		tmp = (x * (y / z)) - x;
	elseif (z <= 5e-38)
		tmp = ((y - z) + 1.0) * (x / z);
	else
		tmp = x * (((y + 1.0) / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+26], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 5e-38], N[(N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999957e26

   1. Initial program 70.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.9%

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

      1. distribute-rgt-in 99.9%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x + -1 \cdot x} \]

      2. neg-mul-1 99.9%

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

      3. unsub-neg 99.9%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x - x} \]

      4. *-commutative 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} - x \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]

   if -8.99999999999999957e26 < z < 5.00000000000000033e-38

   1. Initial program 99.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.2%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   if 5.00000000000000033e-38 < z

   1. Initial program 82.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y + 1}{z} + -1\right)} \]
   4. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-38}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+16}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-199}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-241}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -2.1e+16)
     (- x)
     (if (<= z -4.8e-83)
       t_0
       (if (<= z -3.6e-199)
         (/ x z)
         (if (<= z 3.2e-241) t_0 (if (<= z 1.0) (/ x z) (- x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -2.1e+16) {
		tmp = -x;
	} else if (z <= -4.8e-83) {
		tmp = t_0;
	} else if (z <= -3.6e-199) {
		tmp = x / z;
	} else if (z <= 3.2e-241) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	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 * (y / z)
    if (z <= (-2.1d+16)) then
        tmp = -x
    else if (z <= (-4.8d-83)) then
        tmp = t_0
    else if (z <= (-3.6d-199)) then
        tmp = x / z
    else if (z <= 3.2d-241) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -2.1e+16) {
		tmp = -x;
	} else if (z <= -4.8e-83) {
		tmp = t_0;
	} else if (z <= -3.6e-199) {
		tmp = x / z;
	} else if (z <= 3.2e-241) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -2.1e+16:
		tmp = -x
	elif z <= -4.8e-83:
		tmp = t_0
	elif z <= -3.6e-199:
		tmp = x / z
	elif z <= 3.2e-241:
		tmp = t_0
	elif z <= 1.0:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -2.1e+16)
		tmp = Float64(-x);
	elseif (z <= -4.8e-83)
		tmp = t_0;
	elseif (z <= -3.6e-199)
		tmp = Float64(x / z);
	elseif (z <= 3.2e-241)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (z <= -2.1e+16)
		tmp = -x;
	elseif (z <= -4.8e-83)
		tmp = t_0;
	elseif (z <= -3.6e-199)
		tmp = x / z;
	elseif (z <= 3.2e-241)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+16], (-x), If[LessEqual[z, -4.8e-83], t$95$0, If[LessEqual[z, -3.6e-199], N[(x / z), $MachinePrecision], If[LessEqual[z, 3.2e-241], t$95$0, If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e16 or 1 < z

   1. Initial program 75.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.2%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   6. Step-by-step derivation

      1. neg-mul-1 75.2%

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

   7. Simplified 75.2%

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

   if -2.1e16 < z < -4.8000000000000002e-83 or -3.6000000000000002e-199 < z < 3.2e-241

   1. Initial program 99.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.0%

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

      2. +-commutative 90.0%

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

      3. associate-+r- 90.0%

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

      4. div-sub 90.0%

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

      5. *-inverses 90.0%

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

      6. sub-neg 90.0%

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

      7. +-commutative 90.0%

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

      8. metadata-eval 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in y around inf 71.2%

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

      1. associate-/l* 61.5%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   7. Simplified 61.5%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if -4.8000000000000002e-83 < z < -3.6000000000000002e-199 or 3.2e-241 < z < 1

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. sub-neg 67.1%

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

      3. metadata-eval 67.1%

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

      4. distribute-neg-in 67.1%

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

      5. +-commutative 67.1%

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

      6. associate-/l* 67.1%

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

      7. +-commutative 67.1%

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

      8. distribute-neg-in 67.1%

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

      9. metadata-eval 67.1%

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

      10. sub-neg 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in z around 0 66.7%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-84}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+45}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -2.9e+16)
     (- x)
     (if (<= z -5.4e-84)
       t_0
       (if (<= z -4e-191) (/ x z) (if (<= z 1.55e+45) t_0 (- x)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -2.9e+16) {
		tmp = -x;
	} else if (z <= -5.4e-84) {
		tmp = t_0;
	} else if (z <= -4e-191) {
		tmp = x / z;
	} else if (z <= 1.55e+45) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	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 = y * (x / z)
    if (z <= (-2.9d+16)) then
        tmp = -x
    else if (z <= (-5.4d-84)) then
        tmp = t_0
    else if (z <= (-4d-191)) then
        tmp = x / z
    else if (z <= 1.55d+45) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -2.9e+16) {
		tmp = -x;
	} else if (z <= -5.4e-84) {
		tmp = t_0;
	} else if (z <= -4e-191) {
		tmp = x / z;
	} else if (z <= 1.55e+45) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -2.9e+16:
		tmp = -x
	elif z <= -5.4e-84:
		tmp = t_0
	elif z <= -4e-191:
		tmp = x / z
	elif z <= 1.55e+45:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -2.9e+16)
		tmp = Float64(-x);
	elseif (z <= -5.4e-84)
		tmp = t_0;
	elseif (z <= -4e-191)
		tmp = Float64(x / z);
	elseif (z <= 1.55e+45)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -2.9e+16)
		tmp = -x;
	elseif (z <= -5.4e-84)
		tmp = t_0;
	elseif (z <= -4e-191)
		tmp = x / z;
	elseif (z <= 1.55e+45)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+16], (-x), If[LessEqual[z, -5.4e-84], t$95$0, If[LessEqual[z, -4e-191], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.55e+45], t$95$0, (-x)]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e16 or 1.54999999999999994e45 < z

   1. Initial program 74.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.6%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   6. Step-by-step derivation

      1. neg-mul-1 77.6%

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

   7. Simplified 77.6%

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

   if -2.9e16 < z < -5.3999999999999998e-84 or -4.0000000000000001e-191 < z < 1.54999999999999994e45

   1. Initial program 99.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.0%

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

      2. +-commutative 91.0%

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

      3. associate-+r- 91.0%

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

      4. div-sub 91.0%

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

      5. *-inverses 91.0%

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

      6. sub-neg 91.0%

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

      7. +-commutative 91.0%

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

      8. metadata-eval 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{z} \]

      2. associate-/l* 65.2%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   7. Applied egg-rr 65.2%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   if -5.3999999999999998e-84 < z < -4.0000000000000001e-191

   1. Initial program 100.0%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. metadata-eval 71.9%

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

      4. distribute-neg-in 71.9%

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

      5. +-commutative 71.9%

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

      6. associate-/l* 71.9%

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

      7. +-commutative 71.9%

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

      8. distribute-neg-in 71.9%

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

      9. metadata-eval 71.9%

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

      10. sub-neg 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in z around 0 71.9%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10000000 \lor \neg \left(z \leq 4 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -10000000.0) (not (<= z 4e-39)))
   (* x (+ (/ (+ y 1.0) z) -1.0))
   (/ (* x (+ y 1.0)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -10000000.0) || !(z <= 4e-39)) {
		tmp = x * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x * (y + 1.0)) / 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 <= (-10000000.0d0)) .or. (.not. (z <= 4d-39))) then
        tmp = x * (((y + 1.0d0) / z) + (-1.0d0))
    else
        tmp = (x * (y + 1.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -10000000.0) || !(z <= 4e-39)) {
		tmp = x * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -10000000.0) or not (z <= 4e-39):
		tmp = x * (((y + 1.0) / z) + -1.0)
	else:
		tmp = (x * (y + 1.0)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -10000000.0) || !(z <= 4e-39))
		tmp = Float64(x * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	else
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -10000000.0) || ~((z <= 4e-39)))
		tmp = x * (((y + 1.0) / z) + -1.0);
	else
		tmp = (x * (y + 1.0)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -10000000.0], N[Not[LessEqual[z, 4e-39]], $MachinePrecision]], N[(x * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e7 or 3.99999999999999972e-39 < z

   1. Initial program 77.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   if -1e7 < z < 3.99999999999999972e-39

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.7%

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

      2. +-commutative 91.7%

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

      3. associate-+r- 91.7%

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

      4. div-sub 91.7%

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

      5. *-inverses 91.7%

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

      6. sub-neg 91.7%

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

      7. +-commutative 91.7%

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

      8. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 + y\right)}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10000000 \lor \neg \left(z \leq 4 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4000.0) (not (<= y 1.0)))
   (* x (+ (/ y z) -1.0))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4000.0) || !(y <= 1.0)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * ((y / z) + (-1.0d0))
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4000.0) || !(y <= 1.0)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4000.0) or not (y <= 1.0):
		tmp = x * ((y / z) + -1.0)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4000.0) || !(y <= 1.0))
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4000.0) || ~((y <= 1.0)))
		tmp = x * ((y / z) + -1.0);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e3 or 1 < y

   1. Initial program 88.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.3%

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

      2. +-commutative 92.3%

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

      3. associate-+r- 92.3%

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

      4. div-sub 92.3%

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

      5. *-inverses 92.3%

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

      6. sub-neg 92.3%

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

      7. +-commutative 92.3%

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

      8. metadata-eval 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around inf 92.1%

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

   if -4e3 < y < 1

   1. Initial program 88.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y + 1}{z} + x \cdot -1} \]

      2. clear-num 99.8%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{z}{y + 1}}} + x \cdot -1 \]

      3. un-div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + 1}}} + x \cdot -1 \]

      4. *-commutative 100.0%

         \[\leadsto \frac{x}{\frac{z}{y + 1}} + \color{blue}{-1 \cdot x} \]

      5. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 99.3%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10000000:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -10000000.0)
   (- (* x (/ y z)) x)
   (if (<= z 1.0) (/ (* x (+ y 1.0)) z) (* x (+ (/ y z) -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -10000000.0) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 1.0) {
		tmp = (x * (y + 1.0)) / z;
	} else {
		tmp = x * ((y / z) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-10000000.0d0)) then
        tmp = (x * (y / z)) - x
    else if (z <= 1.0d0) then
        tmp = (x * (y + 1.0d0)) / z
    else
        tmp = x * ((y / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -10000000.0) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 1.0) {
		tmp = (x * (y + 1.0)) / z;
	} else {
		tmp = x * ((y / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -10000000.0:
		tmp = (x * (y / z)) - x
	elif z <= 1.0:
		tmp = (x * (y + 1.0)) / z
	else:
		tmp = x * ((y / z) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -10000000.0)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (z <= 1.0)
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	else
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -10000000.0)
		tmp = (x * (y / z)) - x;
	elseif (z <= 1.0)
		tmp = (x * (y + 1.0)) / z;
	else
		tmp = x * ((y / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -10000000.0], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e7

   1. Initial program 71.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.2%

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

      1. distribute-rgt-in 99.2%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x + -1 \cdot x} \]

      2. neg-mul-1 99.2%

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

      3. unsub-neg 99.2%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x - x} \]

      4. *-commutative 99.2%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} - x \]

   7. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]

   if -1e7 < z < 1

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.1%

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

      2. +-commutative 92.1%

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

      3. associate-+r- 92.1%

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

      4. div-sub 92.1%

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

      5. *-inverses 92.1%

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

      6. sub-neg 92.1%

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

      7. +-commutative 92.1%

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

      8. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around 0 99.7%

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

   if 1 < z

   1. Initial program 80.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.0%

      \[\leadsto x \cdot \left(\frac{\color{blue}{y}}{z} + -1\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10000000:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4000.0)
   (* x (+ (/ y z) -1.0))
   (if (<= y 1.0) (- (/ x z) x) (- (* x (/ y z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4000.0) {
		tmp = x * ((y / z) + -1.0);
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4000.0d0)) then
        tmp = x * ((y / z) + (-1.0d0))
    else if (y <= 1.0d0) then
        tmp = (x / z) - x
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4000.0) {
		tmp = x * ((y / z) + -1.0);
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4000.0:
		tmp = x * ((y / z) + -1.0)
	elif y <= 1.0:
		tmp = (x / z) - x
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4000.0)
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	elseif (y <= 1.0)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4000.0)
		tmp = x * ((y / z) + -1.0);
	elseif (y <= 1.0)
		tmp = (x / z) - x;
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4000.0], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4e3

   1. Initial program 90.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.5%

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

      2. +-commutative 91.5%

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

      3. associate-+r- 91.5%

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

      4. div-sub 91.5%

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

      5. *-inverses 91.5%

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

      6. sub-neg 91.5%

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

      7. +-commutative 91.5%

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

      8. metadata-eval 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in y around inf 91.5%

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

   if -4e3 < y < 1

   1. Initial program 88.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y + 1}{z} + x \cdot -1} \]

      2. clear-num 99.8%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{z}{y + 1}}} + x \cdot -1 \]

      3. un-div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + 1}}} + x \cdot -1 \]

      4. *-commutative 100.0%

         \[\leadsto \frac{x}{\frac{z}{y + 1}} + \color{blue}{-1 \cdot x} \]

      5. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 99.3%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   if 1 < y

   1. Initial program 87.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 93.1%

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

      2. +-commutative 93.1%

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

      3. associate-+r- 93.1%

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

      4. div-sub 93.1%

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

      5. *-inverses 93.1%

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

      6. sub-neg 93.1%

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

      7. +-commutative 93.1%

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

      8. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around inf 92.7%

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

      1. distribute-rgt-in 92.8%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x + -1 \cdot x} \]

      2. neg-mul-1 92.8%

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

      3. unsub-neg 92.8%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot x - x} \]

      4. *-commutative 92.8%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} - x \]

   7. Applied egg-rr 92.8%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -10000 \lor \neg \left(y \leq 1.8 \cdot 10^{+186}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -10000.0) (not (<= y 1.8e+186))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -10000.0) || !(y <= 1.8e+186)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-10000.0d0)) .or. (.not. (y <= 1.8d+186))) then
        tmp = y * (x / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -10000.0) || !(y <= 1.8e+186)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -10000.0) or not (y <= 1.8e+186):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -10000.0) || !(y <= 1.8e+186))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -10000.0) || ~((y <= 1.8e+186)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -10000.0], N[Not[LessEqual[y, 1.8e+186]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e4 or 1.8000000000000001e186 < y

   1. Initial program 89.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.2%

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

      2. +-commutative 90.2%

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

      3. associate-+r- 90.2%

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

      4. div-sub 90.2%

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

      5. *-inverses 90.2%

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

      6. sub-neg 90.2%

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

      7. +-commutative 90.2%

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

      8. metadata-eval 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around inf 80.6%

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

      1. *-commutative 80.6%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{z} \]

      2. associate-/l* 81.3%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   7. Applied egg-rr 81.3%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   if -1e4 < y < 1.8000000000000001e186

   1. Initial program 88.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+r- 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

      6. sub-neg 99.3%

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

      7. +-commutative 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

      1. distribute-lft-in 99.3%

         \[\leadsto \color{blue}{x \cdot \frac{y + 1}{z} + x \cdot -1} \]

      2. clear-num 99.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{z}{y + 1}}} + x \cdot -1 \]

      3. un-div-inv 99.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + 1}}} + x \cdot -1 \]

      4. *-commutative 99.4%

         \[\leadsto \frac{x}{\frac{z}{y + 1}} + \color{blue}{-1 \cdot x} \]

      5. mul-1-neg 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in y around 0 91.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10000 \lor \neg \left(y \leq 1.8 \cdot 10^{+186}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6800:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6800.0)
   (* y (/ x z))
   (if (<= y 1.8e+186) (- (/ x z) x) (/ (* x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6800.0) {
		tmp = y * (x / z);
	} else if (y <= 1.8e+186) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6800.0d0)) then
        tmp = y * (x / z)
    else if (y <= 1.8d+186) then
        tmp = (x / z) - x
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6800.0) {
		tmp = y * (x / z);
	} else if (y <= 1.8e+186) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6800.0:
		tmp = y * (x / z)
	elif y <= 1.8e+186:
		tmp = (x / z) - x
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6800.0)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.8e+186)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6800.0)
		tmp = y * (x / z);
	elseif (y <= 1.8e+186)
		tmp = (x / z) - x;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6800.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+186], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6800

   1. Initial program 90.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.5%

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

      2. +-commutative 91.5%

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

      3. associate-+r- 91.5%

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

      4. div-sub 91.5%

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

      5. *-inverses 91.5%

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

      6. sub-neg 91.5%

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

      7. +-commutative 91.5%

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

      8. metadata-eval 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{z} \]

      2. associate-/l* 83.1%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   7. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

   if -6800 < y < 1.8000000000000001e186

   1. Initial program 88.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-+r- 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

      6. sub-neg 99.3%

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

      7. +-commutative 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

      1. distribute-lft-in 99.3%

         \[\leadsto \color{blue}{x \cdot \frac{y + 1}{z} + x \cdot -1} \]

      2. clear-num 99.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{z}{y + 1}}} + x \cdot -1 \]

      3. un-div-inv 99.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + 1}}} + x \cdot -1 \]

      4. *-commutative 99.4%

         \[\leadsto \frac{x}{\frac{z}{y + 1}} + \color{blue}{-1 \cdot x} \]

      5. mul-1-neg 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in y around 0 91.1%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   if 1.8000000000000001e186 < y

   1. Initial program 86.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.0%

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

      2. +-commutative 87.0%

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

      3. associate-+r- 87.0%

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

      4. div-sub 87.0%

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

      5. *-inverses 87.0%

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

      6. sub-neg 87.0%

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

      7. +-commutative 87.0%

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

      8. metadata-eval 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in y around inf 79.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2e-67) (/ (* x (+ (- y z) 1.0)) z) (- (/ x (/ z (+ y 1.0))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-67) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (x / (z / (y + 1.0))) - x;
	}
	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 <= 2d-67) then
        tmp = (x * ((y - z) + 1.0d0)) / z
    else
        tmp = (x / (z / (y + 1.0d0))) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-67) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (x / (z / (y + 1.0))) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2e-67:
		tmp = (x * ((y - z) + 1.0)) / z
	else:
		tmp = (x / (z / (y + 1.0))) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2e-67)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(Float64(x / Float64(z / Float64(y + 1.0))) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2e-67)
		tmp = (x * ((y - z) + 1.0)) / z;
	else
		tmp = (x / (z / (y + 1.0))) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2e-67], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.99999999999999989e-67

   1. Initial program 89.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   if 1.99999999999999989e-67 < x

   1. Initial program 86.0%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y + 1}{z} + x \cdot -1} \]

      2. clear-num 99.9%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{z}{y + 1}}} + x \cdot -1 \]

      3. un-div-inv 99.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + 1}}} + x \cdot -1 \]

      4. *-commutative 99.9%

         \[\leadsto \frac{x}{\frac{z}{y + 1}} + \color{blue}{-1 \cdot x} \]

      5. mul-1-neg 99.9%

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

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + 1}} + \left(-x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;x \leq 2.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= x 2.5e-46) (/ (* x t_0) z) (* t_0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 2.5e-46) {
		tmp = (x * t_0) / z;
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y - z) + 1.0d0
    if (x <= 2.5d-46) then
        tmp = (x * t_0) / z
    else
        tmp = t_0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 2.5e-46) {
		tmp = (x * t_0) / z;
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if x <= 2.5e-46:
		tmp = (x * t_0) / z
	else:
		tmp = t_0 * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (x <= 2.5e-46)
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(t_0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if (x <= 2.5e-46)
		tmp = (x * t_0) / z;
	else
		tmp = t_0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, 2.5e-46], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 2.49999999999999996e-46

   1. Initial program 90.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   if 2.49999999999999996e-46 < x

   1. Initial program 85.1%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 85.1%

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

      2. associate-/l* 100.0%

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

      3. +-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-15} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e-15) (not (<= z 1.0))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-15) || !(z <= 1.0)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.5d-15)) .or. (.not. (z <= 1.0d0))) then
        tmp = -x
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-15) || !(z <= 1.0)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e-15) or not (z <= 1.0):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e-15) || !(z <= 1.0))
		tmp = Float64(-x);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e-15) || ~((z <= 1.0)))
		tmp = -x;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e-15], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e-15 or 1 < z

   1. Initial program 76.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.1%

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

      2. +-commutative 99.1%

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

      3. associate-+r- 99.1%

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

      4. div-sub 99.1%

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

      5. *-inverses 99.1%

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

      6. sub-neg 99.1%

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

      7. +-commutative 99.1%

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

      8. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   6. Step-by-step derivation

      1. neg-mul-1 72.2%

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

   7. Simplified 72.2%

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

   if -2.5e-15 < z < 1

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 54.4%

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

      1. *-commutative 54.4%

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

      2. sub-neg 54.4%

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

      3. metadata-eval 54.4%

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

      4. distribute-neg-in 54.4%

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

      5. +-commutative 54.4%

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

      6. associate-/l* 54.4%

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

      7. +-commutative 54.4%

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

      8. distribute-neg-in 54.4%

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

      9. metadata-eval 54.4%

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

      10. sub-neg 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in z around 0 54.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-15} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.7% accurate, 4.5× 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 Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 88.6%

   \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 95.9%

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

   2. +-commutative 95.9%

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

   3. associate-+r- 95.9%

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

   4. div-sub 95.9%

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

   5. *-inverses 95.9%

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

   6. sub-neg 95.9%

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

   7. +-commutative 95.9%

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

   8. metadata-eval 95.9%

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

3. Simplified 95.9%

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

5. Taylor expanded in z around inf 37.1%

   \[\leadsto \color{blue}{-1 \cdot x} \]
6. Step-by-step derivation

   1. neg-mul-1 37.1%

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

7. Simplified 37.1%

   \[\leadsto \color{blue}{-x} \]
8. Add Preprocessing

Alternative 14: 3.0% accurate, 9.0× 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 88.6%

   \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 95.9%

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

   2. +-commutative 95.9%

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

   3. associate-+r- 95.9%

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

   4. div-sub 95.9%

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

   5. *-inverses 95.9%

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

   6. sub-neg 95.9%

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

   7. +-commutative 95.9%

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

   8. metadata-eval 95.9%

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

3. Simplified 95.9%

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

5. Taylor expanded in z around inf 37.1%

   \[\leadsto \color{blue}{-1 \cdot x} \]
6. Step-by-step derivation

   1. neg-mul-1 37.1%

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

7. Simplified 37.1%

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

   1. neg-sub0 37.1%

      \[\leadsto \color{blue}{0 - x} \]

   2. sub-neg 37.1%

      \[\leadsto \color{blue}{0 + \left(-x\right)} \]

   3. add-sqr-sqrt 16.6%

      \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   4. sqrt-unprod 18.6%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   5. sqr-neg 18.6%

      \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   6. sqrt-unprod 1.9%

      \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   7. add-sqr-sqrt 3.1%

      \[\leadsto 0 + \color{blue}{x} \]

9. Applied egg-rr 3.1%

   \[\leadsto \color{blue}{0 + x} \]
10. Step-by-step derivation

    1. +-lft-identity 3.1%

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

11. Simplified 3.1%

    \[\leadsto \color{blue}{x} \]
12. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / 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 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / 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 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024191 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -67870776678359/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (+ 1 y) (/ x z)) x) (if (< x 1937054408219773/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x))))

  (/ (* x (+ (- y z) 1.0)) z))