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

Percentage Accurate: 88.1% → 99.7%

Time: 7.1s

Alternatives: 11

Speedup: 1.0×

• 20.7% 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: 88.1% 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: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_0}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + \left(1 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t\_0}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= z -4.2e-72)
     (/ x (/ z t_0))
     (if (<= z 5.5e-63) (* (/ x z) (+ y (- 1.0 z))) (* x (/ t_0 z))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (z <= -4.2e-72) {
		tmp = x / (z / t_0);
	} else if (z <= 5.5e-63) {
		tmp = (x / z) * (y + (1.0 - z));
	} else {
		tmp = x * (t_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) :: t_0
    real(8) :: tmp
    t_0 = (y - z) + 1.0d0
    if (z <= (-4.2d-72)) then
        tmp = x / (z / t_0)
    else if (z <= 5.5d-63) then
        tmp = (x / z) * (y + (1.0d0 - z))
    else
        tmp = x * (t_0 / 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 (z <= -4.2e-72) {
		tmp = x / (z / t_0);
	} else if (z <= 5.5e-63) {
		tmp = (x / z) * (y + (1.0 - z));
	} else {
		tmp = x * (t_0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if z <= -4.2e-72:
		tmp = x / (z / t_0)
	elif z <= 5.5e-63:
		tmp = (x / z) * (y + (1.0 - z))
	else:
		tmp = x * (t_0 / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (z <= -4.2e-72)
		tmp = Float64(x / Float64(z / t_0));
	elseif (z <= 5.5e-63)
		tmp = Float64(Float64(x / z) * Float64(y + Float64(1.0 - z)));
	else
		tmp = Float64(x * Float64(t_0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if (z <= -4.2e-72)
		tmp = x / (z / t_0);
	elseif (z <= 5.5e-63)
		tmp = (x / z) * (y + (1.0 - z));
	else
		tmp = x * (t_0 / 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[z, -4.2e-72], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-63], N[(N[(x / z), $MachinePrecision] * N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e-72

   1. Initial program 78.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -4.2e-72 < z < 5.50000000000000043e-63

   1. Initial program 99.9%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*l/ 99.9%

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

      4. associate-+l- 99.9%

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

   7. Simplified 99.9%

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

   if 5.50000000000000043e-63 < z

   1. Initial program 80.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + \left(1 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-283}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 122000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -1.0)
     (- x)
     (if (<= z -9.2e-255)
       (/ x z)
       (if (<= z 5e-283)
         t_0
         (if (<= z 8.8e-158) (/ x z) (if (<= z 122000.0) t_0 (- x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -9.2e-255) {
		tmp = x / z;
	} else if (z <= 5e-283) {
		tmp = t_0;
	} else if (z <= 8.8e-158) {
		tmp = x / z;
	} else if (z <= 122000.0) {
		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 = x * (y / z)
    if (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= (-9.2d-255)) then
        tmp = x / z
    else if (z <= 5d-283) then
        tmp = t_0
    else if (z <= 8.8d-158) then
        tmp = x / z
    else if (z <= 122000.0d0) 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 = x * (y / z);
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -9.2e-255) {
		tmp = x / z;
	} else if (z <= 5e-283) {
		tmp = t_0;
	} else if (z <= 8.8e-158) {
		tmp = x / z;
	} else if (z <= 122000.0) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= -9.2e-255:
		tmp = x / z
	elif z <= 5e-283:
		tmp = t_0
	elif z <= 8.8e-158:
		tmp = x / z
	elif z <= 122000.0:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= -9.2e-255)
		tmp = Float64(x / z);
	elseif (z <= 5e-283)
		tmp = t_0;
	elseif (z <= 8.8e-158)
		tmp = Float64(x / z);
	elseif (z <= 122000.0)
		tmp = t_0;
	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 <= -1.0)
		tmp = -x;
	elseif (z <= -9.2e-255)
		tmp = x / z;
	elseif (z <= 5e-283)
		tmp = t_0;
	elseif (z <= 8.8e-158)
		tmp = x / z;
	elseif (z <= 122000.0)
		tmp = t_0;
	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, -1.0], (-x), If[LessEqual[z, -9.2e-255], N[(x / z), $MachinePrecision], If[LessEqual[z, 5e-283], t$95$0, If[LessEqual[z, 8.8e-158], N[(x / z), $MachinePrecision], If[LessEqual[z, 122000.0], t$95$0, (-x)]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 122000 < z

   1. Initial program 74.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.4%

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

      1. neg-mul-1 79.4%

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

   7. Simplified 79.4%

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

   if -1 < z < -9.1999999999999995e-255 or 5.0000000000000001e-283 < z < 8.8000000000000004e-158

   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%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in y around 0 68.1%

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

      1. associate-/l* 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in z around 0 67.4%

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

   if -9.1999999999999995e-255 < z < 5.0000000000000001e-283 or 8.8000000000000004e-158 < z < 122000

   1. Initial program 99.8%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 67.9%

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

      1. associate-/l* 61.5%

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

   7. Simplified 61.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 122000:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-255}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 100000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -1.0)
     (- x)
     (if (<= z -4.3e-254)
       (/ x z)
       (if (<= z 6.2e-255)
         t_0
         (if (<= z 1.7e-222) (/ x z) (if (<= z 100000.0) t_0 (- x))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -4.3e-254) {
		tmp = x / z;
	} else if (z <= 6.2e-255) {
		tmp = t_0;
	} else if (z <= 1.7e-222) {
		tmp = x / z;
	} else if (z <= 100000.0) {
		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 <= (-1.0d0)) then
        tmp = -x
    else if (z <= (-4.3d-254)) then
        tmp = x / z
    else if (z <= 6.2d-255) then
        tmp = t_0
    else if (z <= 1.7d-222) then
        tmp = x / z
    else if (z <= 100000.0d0) 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 <= -1.0) {
		tmp = -x;
	} else if (z <= -4.3e-254) {
		tmp = x / z;
	} else if (z <= 6.2e-255) {
		tmp = t_0;
	} else if (z <= 1.7e-222) {
		tmp = x / z;
	} else if (z <= 100000.0) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= -4.3e-254:
		tmp = x / z
	elif z <= 6.2e-255:
		tmp = t_0
	elif z <= 1.7e-222:
		tmp = x / z
	elif z <= 100000.0:
		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 <= -1.0)
		tmp = Float64(-x);
	elseif (z <= -4.3e-254)
		tmp = Float64(x / z);
	elseif (z <= 6.2e-255)
		tmp = t_0;
	elseif (z <= 1.7e-222)
		tmp = Float64(x / z);
	elseif (z <= 100000.0)
		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 <= -1.0)
		tmp = -x;
	elseif (z <= -4.3e-254)
		tmp = x / z;
	elseif (z <= 6.2e-255)
		tmp = t_0;
	elseif (z <= 1.7e-222)
		tmp = x / z;
	elseif (z <= 100000.0)
		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, -1.0], (-x), If[LessEqual[z, -4.3e-254], N[(x / z), $MachinePrecision], If[LessEqual[z, 6.2e-255], t$95$0, If[LessEqual[z, 1.7e-222], N[(x / z), $MachinePrecision], If[LessEqual[z, 100000.0], t$95$0, (-x)]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1e5 < z

   1. Initial program 74.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.4%

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

      1. neg-mul-1 79.4%

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

   7. Simplified 79.4%

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

   if -1 < z < -4.2999999999999997e-254 or 6.19999999999999995e-255 < z < 1.7000000000000001e-222

   1. Initial program 99.9%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around 0 74.0%

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

      1. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in z around 0 73.1%

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

   if -4.2999999999999997e-254 < z < 6.19999999999999995e-255 or 1.7000000000000001e-222 < z < 1e5

   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%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-*r/ 66.7%

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

   7. Simplified 66.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 100000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-14} \lor \neg \left(z \leq 6 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + \left(1 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-14) (not (<= z 6e-63)))
   (* x (/ (+ (- y z) 1.0) z))
   (* (/ x z) (+ y (- 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-14) || !(z <= 6e-63)) {
		tmp = x * (((y - z) + 1.0) / z);
	} else {
		tmp = (x / z) * (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 <= (-5d-14)) .or. (.not. (z <= 6d-63))) then
        tmp = x * (((y - z) + 1.0d0) / z)
    else
        tmp = (x / z) * (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 <= -5e-14) || !(z <= 6e-63)) {
		tmp = x * (((y - z) + 1.0) / z);
	} else {
		tmp = (x / z) * (y + (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-14) or not (z <= 6e-63):
		tmp = x * (((y - z) + 1.0) / z)
	else:
		tmp = (x / z) * (y + (1.0 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-14) || !(z <= 6e-63))
		tmp = Float64(x * Float64(Float64(Float64(y - z) + 1.0) / z));
	else
		tmp = Float64(Float64(x / z) * Float64(y + Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5e-14) || ~((z <= 6e-63)))
		tmp = x * (((y - z) + 1.0) / z);
	else
		tmp = (x / z) * (y + (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-14], N[Not[LessEqual[z, 6e-63]], $MachinePrecision]], N[(x * N[(N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e-14 or 5.99999999999999959e-63 < z

   1. Initial program 78.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -5.0000000000000002e-14 < z < 5.99999999999999959e-63

   1. Initial program 99.9%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in x around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*l/ 99.9%

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

      4. associate-+l- 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-14} \lor \neg \left(z \leq 6 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + \left(1 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.15 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.15e-11)))
   (* x (+ (/ y z) -1.0))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.15e-11)) {
		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 <= (-1.0d0)) .or. (.not. (y <= 1.15d-11))) 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 <= -1.0) || !(y <= 1.15e-11)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.15e-11):
		tmp = x * ((y / z) + -1.0)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.15e-11))
		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 <= -1.0) || ~((y <= 1.15e-11)))
		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, -1.0], N[Not[LessEqual[y, 1.15e-11]], $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 < -1 or 1.15000000000000007e-11 < y

   1. Initial program 85.8%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

      1. associate-+l- 92.6%

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

      2. div-sub 91.8%

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

      3. sub-neg 91.8%

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

      4. metadata-eval 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in z around inf 90.9%

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

   if -1 < y < 1.15000000000000007e-11

   1. Initial program 89.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 89.4%

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

      1. remove-double-neg 89.4%

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

      2. distribute-neg-frac2 89.4%

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

      3. distribute-frac-neg 89.4%

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

      4. distribute-rgt-neg-in 89.4%

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

      5. neg-sub0 89.4%

         \[\leadsto \frac{x \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}}{-z} \]

      6. associate--r- 89.4%

         \[\leadsto \frac{x \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}}{-z} \]

      7. metadata-eval 89.4%

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

      8. +-commutative 89.4%

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

      9. associate-*r/ 99.6%

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

      10. distribute-neg-frac2 99.6%

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

      11. distribute-neg-frac 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. metadata-eval 99.6%

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

      14. +-commutative 99.6%

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

      15. sub-neg 99.6%

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

      16. div-sub 99.6%

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

      17. *-inverses 99.6%

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

      18. sub-neg 99.6%

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

      19. metadata-eval 99.6%

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

      20. +-commutative 99.6%

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

      21. +-commutative 99.6%

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

      22. distribute-rgt-in 99.6%

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

      23. associate-*l/ 99.7%

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

      24. *-lft-identity 99.7%

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

      25. neg-mul-1 99.7%

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

      26. unsub-neg 99.7%

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

   9. Simplified 99.7%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.15 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+57} \lor \neg \left(y \leq 1.55 \cdot 10^{+72}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.05e+57) (not (<= y 1.55e+72))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e+57) || !(y <= 1.55e+72)) {
		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 <= (-2.05d+57)) .or. (.not. (y <= 1.55d+72))) 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 <= -2.05e+57) || !(y <= 1.55e+72)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.05e+57) or not (y <= 1.55e+72):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.05e+57) || !(y <= 1.55e+72))
		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 <= -2.05e+57) || ~((y <= 1.55e+72)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.05e+57], N[Not[LessEqual[y, 1.55e+72]], $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 < -2.05e57 or 1.54999999999999994e72 < y

   1. Initial program 86.3%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*r/ 82.0%

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

   7. Simplified 82.0%

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

   if -2.05e57 < y < 1.54999999999999994e72

   1. Initial program 88.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 82.5%

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

      1. remove-double-neg 82.5%

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

      2. distribute-neg-frac2 82.5%

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

      3. distribute-frac-neg 82.5%

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

      4. distribute-rgt-neg-in 82.5%

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

      5. neg-sub0 82.5%

         \[\leadsto \frac{x \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}}{-z} \]

      6. associate--r- 82.5%

         \[\leadsto \frac{x \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}}{-z} \]

      7. metadata-eval 82.5%

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

      8. +-commutative 82.5%

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

      9. associate-*r/ 93.9%

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

      10. distribute-neg-frac2 93.9%

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

      11. distribute-neg-frac 93.9%

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

      12. distribute-neg-in 93.9%

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

      13. metadata-eval 93.9%

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

      14. +-commutative 93.9%

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

      15. sub-neg 93.9%

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

      16. div-sub 93.9%

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

      17. *-inverses 93.9%

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

      18. sub-neg 93.9%

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

      19. metadata-eval 93.9%

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

      20. +-commutative 93.9%

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

      21. +-commutative 93.9%

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

      22. distribute-rgt-in 93.9%

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

      23. associate-*l/ 94.0%

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

      24. *-lft-identity 94.0%

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

      25. neg-mul-1 94.0%

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

      26. unsub-neg 94.0%

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

   9. Simplified 94.0%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+57} \lor \neg \left(y \leq 1.55 \cdot 10^{+72}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.05e+57)
   (* y (/ x z))
   (if (<= y 2.5e+71) (- (/ x z) x) (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.05e+57) {
		tmp = y * (x / z);
	} else if (y <= 2.5e+71) {
		tmp = (x / z) - x;
	} else {
		tmp = 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 <= (-2.05d+57)) then
        tmp = y * (x / z)
    else if (y <= 2.5d+71) then
        tmp = (x / z) - x
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.05e+57) {
		tmp = y * (x / z);
	} else if (y <= 2.5e+71) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.05e+57:
		tmp = y * (x / z)
	elif y <= 2.5e+71:
		tmp = (x / z) - x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.05e+57)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 2.5e+71)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.05e+57)
		tmp = y * (x / z);
	elseif (y <= 2.5e+71)
		tmp = (x / z) - x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.05e+57], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+71], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e57

   1. Initial program 87.4%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around inf 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-*r/ 91.2%

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

   7. Simplified 91.2%

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

   if -2.05e57 < y < 2.49999999999999986e71

   1. Initial program 88.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 82.5%

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

      1. remove-double-neg 82.5%

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

      2. distribute-neg-frac2 82.5%

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

      3. distribute-frac-neg 82.5%

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

      4. distribute-rgt-neg-in 82.5%

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

      5. neg-sub0 82.5%

         \[\leadsto \frac{x \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}}{-z} \]

      6. associate--r- 82.5%

         \[\leadsto \frac{x \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}}{-z} \]

      7. metadata-eval 82.5%

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

      8. +-commutative 82.5%

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

      9. associate-*r/ 93.9%

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

      10. distribute-neg-frac2 93.9%

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

      11. distribute-neg-frac 93.9%

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

      12. distribute-neg-in 93.9%

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

      13. metadata-eval 93.9%

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

      14. +-commutative 93.9%

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

      15. sub-neg 93.9%

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

      16. div-sub 93.9%

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

      17. *-inverses 93.9%

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

      18. sub-neg 93.9%

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

      19. metadata-eval 93.9%

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

      20. +-commutative 93.9%

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

      21. +-commutative 93.9%

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

      22. distribute-rgt-in 93.9%

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

      23. associate-*l/ 94.0%

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

      24. *-lft-identity 94.0%

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

      25. neg-mul-1 94.0%

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

      26. unsub-neg 94.0%

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

   9. Simplified 94.0%

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

   if 2.49999999999999986e71 < y

   1. Initial program 85.5%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

      1. clear-num 88.9%

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

      2. un-div-inv 90.2%

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

   6. Applied egg-rr 90.2%

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

   7. Taylor expanded in y around inf 69.8%

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

      1. associate-/r/ 74.3%

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

   9. Applied egg-rr 74.3%

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

       1. *-commutative 74.3%

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

       2. clear-num 74.4%

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

       3. un-div-inv 74.5%

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

   11. Applied egg-rr 74.5%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;x \leq 1.5 \cdot 10^{-118}:\\ \;\;\;\;\frac{x \cdot t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= x 1.5e-118) (/ (* x t_0) z) (/ x (/ z t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 1.5e-118) {
		tmp = (x * t_0) / z;
	} else {
		tmp = x / (z / 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 = (y - z) + 1.0d0
    if (x <= 1.5d-118) then
        tmp = (x * t_0) / z
    else
        tmp = x / (z / t_0)
    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 <= 1.5e-118) {
		tmp = (x * t_0) / z;
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if x <= 1.5e-118:
		tmp = (x * t_0) / z
	else:
		tmp = x / (z / t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (x <= 1.5e-118)
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(x / Float64(z / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if (x <= 1.5e-118)
		tmp = (x * t_0) / z;
	else
		tmp = x / (z / t_0);
	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, 1.5e-118], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.50000000000000009e-118

   1. Initial program 87.2%

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

   if 1.50000000000000009e-118 < x

   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%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{-118}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(z <= 1.0)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 74.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.8%

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

      1. neg-mul-1 78.8%

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

   7. Simplified 78.8%

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

   if -1 < 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* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in y around 0 54.4%

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

      1. associate-/l* 54.3%

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

   7. Simplified 54.3%

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

   8. Taylor expanded in z around 0 53.9%

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

4. Final simplification 65.9%

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

Alternative 10: 95.8% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.7%

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

   1. associate-/l* 96.1%

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

3. Simplified 96.1%

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

5. Final simplification 96.1%

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

Alternative 11: 39.1% 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 87.7%

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

   1. associate-/l* 96.1%

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

3. Simplified 96.1%

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

5. Taylor expanded in z around inf 39.7%

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

   1. neg-mul-1 39.7%

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

7. Simplified 39.7%

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

8. Final simplification 39.7%

   \[\leadsto -x \]
9. Add Preprocessing

Developer target: 99.4% 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 2024078 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

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