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

Percentage Accurate: 88.3% → 99.9%

Time: 7.4s

Alternatives: 12

Speedup: 0.6×

• 22.2% 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: 88.3% 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: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.015 \lor \neg \left(z \leq 1.5 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \frac{y + \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \left(y - z\right)\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.015) (not (<= z 1.5e-34)))
   (* x (/ (+ y (- 1.0 z)) z))
   (* (+ 1.0 (- y z)) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.015) || !(z <= 1.5e-34)) {
		tmp = x * ((y + (1.0 - z)) / z);
	} else {
		tmp = (1.0 + (y - z)) * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.015d0)) .or. (.not. (z <= 1.5d-34))) then
        tmp = x * ((y + (1.0d0 - z)) / z)
    else
        tmp = (1.0d0 + (y - z)) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.015) || !(z <= 1.5e-34)) {
		tmp = x * ((y + (1.0 - z)) / z);
	} else {
		tmp = (1.0 + (y - z)) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.015) or not (z <= 1.5e-34):
		tmp = x * ((y + (1.0 - z)) / z)
	else:
		tmp = (1.0 + (y - z)) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.015) || !(z <= 1.5e-34))
		tmp = Float64(x * Float64(Float64(y + Float64(1.0 - z)) / z));
	else
		tmp = Float64(Float64(1.0 + Float64(y - z)) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.015) || ~((z <= 1.5e-34)))
		tmp = x * ((y + (1.0 - z)) / z);
	else
		tmp = (1.0 + (y - z)) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.015], N[Not[LessEqual[z, 1.5e-34]], $MachinePrecision]], N[(x * N[(N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.014999999999999999 or 1.5e-34 < z

   1. Initial program 76.2%

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

   3. Taylor expanded in x around 0 76.2%

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

      1. associate--l+ 76.2%

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

      2. +-commutative 76.2%

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

      3. associate-*r/ 100.0%

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

      4. associate-+l- 100.0%

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

   5. Simplified 100.0%

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

   if -0.014999999999999999 < z < 1.5e-34

   1. Initial program 99.9%

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

      1. associate-/l* 89.1%

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

      2. associate-/r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.015 \lor \neg \left(z \leq 1.5 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \frac{y + \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \left(y - z\right)\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-68}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 30500000000:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -4e+29)
     t_0
     (if (<= y -6.7e-68)
       (- x)
       (if (<= y 1.35e-118) (/ x z) (if (<= y 30500000000.0) (- x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -4e+29) {
		tmp = t_0;
	} else if (y <= -6.7e-68) {
		tmp = -x;
	} else if (y <= 1.35e-118) {
		tmp = x / z;
	} else if (y <= 30500000000.0) {
		tmp = -x;
	} 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 = y * (x / z)
    if (y <= (-4d+29)) then
        tmp = t_0
    else if (y <= (-6.7d-68)) then
        tmp = -x
    else if (y <= 1.35d-118) then
        tmp = x / z
    else if (y <= 30500000000.0d0) then
        tmp = -x
    else
        tmp = t_0
    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 (y <= -4e+29) {
		tmp = t_0;
	} else if (y <= -6.7e-68) {
		tmp = -x;
	} else if (y <= 1.35e-118) {
		tmp = x / z;
	} else if (y <= 30500000000.0) {
		tmp = -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -4e+29:
		tmp = t_0
	elif y <= -6.7e-68:
		tmp = -x
	elif y <= 1.35e-118:
		tmp = x / z
	elif y <= 30500000000.0:
		tmp = -x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -4e+29)
		tmp = t_0;
	elseif (y <= -6.7e-68)
		tmp = Float64(-x);
	elseif (y <= 1.35e-118)
		tmp = Float64(x / z);
	elseif (y <= 30500000000.0)
		tmp = Float64(-x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (y <= -4e+29)
		tmp = t_0;
	elseif (y <= -6.7e-68)
		tmp = -x;
	elseif (y <= 1.35e-118)
		tmp = x / z;
	elseif (y <= 30500000000.0)
		tmp = -x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+29], t$95$0, If[LessEqual[y, -6.7e-68], (-x), If[LessEqual[y, 1.35e-118], N[(x / z), $MachinePrecision], If[LessEqual[y, 30500000000.0], (-x), t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999966e29 or 3.05e10 < y

   1. Initial program 91.4%

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

   3. Taylor expanded in y around inf 82.3%

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

      1. associate-/l* 72.9%

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

      2. associate-/r/ 80.3%

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

   5. Simplified 80.3%

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

   if -3.99999999999999966e29 < y < -6.6999999999999996e-68 or 1.34999999999999997e-118 < y < 3.05e10

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf 71.1%

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

      1. mul-1-neg 71.1%

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

   5. Simplified 71.1%

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

   if -6.6999999999999996e-68 < y < 1.34999999999999997e-118

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 89.2%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 63.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-68}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 30500000000:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-17} \lor \neg \left(z \leq 1.5 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \frac{y + \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.5e-17) (not (<= z 1.5e-34)))
   (* x (/ (+ y (- 1.0 z)) z))
   (* (/ x z) (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-17) || !(z <= 1.5e-34)) {
		tmp = x * ((y + (1.0 - z)) / z);
	} else {
		tmp = (x / z) * (y + 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 <= (-9.5d-17)) .or. (.not. (z <= 1.5d-34))) then
        tmp = x * ((y + (1.0d0 - z)) / z)
    else
        tmp = (x / z) * (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-17) || !(z <= 1.5e-34)) {
		tmp = x * ((y + (1.0 - z)) / z);
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.5e-17) or not (z <= 1.5e-34):
		tmp = x * ((y + (1.0 - z)) / z)
	else:
		tmp = (x / z) * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.5e-17) || !(z <= 1.5e-34))
		tmp = Float64(x * Float64(Float64(y + Float64(1.0 - z)) / z));
	else
		tmp = Float64(Float64(x / z) * Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.5e-17) || ~((z <= 1.5e-34)))
		tmp = x * ((y + (1.0 - z)) / z);
	else
		tmp = (x / z) * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.5e-17], N[Not[LessEqual[z, 1.5e-34]], $MachinePrecision]], N[(x * N[(N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000029e-17 or 1.5e-34 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 76.5%

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

      1. associate--l+ 76.5%

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

      2. +-commutative 76.5%

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

      3. associate-*r/ 99.9%

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

      4. associate-+l- 99.9%

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

   5. Simplified 99.9%

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

   if -9.50000000000000029e-17 < z < 1.5e-34

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. associate-/l* 88.9%

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

      2. associate-/r/ 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-17} \lor \neg \left(z \leq 1.5 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \frac{y + \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y}{z} + \frac{x \cdot \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + \left(1 - z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4.8e-14)
   (+ (/ (* x y) z) (/ (* x (- 1.0 z)) z))
   (/ x (/ z (+ y (- 1.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.8e-14) {
		tmp = ((x * y) / z) + ((x * (1.0 - z)) / 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 (x <= 4.8d-14) then
        tmp = ((x * y) / z) + ((x * (1.0d0 - z)) / 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 (x <= 4.8e-14) {
		tmp = ((x * y) / z) + ((x * (1.0 - z)) / z);
	} else {
		tmp = x / (z / (y + (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.8e-14:
		tmp = ((x * y) / z) + ((x * (1.0 - z)) / z)
	else:
		tmp = x / (z / (y + (1.0 - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.8e-14)
		tmp = Float64(Float64(Float64(x * y) / z) + Float64(Float64(x * Float64(1.0 - z)) / z));
	else
		tmp = Float64(x / Float64(z / Float64(y + Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.8e-14)
		tmp = ((x * y) / z) + ((x * (1.0 - z)) / z);
	else
		tmp = x / (z / (y + (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.8e-14], N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] + N[(N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.8e-14

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0 88.5%

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

   if 4.8e-14 < x

   1. Initial program 75.7%

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

   3. Taylor expanded in x around 0 75.7%

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

      1. associate--l+ 75.7%

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

      2. +-commutative 75.7%

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

      3. associate-*r/ 99.9%

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

      4. associate-+l- 99.9%

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

   5. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. *-un-lft-identity 99.9%

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

      5. sub-neg 99.9%

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

      6. sub-neg 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

      11. sub-neg 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y}{z} + \frac{x \cdot \left(1 - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + \left(1 - z\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 27500000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6e+29)
   (/ (* x y) z)
   (if (<= y 27500000.0) (- (/ x z) x) (* (/ x z) (+ y 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e+29) {
		tmp = (x * y) / z;
	} else if (y <= 27500000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) * (y + 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 (y <= (-2.6d+29)) then
        tmp = (x * y) / z
    else if (y <= 27500000.0d0) then
        tmp = (x / z) - x
    else
        tmp = (x / z) * (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e+29) {
		tmp = (x * y) / z;
	} else if (y <= 27500000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6e+29:
		tmp = (x * y) / z
	elif y <= 27500000.0:
		tmp = (x / z) - x
	else:
		tmp = (x / z) * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6e+29)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 27500000.0)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.6e+29)
		tmp = (x * y) / z;
	elseif (y <= 27500000.0)
		tmp = (x / z) - x;
	else
		tmp = (x / z) * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6e+29], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 27500000.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e29

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 80.6%

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

   if -2.6e29 < y < 2.75e7

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 84.6%

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

      1. associate--l+ 84.6%

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

      2. +-commutative 84.6%

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

      3. associate-*r/ 99.8%

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

      4. associate-+l- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 83.1%

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

      1. associate-*l/ 87.3%

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

      2. sub-neg 87.3%

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

      3. distribute-lft-out 85.8%

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

      4. *-rgt-identity 85.8%

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

      5. *-commutative 85.8%

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

      6. distribute-lft-neg-out 85.8%

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

      7. unsub-neg 85.8%

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

      8. *-commutative 85.8%

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

      9. associate-*l/ 83.2%

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

      10. associate-/l* 98.6%

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

      11. *-inverses 98.6%

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

      12. /-rgt-identity 98.6%

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

   8. Simplified 98.6%

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

   if 2.75e7 < y

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 84.6%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 86.0%

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

   5. Simplified 86.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 27500000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 13800000000:\\ \;\;\;\;\frac{x}{\frac{z}{1 - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.3e+29)
   (/ (* x y) z)
   (if (<= y 13800000000.0) (/ x (/ z (- 1.0 z))) (* (/ x z) (+ y 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.3e+29) {
		tmp = (x * y) / z;
	} else if (y <= 13800000000.0) {
		tmp = x / (z / (1.0 - z));
	} else {
		tmp = (x / z) * (y + 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 (y <= (-5.3d+29)) then
        tmp = (x * y) / z
    else if (y <= 13800000000.0d0) then
        tmp = x / (z / (1.0d0 - z))
    else
        tmp = (x / z) * (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.3e+29) {
		tmp = (x * y) / z;
	} else if (y <= 13800000000.0) {
		tmp = x / (z / (1.0 - z));
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.3e+29:
		tmp = (x * y) / z
	elif y <= 13800000000.0:
		tmp = x / (z / (1.0 - z))
	else:
		tmp = (x / z) * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.3e+29)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 13800000000.0)
		tmp = Float64(x / Float64(z / Float64(1.0 - z)));
	else
		tmp = Float64(Float64(x / z) * Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.3e+29)
		tmp = (x * y) / z;
	elseif (y <= 13800000000.0)
		tmp = x / (z / (1.0 - z));
	else
		tmp = (x / z) * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.3e+29], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 13800000000.0], N[(x / N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3e29

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 80.6%

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

   if -5.3e29 < y < 1.38e10

   1. Initial program 84.6%

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

   3. Taylor expanded in y around 0 83.1%

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

      1. associate-/l* 98.6%

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

   5. Simplified 98.6%

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

   if 1.38e10 < y

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 84.6%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 86.0%

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

   5. Simplified 86.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 13800000000:\\ \;\;\;\;\frac{x}{\frac{z}{1 - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+29} \lor \neg \left(y \leq 92000000000\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.55e+29) (not (<= y 92000000000.0)))
   (* y (/ x z))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.55e+29) || !(y <= 92000000000.0)) {
		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 <= (-2.55d+29)) .or. (.not. (y <= 92000000000.0d0))) 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 <= -2.55e+29) || !(y <= 92000000000.0)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.55e+29) or not (y <= 92000000000.0):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.55e+29) || !(y <= 92000000000.0))
		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 <= -2.55e+29) || ~((y <= 92000000000.0)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.55e+29], N[Not[LessEqual[y, 92000000000.0]], $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 < -2.55e29 or 9.2e10 < y

   1. Initial program 91.4%

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

   3. Taylor expanded in y around inf 82.3%

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

      1. associate-/l* 72.9%

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

      2. associate-/r/ 80.3%

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

   5. Simplified 80.3%

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

   if -2.55e29 < y < 9.2e10

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 84.6%

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

      1. associate--l+ 84.6%

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

      2. +-commutative 84.6%

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

      3. associate-*r/ 99.8%

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

      4. associate-+l- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 83.1%

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

      1. associate-*l/ 87.3%

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

      2. sub-neg 87.3%

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

      3. distribute-lft-out 85.8%

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

      4. *-rgt-identity 85.8%

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

      5. *-commutative 85.8%

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

      6. distribute-lft-neg-out 85.8%

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

      7. unsub-neg 85.8%

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

      8. *-commutative 85.8%

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

      9. associate-*l/ 83.2%

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

      10. associate-/l* 98.6%

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

      11. *-inverses 98.6%

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

      12. /-rgt-identity 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+29} \lor \neg \left(y \leq 92000000000\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1250000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+29)
   (/ (* x y) z)
   (if (<= y 1250000000000.0) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+29) {
		tmp = (x * y) / z;
	} else if (y <= 1250000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.5d+29)) then
        tmp = (x * y) / z
    else if (y <= 1250000000000.0d0) then
        tmp = (x / z) - x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+29) {
		tmp = (x * y) / z;
	} else if (y <= 1250000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e+29:
		tmp = (x * y) / z
	elif y <= 1250000000000.0:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+29)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 1250000000000.0)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.5e+29)
		tmp = (x * y) / z;
	elseif (y <= 1250000000000.0)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e+29], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1250000000000.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999979e29

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 80.6%

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

   if -3.49999999999999979e29 < y < 1.25e12

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 84.6%

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

      1. associate--l+ 84.6%

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

      2. +-commutative 84.6%

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

      3. associate-*r/ 99.8%

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

      4. associate-+l- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 83.1%

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

      1. associate-*l/ 87.3%

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

      2. sub-neg 87.3%

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

      3. distribute-lft-out 85.8%

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

      4. *-rgt-identity 85.8%

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

      5. *-commutative 85.8%

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

      6. distribute-lft-neg-out 85.8%

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

      7. unsub-neg 85.8%

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

      8. *-commutative 85.8%

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

      9. associate-*l/ 83.2%

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

      10. associate-/l* 98.6%

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

      11. *-inverses 98.6%

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

      12. /-rgt-identity 98.6%

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

   8. Simplified 98.6%

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

   if 1.25e12 < y

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 84.1%

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

      1. associate-/l* 75.9%

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

      2. associate-/r/ 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1250000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + \left(1 - z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2e-15) (/ (* x (+ 1.0 (- y z))) z) (/ x (/ z (+ y (- 1.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-15) {
		tmp = (x * (1.0 + (y - z))) / 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 (x <= 2d-15) then
        tmp = (x * (1.0d0 + (y - z))) / 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 (x <= 2e-15) {
		tmp = (x * (1.0 + (y - z))) / z;
	} else {
		tmp = x / (z / (y + (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2e-15:
		tmp = (x * (1.0 + (y - z))) / z
	else:
		tmp = x / (z / (y + (1.0 - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2e-15)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(y - z))) / z);
	else
		tmp = Float64(x / Float64(z / Float64(y + Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2e-15)
		tmp = (x * (1.0 + (y - z))) / z;
	else
		tmp = x / (z / (y + (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2e-15], N[(N[(x * N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / N[(y + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.0000000000000002e-15

   1. Initial program 91.1%

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

   if 2.0000000000000002e-15 < x

   1. Initial program 75.7%

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

   3. Taylor expanded in x around 0 75.7%

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

      1. associate--l+ 75.7%

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

      2. +-commutative 75.7%

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

      3. associate-*r/ 99.9%

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

      4. associate-+l- 99.9%

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

   5. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. *-un-lft-identity 99.9%

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

      5. sub-neg 99.9%

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

      6. sub-neg 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

      11. sub-neg 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + \left(1 - z\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.8% 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 74.0%

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

   3. Taylor expanded in z around inf 72.8%

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

      1. mul-1-neg 72.8%

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

   5. Simplified 72.8%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 54.8%

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

      1. associate-/l* 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in z around 0 53.6%

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

4. Final simplification 62.5%

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

Alternative 11: 37.5% 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 87.8%

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

3. Taylor expanded in z around inf 35.6%

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

   1. mul-1-neg 35.6%

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

5. Simplified 35.6%

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

6. Final simplification 35.6%

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

Alternative 12: 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 87.8%

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

3. Taylor expanded in z around inf 24.9%

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

   1. associate-*r* 24.9%

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

   2. mul-1-neg 24.9%

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

5. Simplified 24.9%

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

   1. div-inv 24.9%

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

   2. associate-*l* 35.5%

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

   3. div-inv 35.6%

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

   4. *-inverses 35.6%

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

   5. *-commutative 35.6%

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

   6. *-un-lft-identity 35.6%

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

   7. neg-sub0 35.6%

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

   8. sub-neg 35.6%

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

   9. add-sqr-sqrt 18.4%

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

   10. sqrt-unprod 17.6%

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

   11. sqr-neg 17.6%

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

   12. sqrt-unprod 1.4%

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

   13. add-sqr-sqrt 3.2%

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

7. Applied egg-rr 3.2%

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

   1. +-lft-identity 3.2%

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

9. Simplified 3.2%

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

10. Final simplification 3.2%

    \[\leadsto x \]
11. 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 2024024 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (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))