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

Percentage Accurate: 88.0% → 99.9%

Time: 5.6s

Alternatives: 12

Speedup: 0.8×

• 20.8% 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: 88.0% 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, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+32} \lor \neg \left(z \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y + 1\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e+32) (not (<= z 5e+16)))
   (- (* x (/ y z)) x)
   (* (/ x z) (- (+ y 1.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e+32) || !(z <= 5e+16)) {
		tmp = (x * (y / z)) - x;
	} 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 <= (-3.5d+32)) .or. (.not. (z <= 5d+16))) then
        tmp = (x * (y / z)) - x
    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 <= -3.5e+32) || !(z <= 5e+16)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * ((y + 1.0) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e+32) or not (z <= 5e+16):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x / z) * ((y + 1.0) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.5e+32) || !(z <= 5e+16))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(Float64(y + 1.0) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.5e+32) || ~((z <= 5e+16)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x / z) * ((y + 1.0) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e+32], N[Not[LessEqual[z, 5e+16]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(N[(y + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000001e32 or 5e16 < z

   1. Initial program 77.5%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around inf 92.1%

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

      1. associate-/l* 89.9%

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

      2. associate-/r/ 99.9%

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

   6. Simplified 99.9%

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

   if -3.5000000000000001e32 < z < 5e16

   1. Initial program 99.8%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in x around 0 99.8%

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

      1. associate-*l/ 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+32} \lor \neg \left(z \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y + 1\right) - z\right)\\ \end{array} \]

Alternative 2: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-250}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -2.4e+58)
     (- x)
     (if (<= z -2.8e-12)
       t_0
       (if (<= z -4.1e-132)
         (/ x z)
         (if (<= z -3.6e-154)
           t_0
           (if (<= z 1.16e-250)
             (/ x z)
             (if (<= z 5.5e-187)
               t_0
               (if (<= z 8.5e-45)
                 (/ x z)
                 (if (<= z 2.3e+36) t_0 (- x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -2.4e+58) {
		tmp = -x;
	} else if (z <= -2.8e-12) {
		tmp = t_0;
	} else if (z <= -4.1e-132) {
		tmp = x / z;
	} else if (z <= -3.6e-154) {
		tmp = t_0;
	} else if (z <= 1.16e-250) {
		tmp = x / z;
	} else if (z <= 5.5e-187) {
		tmp = t_0;
	} else if (z <= 8.5e-45) {
		tmp = x / z;
	} else if (z <= 2.3e+36) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (z <= (-2.4d+58)) then
        tmp = -x
    else if (z <= (-2.8d-12)) then
        tmp = t_0
    else if (z <= (-4.1d-132)) then
        tmp = x / z
    else if (z <= (-3.6d-154)) then
        tmp = t_0
    else if (z <= 1.16d-250) then
        tmp = x / z
    else if (z <= 5.5d-187) then
        tmp = t_0
    else if (z <= 8.5d-45) then
        tmp = x / z
    else if (z <= 2.3d+36) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -2.4e+58) {
		tmp = -x;
	} else if (z <= -2.8e-12) {
		tmp = t_0;
	} else if (z <= -4.1e-132) {
		tmp = x / z;
	} else if (z <= -3.6e-154) {
		tmp = t_0;
	} else if (z <= 1.16e-250) {
		tmp = x / z;
	} else if (z <= 5.5e-187) {
		tmp = t_0;
	} else if (z <= 8.5e-45) {
		tmp = x / z;
	} else if (z <= 2.3e+36) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -2.4e+58:
		tmp = -x
	elif z <= -2.8e-12:
		tmp = t_0
	elif z <= -4.1e-132:
		tmp = x / z
	elif z <= -3.6e-154:
		tmp = t_0
	elif z <= 1.16e-250:
		tmp = x / z
	elif z <= 5.5e-187:
		tmp = t_0
	elif z <= 8.5e-45:
		tmp = x / z
	elif z <= 2.3e+36:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -2.4e+58)
		tmp = Float64(-x);
	elseif (z <= -2.8e-12)
		tmp = t_0;
	elseif (z <= -4.1e-132)
		tmp = Float64(x / z);
	elseif (z <= -3.6e-154)
		tmp = t_0;
	elseif (z <= 1.16e-250)
		tmp = Float64(x / z);
	elseif (z <= 5.5e-187)
		tmp = t_0;
	elseif (z <= 8.5e-45)
		tmp = Float64(x / z);
	elseif (z <= 2.3e+36)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -2.4e+58)
		tmp = -x;
	elseif (z <= -2.8e-12)
		tmp = t_0;
	elseif (z <= -4.1e-132)
		tmp = x / z;
	elseif (z <= -3.6e-154)
		tmp = t_0;
	elseif (z <= 1.16e-250)
		tmp = x / z;
	elseif (z <= 5.5e-187)
		tmp = t_0;
	elseif (z <= 8.5e-45)
		tmp = x / z;
	elseif (z <= 2.3e+36)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+58], (-x), If[LessEqual[z, -2.8e-12], t$95$0, If[LessEqual[z, -4.1e-132], N[(x / z), $MachinePrecision], If[LessEqual[z, -3.6e-154], t$95$0, If[LessEqual[z, 1.16e-250], N[(x / z), $MachinePrecision], If[LessEqual[z, 5.5e-187], t$95$0, If[LessEqual[z, 8.5e-45], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.3e+36], t$95$0, (-x)]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e58 or 2.29999999999999996e36 < z

   1. Initial program 75.8%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around inf 72.3%

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

      1. neg-mul-1 72.3%

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

   6. Simplified 72.3%

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

   if -2.4e58 < z < -2.8000000000000002e-12 or -4.10000000000000007e-132 < z < -3.6000000000000003e-154 or 1.16e-250 < z < 5.50000000000000033e-187 or 8.50000000000000041e-45 < z < 2.29999999999999996e36

   1. Initial program 99.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 64.4%

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

      1. associate-/r/ 69.0%

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

   6. Applied egg-rr 69.0%

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

   if -2.8000000000000002e-12 < z < -4.10000000000000007e-132 or -3.6000000000000003e-154 < z < 1.16e-250 or 5.50000000000000033e-187 < z < 8.50000000000000041e-45

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in y around 0 70.1%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-250}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-151}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 10^{-250}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))) (t_1 (* y (/ x z))))
   (if (<= z -5e+58)
     (- x)
     (if (<= z -1.55e-10)
       t_0
       (if (<= z -3.35e-133)
         (/ x z)
         (if (<= z -2.5e-151)
           t_0
           (if (<= z 1e-250)
             (/ x z)
             (if (<= z 3.45e-189)
               t_1
               (if (<= z 1.3e-42)
                 (/ x z)
                 (if (<= z 7.4e+31) t_1 (- x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double t_1 = y * (x / z);
	double tmp;
	if (z <= -5e+58) {
		tmp = -x;
	} else if (z <= -1.55e-10) {
		tmp = t_0;
	} else if (z <= -3.35e-133) {
		tmp = x / z;
	} else if (z <= -2.5e-151) {
		tmp = t_0;
	} else if (z <= 1e-250) {
		tmp = x / z;
	} else if (z <= 3.45e-189) {
		tmp = t_1;
	} else if (z <= 1.3e-42) {
		tmp = x / z;
	} else if (z <= 7.4e+31) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * (y / z)
    t_1 = y * (x / z)
    if (z <= (-5d+58)) then
        tmp = -x
    else if (z <= (-1.55d-10)) then
        tmp = t_0
    else if (z <= (-3.35d-133)) then
        tmp = x / z
    else if (z <= (-2.5d-151)) then
        tmp = t_0
    else if (z <= 1d-250) then
        tmp = x / z
    else if (z <= 3.45d-189) then
        tmp = t_1
    else if (z <= 1.3d-42) then
        tmp = x / z
    else if (z <= 7.4d+31) then
        tmp = t_1
    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 t_1 = y * (x / z);
	double tmp;
	if (z <= -5e+58) {
		tmp = -x;
	} else if (z <= -1.55e-10) {
		tmp = t_0;
	} else if (z <= -3.35e-133) {
		tmp = x / z;
	} else if (z <= -2.5e-151) {
		tmp = t_0;
	} else if (z <= 1e-250) {
		tmp = x / z;
	} else if (z <= 3.45e-189) {
		tmp = t_1;
	} else if (z <= 1.3e-42) {
		tmp = x / z;
	} else if (z <= 7.4e+31) {
		tmp = t_1;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	t_1 = y * (x / z)
	tmp = 0
	if z <= -5e+58:
		tmp = -x
	elif z <= -1.55e-10:
		tmp = t_0
	elif z <= -3.35e-133:
		tmp = x / z
	elif z <= -2.5e-151:
		tmp = t_0
	elif z <= 1e-250:
		tmp = x / z
	elif z <= 3.45e-189:
		tmp = t_1
	elif z <= 1.3e-42:
		tmp = x / z
	elif z <= 7.4e+31:
		tmp = t_1
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -5e+58)
		tmp = Float64(-x);
	elseif (z <= -1.55e-10)
		tmp = t_0;
	elseif (z <= -3.35e-133)
		tmp = Float64(x / z);
	elseif (z <= -2.5e-151)
		tmp = t_0;
	elseif (z <= 1e-250)
		tmp = Float64(x / z);
	elseif (z <= 3.45e-189)
		tmp = t_1;
	elseif (z <= 1.3e-42)
		tmp = Float64(x / z);
	elseif (z <= 7.4e+31)
		tmp = t_1;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	t_1 = y * (x / z);
	tmp = 0.0;
	if (z <= -5e+58)
		tmp = -x;
	elseif (z <= -1.55e-10)
		tmp = t_0;
	elseif (z <= -3.35e-133)
		tmp = x / z;
	elseif (z <= -2.5e-151)
		tmp = t_0;
	elseif (z <= 1e-250)
		tmp = x / z;
	elseif (z <= 3.45e-189)
		tmp = t_1;
	elseif (z <= 1.3e-42)
		tmp = x / z;
	elseif (z <= 7.4e+31)
		tmp = t_1;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+58], (-x), If[LessEqual[z, -1.55e-10], t$95$0, If[LessEqual[z, -3.35e-133], N[(x / z), $MachinePrecision], If[LessEqual[z, -2.5e-151], t$95$0, If[LessEqual[z, 1e-250], N[(x / z), $MachinePrecision], If[LessEqual[z, 3.45e-189], t$95$1, If[LessEqual[z, 1.3e-42], N[(x / z), $MachinePrecision], If[LessEqual[z, 7.4e+31], t$95$1, (-x)]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.99999999999999986e58 or 7.3999999999999996e31 < z

   1. Initial program 75.8%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around inf 72.3%

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

      1. neg-mul-1 72.3%

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

   6. Simplified 72.3%

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

   if -4.99999999999999986e58 < z < -1.55000000000000008e-10 or -3.3500000000000001e-133 < z < -2.50000000000000002e-151

   1. Initial program 99.5%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 65.9%

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

      1. div-inv 65.7%

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

      2. clear-num 66.1%

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

      3. *-commutative 66.1%

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

   6. Applied egg-rr 66.1%

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

   if -1.55000000000000008e-10 < z < -3.3500000000000001e-133 or -2.50000000000000002e-151 < z < 1.0000000000000001e-250 or 3.4500000000000001e-189 < z < 1.3e-42

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in y around 0 70.1%

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

   if 1.0000000000000001e-250 < z < 3.4500000000000001e-189 or 1.3e-42 < z < 7.3999999999999996e31

   1. Initial program 99.9%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around inf 62.8%

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

      1. associate-/r/ 72.3%

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

   6. Applied egg-rr 72.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+58}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{-250}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-189}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 97.6% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (+ (- y z) 1.0)) z) -5e+63)
   (* (/ x z) (- (+ y 1.0) z))
   (* x (+ (+ (/ 1.0 z) (/ y z)) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * ((y - z) + 1.0)) / z) <= -5e+63) {
		tmp = (x / z) * ((y + 1.0) - z);
	} else {
		tmp = x * (((1.0 / z) + (y / z)) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((x * ((y - z) + 1.0d0)) / z) <= (-5d+63)) then
        tmp = (x / z) * ((y + 1.0d0) - z)
    else
        tmp = x * (((1.0d0 / z) + (y / z)) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * ((y - z) + 1.0)) / z) <= -5e+63) {
		tmp = (x / z) * ((y + 1.0) - z);
	} else {
		tmp = x * (((1.0 / z) + (y / z)) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * ((y - z) + 1.0)) / z) <= -5e+63:
		tmp = (x / z) * ((y + 1.0) - z)
	else:
		tmp = x * (((1.0 / z) + (y / z)) + -1.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], -5e+63], N[(N[(x / z), $MachinePrecision] * N[(N[(y + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(1.0 / z), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z) < -5.00000000000000011e63

   1. Initial program 80.3%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around 0 80.3%

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

      1. associate-*l/ 99.9%

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

   6. Simplified 99.9%

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

   if -5.00000000000000011e63 < (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

   1. Initial program 92.7%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around 0 98.8%

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

4. Final simplification 99.1%

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

Alternative 5: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;\frac{x \cdot t_0}{z} \leq -5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y + 1\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= (/ (* x t_0) z) -5e+63)
     (* (/ x z) (- (+ y 1.0) 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 * t_0) / z) <= -5e+63) {
		tmp = (x / z) * ((y + 1.0) - 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 * t_0) / z) <= (-5d+63)) then
        tmp = (x / z) * ((y + 1.0d0) - 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 * t_0) / z) <= -5e+63) {
		tmp = (x / z) * ((y + 1.0) - 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 * t_0) / z) <= -5e+63:
		tmp = (x / z) * ((y + 1.0) - 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 (Float64(Float64(x * t_0) / z) <= -5e+63)
		tmp = Float64(Float64(x / z) * Float64(Float64(y + 1.0) - 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 * t_0) / z) <= -5e+63)
		tmp = (x / z) * ((y + 1.0) - 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[N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], -5e+63], N[(N[(x / z), $MachinePrecision] * N[(N[(y + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z) < -5.00000000000000011e63

   1. Initial program 80.3%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around 0 80.3%

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

      1. associate-*l/ 99.9%

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

   6. Simplified 99.9%

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

   if -5.00000000000000011e63 < (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

   1. Initial program 92.7%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

4. Final simplification 99.1%

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

Alternative 6: 83.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+88}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -26:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= y -3.2e+106)
     t_0
     (if (<= y -1.12e+88)
       (- x)
       (if (<= y -26.0)
         (* y (/ x z))
         (if (<= y 1.48e+63) (- (/ x z) x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (y <= -3.2e+106) {
		tmp = t_0;
	} else if (y <= -1.12e+88) {
		tmp = -x;
	} else if (y <= -26.0) {
		tmp = y * (x / z);
	} else if (y <= 1.48e+63) {
		tmp = (x / z) - 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 = x * (y / z)
    if (y <= (-3.2d+106)) then
        tmp = t_0
    else if (y <= (-1.12d+88)) then
        tmp = -x
    else if (y <= (-26.0d0)) then
        tmp = y * (x / z)
    else if (y <= 1.48d+63) then
        tmp = (x / z) - 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 = x * (y / z);
	double tmp;
	if (y <= -3.2e+106) {
		tmp = t_0;
	} else if (y <= -1.12e+88) {
		tmp = -x;
	} else if (y <= -26.0) {
		tmp = y * (x / z);
	} else if (y <= 1.48e+63) {
		tmp = (x / z) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if y <= -3.2e+106:
		tmp = t_0
	elif y <= -1.12e+88:
		tmp = -x
	elif y <= -26.0:
		tmp = y * (x / z)
	elif y <= 1.48e+63:
		tmp = (x / z) - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -3.2e+106)
		tmp = t_0;
	elseif (y <= -1.12e+88)
		tmp = Float64(-x);
	elseif (y <= -26.0)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.48e+63)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (y <= -3.2e+106)
		tmp = t_0;
	elseif (y <= -1.12e+88)
		tmp = -x;
	elseif (y <= -26.0)
		tmp = y * (x / z);
	elseif (y <= 1.48e+63)
		tmp = (x / z) - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+106], t$95$0, If[LessEqual[y, -1.12e+88], (-x), If[LessEqual[y, -26.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.48e+63], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1999999999999998e106 or 1.48000000000000006e63 < y

   1. Initial program 88.9%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 73.7%

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

      1. div-inv 73.5%

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

      2. clear-num 73.6%

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

      3. *-commutative 73.6%

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

   6. Applied egg-rr 73.6%

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

   if -3.1999999999999998e106 < y < -1.12000000000000006e88

   1. Initial program 99.8%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 72.3%

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

      1. neg-mul-1 72.3%

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

   6. Simplified 72.3%

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

   if -1.12000000000000006e88 < y < -26

   1. Initial program 94.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 68.8%

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

      1. associate-/r/ 68.8%

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

   6. Applied egg-rr 68.8%

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

   if -26 < y < 1.48000000000000006e63

   1. Initial program 88.1%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+88}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -26:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 7: 95.1% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	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 <= 1.0)))
		tmp = (x * (y / z)) - x;
	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, 1.0]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 89.4%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 91.7%

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

      1. associate-/l* 89.6%

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

      2. associate-/r/ 92.6%

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

   6. Simplified 92.6%

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

   if -1 < y < 1

   1. Initial program 88.9%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.8%

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

4. Final simplification 96.2%

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

Alternative 8: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -115 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -115.0) (not (<= z 1.0)))
   (- (* x (/ y z)) x)
   (/ (* x (+ y 1.0)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -115.0) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-115.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x * (y + 1.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -115.0) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -115.0) or not (z <= 1.0):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x * (y + 1.0)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -115.0) || !(z <= 1.0))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -115.0) || ~((z <= 1.0)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x * (y + 1.0)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -115.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -115 or 1 < z

   1. Initial program 79.6%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 91.5%

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

      1. associate-/l* 89.5%

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

      2. associate-/r/ 98.6%

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

   6. Simplified 98.6%

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

   if -115 < z < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 97.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -115 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]

Alternative 9: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -26 \lor \neg \left(y \leq 4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -26.0) (not (<= y 4e+57))) (/ (* x y) z) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -26.0) || !(y <= 4e+57)) {
		tmp = (x * y) / 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 <= (-26.0d0)) .or. (.not. (y <= 4d+57))) then
        tmp = (x * y) / 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 <= -26.0) || !(y <= 4e+57)) {
		tmp = (x * y) / z;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -26.0) or not (y <= 4e+57):
		tmp = (x * y) / z
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -26.0) || !(y <= 4e+57))
		tmp = Float64(Float64(x * y) / 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 <= -26.0) || ~((y <= 4e+57)))
		tmp = (x * y) / z;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -26.0], N[Not[LessEqual[y, 4e+57]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -26 or 4.00000000000000019e57 < y

   1. Initial program 90.4%

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

   2. Taylor expanded in y around inf 73.3%

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

   if -26 < y < 4.00000000000000019e57

   1. Initial program 88.1%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.4%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -26 \lor \neg \left(y \leq 4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 10: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -15.0)
   (/ x (/ z y))
   (if (<= y 1.95e+56) (- (/ x z) x) (* x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -15.0) {
		tmp = x / (z / y);
	} else if (y <= 1.95e+56) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-15.0d0)) then
        tmp = x / (z / y)
    else if (y <= 1.95d+56) then
        tmp = (x / z) - x
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -15.0) {
		tmp = x / (z / y);
	} else if (y <= 1.95e+56) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -15.0:
		tmp = x / (z / y)
	elif y <= 1.95e+56:
		tmp = (x / z) - x
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -15.0)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 1.95e+56)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -15.0)
		tmp = x / (z / y);
	elseif (y <= 1.95e+56)
		tmp = (x / z) - x;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -15.0], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+56], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -15

   1. Initial program 86.5%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 61.4%

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

   if -15 < y < 1.94999999999999997e56

   1. Initial program 88.1%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.4%

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

   if 1.94999999999999997e56 < y

   1. Initial program 94.8%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around inf 79.4%

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

      1. div-inv 79.4%

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

      2. clear-num 79.6%

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

      3. *-commutative 79.6%

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

   6. Applied egg-rr 79.6%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 11: 65.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 79.9%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around inf 66.6%

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

      1. neg-mul-1 66.6%

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

   6. Simplified 66.6%

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

   if -1 < z < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 97.6%

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

   3. Taylor expanded in y around 0 57.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 12: 38.9% 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 89.2%

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

3. Simplified 96.1%

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

4. Taylor expanded in z around inf 37.1%

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

   1. neg-mul-1 37.1%

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

6. Simplified 37.1%

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

7. Final simplification 37.1%

   \[\leadsto -x \]

Developer target: 99.4% accurate, 0.6× 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 2023215 
(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))