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

Percentage Accurate: 87.4% → 96.3%

Time: 5.3s

Alternatives: 7

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * ((y - z) + 1.0d0)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.4% 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: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x / (z / ((y - z) + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

   1. associate-/l* 97.0%

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

3. Simplified 97.0%

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

4. Final simplification 97.0%

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

Alternative 2: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+73}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-270}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -4.1e+73)
     (- x)
     (if (<= z -1.25e-44)
       t_0
       (if (<= z -3e-208)
         (/ x z)
         (if (<= z -5.8e-270)
           t_0
           (if (<= z 1.06e-191)
             (/ x z)
             (if (<= z 6.2e-65) t_0 (if (<= z 1.0) (/ x z) (- x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -4.1e+73) {
		tmp = -x;
	} else if (z <= -1.25e-44) {
		tmp = t_0;
	} else if (z <= -3e-208) {
		tmp = x / z;
	} else if (z <= -5.8e-270) {
		tmp = t_0;
	} else if (z <= 1.06e-191) {
		tmp = x / z;
	} else if (z <= 6.2e-65) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (z <= (-4.1d+73)) then
        tmp = -x
    else if (z <= (-1.25d-44)) then
        tmp = t_0
    else if (z <= (-3d-208)) then
        tmp = x / z
    else if (z <= (-5.8d-270)) then
        tmp = t_0
    else if (z <= 1.06d-191) then
        tmp = x / z
    else if (z <= 6.2d-65) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -4.1e+73) {
		tmp = -x;
	} else if (z <= -1.25e-44) {
		tmp = t_0;
	} else if (z <= -3e-208) {
		tmp = x / z;
	} else if (z <= -5.8e-270) {
		tmp = t_0;
	} else if (z <= 1.06e-191) {
		tmp = x / z;
	} else if (z <= 6.2e-65) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -4.1e+73:
		tmp = -x
	elif z <= -1.25e-44:
		tmp = t_0
	elif z <= -3e-208:
		tmp = x / z
	elif z <= -5.8e-270:
		tmp = t_0
	elif z <= 1.06e-191:
		tmp = x / z
	elif z <= 6.2e-65:
		tmp = t_0
	elif z <= 1.0:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -4.1e+73)
		tmp = Float64(-x);
	elseif (z <= -1.25e-44)
		tmp = t_0;
	elseif (z <= -3e-208)
		tmp = Float64(x / z);
	elseif (z <= -5.8e-270)
		tmp = t_0;
	elseif (z <= 1.06e-191)
		tmp = Float64(x / z);
	elseif (z <= 6.2e-65)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -4.1e+73)
		tmp = -x;
	elseif (z <= -1.25e-44)
		tmp = t_0;
	elseif (z <= -3e-208)
		tmp = x / z;
	elseif (z <= -5.8e-270)
		tmp = t_0;
	elseif (z <= 1.06e-191)
		tmp = x / z;
	elseif (z <= 6.2e-65)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+73], (-x), If[LessEqual[z, -1.25e-44], t$95$0, If[LessEqual[z, -3e-208], N[(x / z), $MachinePrecision], If[LessEqual[z, -5.8e-270], t$95$0, If[LessEqual[z, 1.06e-191], N[(x / z), $MachinePrecision], If[LessEqual[z, 6.2e-65], t$95$0, If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999998e73 or 1 < z

   1. Initial program 74.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.9%

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

      1. neg-mul-1 76.9%

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

   6. Simplified 76.9%

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

   if -4.0999999999999998e73 < z < -1.2500000000000001e-44 or -2.99999999999999986e-208 < z < -5.79999999999999965e-270 or 1.05999999999999994e-191 < z < 6.20000000000000032e-65

   1. Initial program 96.7%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. associate-/l* 64.1%

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

   6. Simplified 64.1%

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

      1. associate-/r/ 75.2%

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

   8. Applied egg-rr 75.2%

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

   if -1.2500000000000001e-44 < z < -2.99999999999999986e-208 or -5.79999999999999965e-270 < z < 1.05999999999999994e-191 or 6.20000000000000032e-65 < z < 1

   1. Initial program 99.9%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 95.1%

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

   5. Taylor expanded in y around 0 72.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+73}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+74}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-270}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -1.7e+74)
     (- x)
     (if (<= z -5.8e-43)
       (* x (/ y z))
       (if (<= z -1.25e-208)
         (/ x z)
         (if (<= z -3.6e-270)
           t_0
           (if (<= z 4.8e-191)
             (/ x z)
             (if (<= z 4e-65) t_0 (if (<= z 1.0) (/ x z) (- x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.7e+74) {
		tmp = -x;
	} else if (z <= -5.8e-43) {
		tmp = x * (y / z);
	} else if (z <= -1.25e-208) {
		tmp = x / z;
	} else if (z <= -3.6e-270) {
		tmp = t_0;
	} else if (z <= 4.8e-191) {
		tmp = x / z;
	} else if (z <= 4e-65) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (z <= (-1.7d+74)) then
        tmp = -x
    else if (z <= (-5.8d-43)) then
        tmp = x * (y / z)
    else if (z <= (-1.25d-208)) then
        tmp = x / z
    else if (z <= (-3.6d-270)) then
        tmp = t_0
    else if (z <= 4.8d-191) then
        tmp = x / z
    else if (z <= 4d-65) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.7e+74) {
		tmp = -x;
	} else if (z <= -5.8e-43) {
		tmp = x * (y / z);
	} else if (z <= -1.25e-208) {
		tmp = x / z;
	} else if (z <= -3.6e-270) {
		tmp = t_0;
	} else if (z <= 4.8e-191) {
		tmp = x / z;
	} else if (z <= 4e-65) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -1.7e+74:
		tmp = -x
	elif z <= -5.8e-43:
		tmp = x * (y / z)
	elif z <= -1.25e-208:
		tmp = x / z
	elif z <= -3.6e-270:
		tmp = t_0
	elif z <= 4.8e-191:
		tmp = x / z
	elif z <= 4e-65:
		tmp = t_0
	elif z <= 1.0:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -1.7e+74)
		tmp = Float64(-x);
	elseif (z <= -5.8e-43)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -1.25e-208)
		tmp = Float64(x / z);
	elseif (z <= -3.6e-270)
		tmp = t_0;
	elseif (z <= 4.8e-191)
		tmp = Float64(x / z);
	elseif (z <= 4e-65)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -1.7e+74)
		tmp = -x;
	elseif (z <= -5.8e-43)
		tmp = x * (y / z);
	elseif (z <= -1.25e-208)
		tmp = x / z;
	elseif (z <= -3.6e-270)
		tmp = t_0;
	elseif (z <= 4.8e-191)
		tmp = x / z;
	elseif (z <= 4e-65)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+74], (-x), If[LessEqual[z, -5.8e-43], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-208], N[(x / z), $MachinePrecision], If[LessEqual[z, -3.6e-270], t$95$0, If[LessEqual[z, 4.8e-191], N[(x / z), $MachinePrecision], If[LessEqual[z, 4e-65], t$95$0, If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7e74 or 1 < z

   1. Initial program 74.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.9%

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

      1. neg-mul-1 76.9%

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

   6. Simplified 76.9%

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

   if -1.7e74 < z < -5.8000000000000003e-43

   1. Initial program 89.5%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around inf 73.7%

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

      1. associate-/l* 78.5%

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

      2. associate-/r/ 83.8%

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

   6. Simplified 83.8%

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

   if -5.8000000000000003e-43 < z < -1.24999999999999991e-208 or -3.5999999999999998e-270 < z < 4.7999999999999998e-191 or 3.99999999999999969e-65 < z < 1

   1. Initial program 99.9%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 95.1%

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

   5. Taylor expanded in y around 0 72.2%

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

   if -1.24999999999999991e-208 < z < -3.5999999999999998e-270 or 4.7999999999999998e-191 < z < 3.99999999999999969e-65

   1. Initial program 99.9%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-/l* 55.6%

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

   6. Simplified 55.6%

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

      1. associate-/r/ 73.7%

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

   8. Applied egg-rr 73.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+74}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+19} \lor \neg \left(y \leq 5.8 \cdot 10^{+69}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e+19) (not (<= y 5.8e+69))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e+19) || !(y <= 5.8e+69)) {
		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 <= (-7.5d+19)) .or. (.not. (y <= 5.8d+69))) 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 <= -7.5e+19) || !(y <= 5.8e+69)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e+19) or not (y <= 5.8e+69):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e+19) || !(y <= 5.8e+69))
		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 <= -7.5e+19) || ~((y <= 5.8e+69)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e+19], N[Not[LessEqual[y, 5.8e+69]], $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 < -7.5e19 or 5.7999999999999997e69 < y

   1. Initial program 86.1%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

      2. associate-/l* 72.4%

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

   6. Simplified 72.4%

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

      1. associate-/r/ 76.6%

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

   8. Applied egg-rr 76.6%

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

   if -7.5e19 < y < 5.7999999999999997e69

   1. Initial program 88.4%

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

   2. Taylor expanded in y around 0 84.1%

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

      1. *-commutative 84.1%

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

      2. sub-neg 84.1%

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

      3. distribute-lft-in 84.2%

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

      4. *-rgt-identity 84.2%

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

      5. distribute-rgt-neg-in 84.2%

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

      6. *-commutative 84.2%

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

      7. unsub-neg 84.2%

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

      8. *-commutative 84.2%

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

   4. Simplified 84.2%

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

   5. Taylor expanded in x around 0 84.1%

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

      1. *-commutative 84.1%

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

      2. sub-neg 84.1%

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

      3. distribute-lft-in 84.2%

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

      4. *-rgt-identity 84.2%

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

      5. distribute-rgt-neg-out 84.2%

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

      6. sub-neg 84.2%

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

      7. div-sub 84.1%

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

      8. associate-*l/ 79.7%

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

      9. associate-/r/ 95.7%

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

      10. *-inverses 95.7%

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

      11. /-rgt-identity 95.7%

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

   7. Simplified 95.7%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+19} \lor \neg \left(y \leq 5.8 \cdot 10^{+69}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 5: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+20)
   (* y (/ x z))
   (if (<= y 5.5e+69) (- (/ x z) x) (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+20) {
		tmp = y * (x / z);
	} else if (y <= 5.5e+69) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.8d+20)) then
        tmp = y * (x / z)
    else if (y <= 5.5d+69) then
        tmp = (x / z) - x
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+20) {
		tmp = y * (x / z);
	} else if (y <= 5.5e+69) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+20:
		tmp = y * (x / z)
	elif y <= 5.5e+69:
		tmp = (x / z) - x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+20)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 5.5e+69)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e+20)
		tmp = y * (x / z);
	elseif (y <= 5.5e+69)
		tmp = (x / z) - x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+20], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+69], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8e20

   1. Initial program 81.0%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-/l* 64.6%

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

   6. Simplified 64.6%

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

      1. associate-/r/ 71.3%

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

   8. Applied egg-rr 71.3%

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

   if -5.8e20 < y < 5.50000000000000002e69

   1. Initial program 88.4%

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

   2. Taylor expanded in y around 0 84.1%

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

      1. *-commutative 84.1%

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

      2. sub-neg 84.1%

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

      3. distribute-lft-in 84.2%

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

      4. *-rgt-identity 84.2%

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

      5. distribute-rgt-neg-in 84.2%

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

      6. *-commutative 84.2%

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

      7. unsub-neg 84.2%

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

      8. *-commutative 84.2%

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

   4. Simplified 84.2%

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

   5. Taylor expanded in x around 0 84.1%

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

      1. *-commutative 84.1%

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

      2. sub-neg 84.1%

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

      3. distribute-lft-in 84.2%

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

      4. *-rgt-identity 84.2%

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

      5. distribute-rgt-neg-out 84.2%

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

      6. sub-neg 84.2%

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

      7. div-sub 84.1%

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

      8. associate-*l/ 79.7%

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

      9. associate-/r/ 95.7%

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

      10. *-inverses 95.7%

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

      11. /-rgt-identity 95.7%

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

   7. Simplified 95.7%

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

   if 5.50000000000000002e69 < y

   1. Initial program 91.2%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 78.4%

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

      1. associate-/l* 81.8%

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

   6. Simplified 81.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 6: 64.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0016:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0016) (- x) (if (<= z 1.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0016) {
		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 <= (-0.0016d0)) 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 <= -0.0016) {
		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 <= -0.0016:
		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 <= -0.0016)
		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 <= -0.0016)
		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, -0.0016], (-x), If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00160000000000000008 or 1 < z

   1. Initial program 76.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. neg-mul-1 70.3%

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

   6. Simplified 70.3%

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

   if -0.00160000000000000008 < z < 1

   1. Initial program 99.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 92.8%

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

   5. Taylor expanded in y around 0 62.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0016:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 7: 38.0% 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 87.4%

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

   1. associate-/l* 97.0%

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

3. Simplified 97.0%

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

4. Taylor expanded in z around inf 38.3%

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

   1. neg-mul-1 38.3%

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

6. Simplified 38.3%

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

7. Final simplification 38.3%

   \[\leadsto -x \]

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 2023174 
(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))