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

Percentage Accurate: 88.3% → 96.2%

Time: 4.6s

Alternatives: 8

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

2. Taylor expanded in x around 0 88.2%

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

   1. associate--l+ 88.2%

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

   2. +-commutative 88.2%

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

   3. associate-*r/ 97.0%

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

   4. +-commutative 97.0%

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

4. Simplified 97.0%

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

5. Final simplification 97.0%

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

Alternative 2: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-298}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-259}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -1.0)
     (- x)
     (if (<= z 3.4e-298)
       (/ x z)
       (if (<= z 4.3e-259)
         t_0
         (if (<= z 2.8e-83) (/ x z) (if (<= z 1.55e+34) t_0 (- x))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 3.4e-298) {
		tmp = x / z;
	} else if (z <= 4.3e-259) {
		tmp = t_0;
	} else if (z <= 2.8e-83) {
		tmp = x / z;
	} else if (z <= 1.55e+34) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= 3.4d-298) then
        tmp = x / z
    else if (z <= 4.3d-259) then
        tmp = t_0
    else if (z <= 2.8d-83) then
        tmp = x / z
    else if (z <= 1.55d+34) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 3.4e-298) {
		tmp = x / z;
	} else if (z <= 4.3e-259) {
		tmp = t_0;
	} else if (z <= 2.8e-83) {
		tmp = x / z;
	} else if (z <= 1.55e+34) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 3.4e-298:
		tmp = x / z
	elif z <= 4.3e-259:
		tmp = t_0
	elif z <= 2.8e-83:
		tmp = x / z
	elif z <= 1.55e+34:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= 3.4e-298)
		tmp = Float64(x / z);
	elseif (z <= 4.3e-259)
		tmp = t_0;
	elseif (z <= 2.8e-83)
		tmp = Float64(x / z);
	elseif (z <= 1.55e+34)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -x;
	elseif (z <= 3.4e-298)
		tmp = x / z;
	elseif (z <= 4.3e-259)
		tmp = t_0;
	elseif (z <= 2.8e-83)
		tmp = x / z;
	elseif (z <= 1.55e+34)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], (-x), If[LessEqual[z, 3.4e-298], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.3e-259], t$95$0, If[LessEqual[z, 2.8e-83], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.55e+34], t$95$0, (-x)]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1.54999999999999989e34 < z

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 81.8%

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

      1. mul-1-neg 81.8%

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

   4. Simplified 81.8%

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

   if -1 < z < 3.4e-298 or 4.3000000000000001e-259 < z < 2.8000000000000001e-83

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.4%

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

   3. Taylor expanded in y around 0 64.7%

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

   if 3.4e-298 < z < 4.3000000000000001e-259 or 2.8000000000000001e-83 < z < 1.54999999999999989e34

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 62.9%

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

      1. associate-*l/ 68.0%

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

   4. Simplified 68.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-298}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -6800000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+148} \lor \neg \left(y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -6800000.0)
     t_0
     (if (<= y 1.2e+51)
       (- (/ x z) x)
       (if (or (<= y 6.5e+148) (not (<= y 3.6e+176))) t_0 (- x))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -6800000.0) {
		tmp = t_0;
	} else if (y <= 1.2e+51) {
		tmp = (x / z) - x;
	} else if ((y <= 6.5e+148) || !(y <= 3.6e+176)) {
		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 (y <= (-6800000.0d0)) then
        tmp = t_0
    else if (y <= 1.2d+51) then
        tmp = (x / z) - x
    else if ((y <= 6.5d+148) .or. (.not. (y <= 3.6d+176))) 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 (y <= -6800000.0) {
		tmp = t_0;
	} else if (y <= 1.2e+51) {
		tmp = (x / z) - x;
	} else if ((y <= 6.5e+148) || !(y <= 3.6e+176)) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -6800000.0:
		tmp = t_0
	elif y <= 1.2e+51:
		tmp = (x / z) - x
	elif (y <= 6.5e+148) or not (y <= 3.6e+176):
		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 (y <= -6800000.0)
		tmp = t_0;
	elseif (y <= 1.2e+51)
		tmp = Float64(Float64(x / z) - x);
	elseif ((y <= 6.5e+148) || !(y <= 3.6e+176))
		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 (y <= -6800000.0)
		tmp = t_0;
	elseif (y <= 1.2e+51)
		tmp = (x / z) - x;
	elseif ((y <= 6.5e+148) || ~((y <= 3.6e+176)))
		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[y, -6800000.0], t$95$0, If[LessEqual[y, 1.2e+51], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], If[Or[LessEqual[y, 6.5e+148], N[Not[LessEqual[y, 3.6e+176]], $MachinePrecision]], t$95$0, (-x)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.8e6 or 1.1999999999999999e51 < y < 6.49999999999999947e148 or 3.59999999999999991e176 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in y around inf 78.4%

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

      1. associate-*l/ 74.5%

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

   4. Simplified 74.5%

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

   if -6.8e6 < y < 1.1999999999999999e51

   1. Initial program 84.7%

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

   2. Taylor expanded in y around 0 83.0%

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

      1. associate-/l* 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in x around 0 83.0%

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

      1. associate-*l/ 86.0%

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

      2. sub-neg 86.0%

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

      3. distribute-rgt-in 80.5%

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

      4. associate-*r/ 83.0%

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

      5. distribute-lft-neg-out 83.0%

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

      6. *-commutative 83.0%

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

      7. distribute-lft-neg-in 83.0%

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

      8. associate-/l* 98.4%

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

      9. *-inverses 98.4%

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

      10. distribute-neg-frac 98.4%

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

      11. /-rgt-identity 98.4%

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

      12. *-lft-identity 98.4%

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

      13. unsub-neg 98.4%

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

   7. Simplified 98.4%

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

   if 6.49999999999999947e148 < y < 3.59999999999999991e176

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6800000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+148} \lor \neg \left(y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;y \leq -14500000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 10^{+146} \lor \neg \left(y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (/ z x))))
   (if (<= y -14500000.0)
     t_0
     (if (<= y 1.05e+51)
       (- (/ x z) x)
       (if (or (<= y 1e+146) (not (<= y 3.6e+176))) t_0 (- x))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (z / x);
	double tmp;
	if (y <= -14500000.0) {
		tmp = t_0;
	} else if (y <= 1.05e+51) {
		tmp = (x / z) - x;
	} else if ((y <= 1e+146) || !(y <= 3.6e+176)) {
		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 / (z / x)
    if (y <= (-14500000.0d0)) then
        tmp = t_0
    else if (y <= 1.05d+51) then
        tmp = (x / z) - x
    else if ((y <= 1d+146) .or. (.not. (y <= 3.6d+176))) 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 / (z / x);
	double tmp;
	if (y <= -14500000.0) {
		tmp = t_0;
	} else if (y <= 1.05e+51) {
		tmp = (x / z) - x;
	} else if ((y <= 1e+146) || !(y <= 3.6e+176)) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (z / x)
	tmp = 0
	if y <= -14500000.0:
		tmp = t_0
	elif y <= 1.05e+51:
		tmp = (x / z) - x
	elif (y <= 1e+146) or not (y <= 3.6e+176):
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(z / x))
	tmp = 0.0
	if (y <= -14500000.0)
		tmp = t_0;
	elseif (y <= 1.05e+51)
		tmp = Float64(Float64(x / z) - x);
	elseif ((y <= 1e+146) || !(y <= 3.6e+176))
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (z / x);
	tmp = 0.0;
	if (y <= -14500000.0)
		tmp = t_0;
	elseif (y <= 1.05e+51)
		tmp = (x / z) - x;
	elseif ((y <= 1e+146) || ~((y <= 3.6e+176)))
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -14500000.0], t$95$0, If[LessEqual[y, 1.05e+51], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], If[Or[LessEqual[y, 1e+146], N[Not[LessEqual[y, 3.6e+176]], $MachinePrecision]], t$95$0, (-x)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e7 or 1.0500000000000001e51 < y < 9.99999999999999934e145 or 3.59999999999999991e176 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-/l* 74.6%

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

   4. Simplified 74.6%

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

   if -1.45e7 < y < 1.0500000000000001e51

   1. Initial program 84.7%

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

   2. Taylor expanded in y around 0 83.0%

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

      1. associate-/l* 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in x around 0 83.0%

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

      1. associate-*l/ 86.0%

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

      2. sub-neg 86.0%

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

      3. distribute-rgt-in 80.5%

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

      4. associate-*r/ 83.0%

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

      5. distribute-lft-neg-out 83.0%

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

      6. *-commutative 83.0%

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

      7. distribute-lft-neg-in 83.0%

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

      8. associate-/l* 98.4%

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

      9. *-inverses 98.4%

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

      10. distribute-neg-frac 98.4%

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

      11. /-rgt-identity 98.4%

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

      12. *-lft-identity 98.4%

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

      13. unsub-neg 98.4%

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

   7. Simplified 98.4%

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

   if 9.99999999999999934e145 < y < 3.59999999999999991e176

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14500000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 10^{+146} \lor \neg \left(y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot y}{z}\\ \mathbf{if}\;y \leq -14000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+149} \lor \neg \left(y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) z)))
   (if (<= y -14000000.0)
     t_0
     (if (<= y 6.3e+50)
       (- (/ x z) x)
       (if (or (<= y 6e+149) (not (<= y 3.6e+176))) t_0 (- x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if (y <= -14000000.0) {
		tmp = t_0;
	} else if (y <= 6.3e+50) {
		tmp = (x / z) - x;
	} else if ((y <= 6e+149) || !(y <= 3.6e+176)) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * y) / z
    if (y <= (-14000000.0d0)) then
        tmp = t_0
    else if (y <= 6.3d+50) then
        tmp = (x / z) - x
    else if ((y <= 6d+149) .or. (.not. (y <= 3.6d+176))) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if (y <= -14000000.0) {
		tmp = t_0;
	} else if (y <= 6.3e+50) {
		tmp = (x / z) - x;
	} else if ((y <= 6e+149) || !(y <= 3.6e+176)) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) / z
	tmp = 0
	if y <= -14000000.0:
		tmp = t_0
	elif y <= 6.3e+50:
		tmp = (x / z) - x
	elif (y <= 6e+149) or not (y <= 3.6e+176):
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (y <= -14000000.0)
		tmp = t_0;
	elseif (y <= 6.3e+50)
		tmp = Float64(Float64(x / z) - x);
	elseif ((y <= 6e+149) || !(y <= 3.6e+176))
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) / z;
	tmp = 0.0;
	if (y <= -14000000.0)
		tmp = t_0;
	elseif (y <= 6.3e+50)
		tmp = (x / z) - x;
	elseif ((y <= 6e+149) || ~((y <= 3.6e+176)))
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -14000000.0], t$95$0, If[LessEqual[y, 6.3e+50], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], If[Or[LessEqual[y, 6e+149], N[Not[LessEqual[y, 3.6e+176]], $MachinePrecision]], t$95$0, (-x)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e7 or 6.29999999999999986e50 < y < 6.00000000000000007e149 or 3.59999999999999991e176 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in y around inf 78.4%

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

   if -1.4e7 < y < 6.29999999999999986e50

   1. Initial program 84.7%

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

   2. Taylor expanded in y around 0 83.0%

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

      1. associate-/l* 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in x around 0 83.0%

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

      1. associate-*l/ 86.0%

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

      2. sub-neg 86.0%

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

      3. distribute-rgt-in 80.5%

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

      4. associate-*r/ 83.0%

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

      5. distribute-lft-neg-out 83.0%

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

      6. *-commutative 83.0%

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

      7. distribute-lft-neg-in 83.0%

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

      8. associate-/l* 98.4%

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

      9. *-inverses 98.4%

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

      10. distribute-neg-frac 98.4%

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

      11. /-rgt-identity 98.4%

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

      12. *-lft-identity 98.4%

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

      13. unsub-neg 98.4%

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

   7. Simplified 98.4%

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

   if 6.00000000000000007e149 < y < 3.59999999999999991e176

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14000000:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+149} \lor \neg \left(y \leq 3.6 \cdot 10^{+176}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 6: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+67}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(1 + y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.12e+67)
   (- x)
   (if (<= z 7.7e-7) (/ (* x (+ 1.0 y)) z) (- (/ x z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.12e+67) {
		tmp = -x;
	} else if (z <= 7.7e-7) {
		tmp = (x * (1.0 + 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 (z <= (-1.12d+67)) then
        tmp = -x
    else if (z <= 7.7d-7) then
        tmp = (x * (1.0d0 + 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 (z <= -1.12e+67) {
		tmp = -x;
	} else if (z <= 7.7e-7) {
		tmp = (x * (1.0 + y)) / z;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.12e+67:
		tmp = -x
	elif z <= 7.7e-7:
		tmp = (x * (1.0 + y)) / z
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.12e+67)
		tmp = Float64(-x);
	elseif (z <= 7.7e-7)
		tmp = Float64(Float64(x * Float64(1.0 + 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 (z <= -1.12e+67)
		tmp = -x;
	elseif (z <= 7.7e-7)
		tmp = (x * (1.0 + y)) / z;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.12e+67], (-x), If[LessEqual[z, 7.7e-7], N[(N[(x * N[(1.0 + y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12e67

   1. Initial program 73.6%

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

   2. Taylor expanded in z around inf 84.1%

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

      1. mul-1-neg 84.1%

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

   4. Simplified 84.1%

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

   if -1.12e67 < z < 7.7000000000000004e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.6%

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

   if 7.7000000000000004e-7 < z

   1. Initial program 75.8%

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

   2. Taylor expanded in y around 0 59.4%

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

      1. associate-/l* 83.6%

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

   4. Simplified 83.6%

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

   5. Taylor expanded in x around 0 59.4%

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

      1. associate-*l/ 65.2%

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

      2. sub-neg 65.2%

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

      3. distribute-rgt-in 65.2%

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

      4. associate-*r/ 59.5%

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

      5. distribute-lft-neg-out 59.5%

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

      6. *-commutative 59.5%

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

      7. distribute-lft-neg-in 59.5%

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

      8. associate-/l* 83.6%

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

      9. *-inverses 83.6%

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

      10. distribute-neg-frac 83.6%

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

      11. /-rgt-identity 83.6%

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

      12. *-lft-identity 83.6%

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

      13. unsub-neg 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+67}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(1 + y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 7: 65.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 76.5%

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

   2. Taylor expanded in z around inf 78.8%

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

      1. mul-1-neg 78.8%

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

   4. Simplified 78.8%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.1%

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

   3. Taylor expanded in y around 0 58.4%

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

4. Final simplification 68.6%

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

Alternative 8: 39.0% 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 88.2%

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

2. Taylor expanded in z around inf 41.1%

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

   1. mul-1-neg 41.1%

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

4. Simplified 41.1%

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

5. Final simplification 41.1%

   \[\leadsto -x \]

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 2023310 
(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))