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

Percentage Accurate: 87.9% → 98.4%

Time: 8.6s

Alternatives: 13

Speedup: 0.8×

• 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: 87.9% 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: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+19} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e+19) (not (<= z 1.0)))
   (- (* x (/ y z)) x)
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+19) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x + (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 ((z <= (-1.35d+19)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x + (x * y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+19) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e+19) or not (z <= 1.0):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x + (x * y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e+19) || !(z <= 1.0))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e+19) || ~((z <= 1.0)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x + (x * y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e+19], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e19 or 1 < z

   1. Initial program 78.2%

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

   2. Taylor expanded in z around 0 95.3%

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

      1. neg-mul-1 95.3%

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

      2. +-commutative 95.3%

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

      3. unsub-neg 95.3%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 94.2%

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

   4. Simplified 94.2%

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

   5. Taylor expanded in y around inf 95.1%

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

      1. associate-*r/ 99.6%

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

   7. Simplified 99.6%

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

   if -1.35e19 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.6%

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

      1. distribute-lft-in 98.6%

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

      2. *-rgt-identity 98.6%

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

   4. Simplified 98.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+19} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \]

Alternative 2: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-42}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-143}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+75}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) y)))
   (if (<= y -5.5e+39)
     t_0
     (if (<= y -1.85e-42)
       (- x)
       (if (<= y -1.5e-76)
         (/ x z)
         (if (<= y -3.6e-143)
           (- x)
           (if (<= y 7.6e-10) (/ x z) (if (<= y 1.8e+75) (- x) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (y <= -5.5e+39) {
		tmp = t_0;
	} else if (y <= -1.85e-42) {
		tmp = -x;
	} else if (y <= -1.5e-76) {
		tmp = x / z;
	} else if (y <= -3.6e-143) {
		tmp = -x;
	} else if (y <= 7.6e-10) {
		tmp = x / z;
	} else if (y <= 1.8e+75) {
		tmp = -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / z) * y
    if (y <= (-5.5d+39)) then
        tmp = t_0
    else if (y <= (-1.85d-42)) then
        tmp = -x
    else if (y <= (-1.5d-76)) then
        tmp = x / z
    else if (y <= (-3.6d-143)) then
        tmp = -x
    else if (y <= 7.6d-10) then
        tmp = x / z
    else if (y <= 1.8d+75) then
        tmp = -x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (y <= -5.5e+39) {
		tmp = t_0;
	} else if (y <= -1.85e-42) {
		tmp = -x;
	} else if (y <= -1.5e-76) {
		tmp = x / z;
	} else if (y <= -3.6e-143) {
		tmp = -x;
	} else if (y <= 7.6e-10) {
		tmp = x / z;
	} else if (y <= 1.8e+75) {
		tmp = -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * y
	tmp = 0
	if y <= -5.5e+39:
		tmp = t_0
	elif y <= -1.85e-42:
		tmp = -x
	elif y <= -1.5e-76:
		tmp = x / z
	elif y <= -3.6e-143:
		tmp = -x
	elif y <= 7.6e-10:
		tmp = x / z
	elif y <= 1.8e+75:
		tmp = -x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) * y)
	tmp = 0.0
	if (y <= -5.5e+39)
		tmp = t_0;
	elseif (y <= -1.85e-42)
		tmp = Float64(-x);
	elseif (y <= -1.5e-76)
		tmp = Float64(x / z);
	elseif (y <= -3.6e-143)
		tmp = Float64(-x);
	elseif (y <= 7.6e-10)
		tmp = Float64(x / z);
	elseif (y <= 1.8e+75)
		tmp = Float64(-x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) * y;
	tmp = 0.0;
	if (y <= -5.5e+39)
		tmp = t_0;
	elseif (y <= -1.85e-42)
		tmp = -x;
	elseif (y <= -1.5e-76)
		tmp = x / z;
	elseif (y <= -3.6e-143)
		tmp = -x;
	elseif (y <= 7.6e-10)
		tmp = x / z;
	elseif (y <= 1.8e+75)
		tmp = -x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5.5e+39], t$95$0, If[LessEqual[y, -1.85e-42], (-x), If[LessEqual[y, -1.5e-76], N[(x / z), $MachinePrecision], If[LessEqual[y, -3.6e-143], (-x), If[LessEqual[y, 7.6e-10], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.8e+75], (-x), t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999997e39 or 1.8e75 < y

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 85.2%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 81.1%

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

   4. Simplified 81.1%

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

   if -5.4999999999999997e39 < y < -1.8500000000000001e-42 or -1.50000000000000012e-76 < y < -3.5999999999999998e-143 or 7.5999999999999996e-10 < y < 1.8e75

   1. Initial program 82.5%

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

   2. Taylor expanded in z around inf 70.9%

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

      1. neg-mul-1 70.9%

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

   4. Simplified 70.9%

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

   if -1.8500000000000001e-42 < y < -1.50000000000000012e-76 or -3.5999999999999998e-143 < y < 7.5999999999999996e-10

   1. Initial program 89.0%

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

   2. Taylor expanded in z around 0 63.8%

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

      1. distribute-lft-in 63.8%

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

      2. *-rgt-identity 63.8%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in y around 0 63.5%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-42}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-143}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+75}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]

Alternative 3: 94.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z} - x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+137}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (/ y z)) x)))
   (if (<= y -1.0)
     t_0
     (if (<= y 1.0) (- (/ x z) x) (if (<= y 2.5e+137) t_0 (/ (* x y) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y / z)) - x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else if (y <= 2.5e+137) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x * (y / z)) - x
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 1.0d0) then
        tmp = (x / z) - x
    else if (y <= 2.5d+137) then
        tmp = t_0
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y / z)) - x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else if (y <= 2.5e+137) {
		tmp = t_0;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y / z)) - x
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 1.0:
		tmp = (x / z) - x
	elif y <= 2.5e+137:
		tmp = t_0
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y / z)) - x)
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = Float64(Float64(x / z) - x);
	elseif (y <= 2.5e+137)
		tmp = t_0;
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y / z)) - x;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = (x / z) - x;
	elseif (y <= 2.5e+137)
		tmp = t_0;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 1.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 2.5e+137], t$95$0, N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1 < y < 2.5000000000000001e137

   1. Initial program 90.9%

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

   2. Taylor expanded in z around 0 96.7%

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

      1. neg-mul-1 96.7%

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

      2. +-commutative 96.7%

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

      3. unsub-neg 96.7%

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

      4. associate-/l* 98.8%

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

      5. associate-/r/ 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in y around inf 95.9%

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

      1. associate-*r/ 97.9%

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

   7. Simplified 97.9%

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

   if -1 < y < 1

   1. Initial program 87.8%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.2%

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

   if 2.5000000000000001e137 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 91.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 4: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0)
   (- (* x (/ y z)) x)
   (if (<= y 1.0)
     (- (/ x z) x)
     (if (<= y 2.5e+137) (- (/ x (/ z y)) x) (/ (* x y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = (x * (y / z)) - x;
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else if (y <= 2.5e+137) {
		tmp = (x / (z / y)) - 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 <= (-1.0d0)) then
        tmp = (x * (y / z)) - x
    else if (y <= 1.0d0) then
        tmp = (x / z) - x
    else if (y <= 2.5d+137) then
        tmp = (x / (z / y)) - 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 <= -1.0) {
		tmp = (x * (y / z)) - x;
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else if (y <= 2.5e+137) {
		tmp = (x / (z / y)) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = (x * (y / z)) - x
	elif y <= 1.0:
		tmp = (x / z) - x
	elif y <= 2.5e+137:
		tmp = (x / (z / y)) - x
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (y <= 1.0)
		tmp = Float64(Float64(x / z) - x);
	elseif (y <= 2.5e+137)
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = (x * (y / z)) - x;
	elseif (y <= 1.0)
		tmp = (x / z) - x;
	elseif (y <= 2.5e+137)
		tmp = (x / (z / y)) - x;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 1.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 2.5e+137], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 96.8%

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

      1. neg-mul-1 96.8%

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

      2. +-commutative 96.8%

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

      3. unsub-neg 96.8%

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

      4. associate-/l* 98.2%

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

      5. associate-/r/ 95.9%

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

   4. Simplified 95.9%

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

   5. Taylor expanded in y around inf 96.8%

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

      1. associate-*r/ 98.2%

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

   7. Simplified 98.2%

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

   if -1 < y < 1

   1. Initial program 87.8%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. +-commutative 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.2%

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

   if 1 < y < 2.5000000000000001e137

   1. Initial program 85.9%

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

   2. Taylor expanded in z around 0 96.4%

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

      1. neg-mul-1 96.4%

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

      2. +-commutative 96.4%

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

      3. unsub-neg 96.4%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 93.9%

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

      1. associate-*r/ 97.3%

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

   7. Simplified 97.3%

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

      1. clear-num 97.4%

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

      2. un-div-inv 97.4%

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

   9. Applied egg-rr 97.4%

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

   if 2.5000000000000001e137 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 91.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 5: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{\frac{z}{1 - z}}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0)
   (- (* x (/ y z)) x)
   (if (<= y 1.0)
     (/ x (/ z (- 1.0 z)))
     (if (<= y 2.45e+137) (- (/ x (/ z y)) x) (/ (* x y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = (x * (y / z)) - x;
	} else if (y <= 1.0) {
		tmp = x / (z / (1.0 - z));
	} else if (y <= 2.45e+137) {
		tmp = (x / (z / y)) - 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 <= (-1.0d0)) then
        tmp = (x * (y / z)) - x
    else if (y <= 1.0d0) then
        tmp = x / (z / (1.0d0 - z))
    else if (y <= 2.45d+137) then
        tmp = (x / (z / y)) - 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 <= -1.0) {
		tmp = (x * (y / z)) - x;
	} else if (y <= 1.0) {
		tmp = x / (z / (1.0 - z));
	} else if (y <= 2.45e+137) {
		tmp = (x / (z / y)) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = (x * (y / z)) - x
	elif y <= 1.0:
		tmp = x / (z / (1.0 - z))
	elif y <= 2.45e+137:
		tmp = (x / (z / y)) - x
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (y <= 1.0)
		tmp = Float64(x / Float64(z / Float64(1.0 - z)));
	elseif (y <= 2.45e+137)
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = (x * (y / z)) - x;
	elseif (y <= 1.0)
		tmp = x / (z / (1.0 - z));
	elseif (y <= 2.45e+137)
		tmp = (x / (z / y)) - x;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 1.0], N[(x / N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+137], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 96.8%

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

      1. neg-mul-1 96.8%

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

      2. +-commutative 96.8%

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

      3. unsub-neg 96.8%

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

      4. associate-/l* 98.2%

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

      5. associate-/r/ 95.9%

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

   4. Simplified 95.9%

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

   5. Taylor expanded in y around inf 96.8%

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

      1. associate-*r/ 98.2%

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

   7. Simplified 98.2%

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

   if -1 < y < 1

   1. Initial program 87.8%

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

   2. Taylor expanded in y around 0 87.0%

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

      1. associate-/l* 99.2%

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

   4. Simplified 99.2%

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

   if 1 < y < 2.45000000000000016e137

   1. Initial program 85.9%

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

   2. Taylor expanded in z around 0 96.4%

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

      1. neg-mul-1 96.4%

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

      2. +-commutative 96.4%

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

      3. unsub-neg 96.4%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 93.9%

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

      1. associate-*r/ 97.3%

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

   7. Simplified 97.3%

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

      1. clear-num 97.4%

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

      2. un-div-inv 97.4%

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

   9. Applied egg-rr 97.4%

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

   if 2.45000000000000016e137 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 91.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{\frac{z}{1 - z}}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 6: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1 + \left(y - z\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 5e-129) (- (* (/ x z) (+ 1.0 y)) x) (* x (/ (+ 1.0 (- y z)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e-129) {
		tmp = ((x / z) * (1.0 + y)) - x;
	} else {
		tmp = x * ((1.0 + (y - z)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 5d-129) then
        tmp = ((x / z) * (1.0d0 + y)) - x
    else
        tmp = x * ((1.0d0 + (y - z)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e-129) {
		tmp = ((x / z) * (1.0 + y)) - x;
	} else {
		tmp = x * ((1.0 + (y - z)) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5e-129:
		tmp = ((x / z) * (1.0 + y)) - x
	else:
		tmp = x * ((1.0 + (y - z)) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5e-129)
		tmp = Float64(Float64(Float64(x / z) * Float64(1.0 + y)) - x);
	else
		tmp = Float64(x * Float64(Float64(1.0 + Float64(y - z)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 5e-129)
		tmp = ((x / z) * (1.0 + y)) - x;
	else
		tmp = x * ((1.0 + (y - z)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5e-129], N[(N[(N[(x / z), $MachinePrecision] * N[(1.0 + y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(x * N[(N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.00000000000000027e-129

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 98.2%

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

      1. neg-mul-1 98.2%

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

      2. +-commutative 98.2%

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

      3. unsub-neg 98.2%

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

      4. associate-/l* 93.4%

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

      5. associate-/r/ 98.2%

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

   4. Simplified 98.2%

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

   if 5.00000000000000027e-129 < z

   1. Initial program 85.4%

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

      1. *-un-lft-identity 85.4%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1 + \left(y - z\right)}{z}\\ \end{array} \]

Alternative 7: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 54000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 54000000000.0) (- (* (/ x z) (+ 1.0 y)) x) (- (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 54000000000.0) {
		tmp = ((x / z) * (1.0 + y)) - x;
	} else {
		tmp = (x * (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 (z <= 54000000000.0d0) then
        tmp = ((x / z) * (1.0d0 + y)) - x
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 54000000000.0) {
		tmp = ((x / z) * (1.0 + y)) - x;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 54000000000.0:
		tmp = ((x / z) * (1.0 + y)) - x
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 54000000000.0)
		tmp = Float64(Float64(Float64(x / z) * Float64(1.0 + y)) - x);
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 54000000000.0)
		tmp = ((x / z) * (1.0 + y)) - x;
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 54000000000.0], N[(N[(N[(x / z), $MachinePrecision] * N[(1.0 + y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.4e10

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 98.4%

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

      1. neg-mul-1 98.4%

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

      2. +-commutative 98.4%

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

      3. unsub-neg 98.4%

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

      4. associate-/l* 94.3%

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

      5. associate-/r/ 98.4%

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

   4. Simplified 98.4%

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

   if 5.4e10 < z

   1. Initial program 78.9%

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

   2. Taylor expanded in z around 0 95.5%

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

      1. neg-mul-1 95.5%

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

      2. +-commutative 95.5%

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

      3. unsub-neg 95.5%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in y around inf 95.5%

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

      1. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 54000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \]

Alternative 8: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+40} \lor \neg \left(y \leq 1.55 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.7e+40) (not (<= y 1.55e+75))) (* (/ x z) y) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+40) || !(y <= 1.55e+75)) {
		tmp = (x / z) * y;
	} 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 <= (-3.7d+40)) .or. (.not. (y <= 1.55d+75))) then
        tmp = (x / z) * y
    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 <= -3.7e+40) || !(y <= 1.55e+75)) {
		tmp = (x / z) * y;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.7e+40) or not (y <= 1.55e+75):
		tmp = (x / z) * y
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.7e+40) || !(y <= 1.55e+75))
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.7e+40) || ~((y <= 1.55e+75)))
		tmp = (x / z) * y;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.7e+40], N[Not[LessEqual[y, 1.55e+75]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e40 or 1.5500000000000001e75 < y

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 85.2%

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

      1. associate-/l* 76.3%

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

      2. associate-/r/ 81.1%

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

   4. Simplified 81.1%

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

   if -3.7e40 < y < 1.5500000000000001e75

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. +-commutative 99.4%

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

      3. unsub-neg 99.4%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 94.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+40} \lor \neg \left(y \leq 1.55 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 9: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+41} \lor \neg \left(y \leq 1.05 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.16e+41) (not (<= y 1.05e+75))) (/ (* x y) z) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.16e+41) || !(y <= 1.05e+75)) {
		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 <= (-1.16d+41)) .or. (.not. (y <= 1.05d+75))) 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 <= -1.16e+41) || !(y <= 1.05e+75)) {
		tmp = (x * y) / z;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.16e+41) or not (y <= 1.05e+75):
		tmp = (x * y) / z
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.16e+41) || !(y <= 1.05e+75))
		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 <= -1.16e+41) || ~((y <= 1.05e+75)))
		tmp = (x * y) / z;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.16e+41], N[Not[LessEqual[y, 1.05e+75]], $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 < -1.16000000000000007e41 or 1.04999999999999999e75 < y

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 85.2%

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

   if -1.16000000000000007e41 < y < 1.04999999999999999e75

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. +-commutative 99.4%

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

      3. unsub-neg 99.4%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 94.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+41} \lor \neg \left(y \leq 1.05 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 10: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.7e+40)
   (/ x (/ z y))
   (if (<= y 8.6e+74) (- (/ x z) x) (* (/ x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+40) {
		tmp = x / (z / y);
	} else if (y <= 8.6e+74) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.7d+40)) then
        tmp = x / (z / y)
    else if (y <= 8.6d+74) then
        tmp = (x / z) - x
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+40) {
		tmp = x / (z / y);
	} else if (y <= 8.6e+74) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.7e+40:
		tmp = x / (z / y)
	elif y <= 8.6e+74:
		tmp = (x / z) - x
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.7e+40)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 8.6e+74)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.7e+40)
		tmp = x / (z / y);
	elseif (y <= 8.6e+74)
		tmp = (x / z) - x;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.7e+40], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e+74], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7e40

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 84.3%

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

      1. associate-/l* 84.1%

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

   4. Simplified 84.1%

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

   if -3.7e40 < y < 8.60000000000000001e74

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. +-commutative 99.4%

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

      3. unsub-neg 99.4%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 94.9%

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

   if 8.60000000000000001e74 < y

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 85.9%

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

      1. associate-/l* 69.1%

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

      2. associate-/r/ 80.2%

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

   4. Simplified 80.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]

Alternative 11: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+39)
   (/ x (/ z y))
   (if (<= y 1.05e+75) (- (/ x z) x) (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+39) {
		tmp = x / (z / y);
	} else if (y <= 1.05e+75) {
		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+39)) then
        tmp = x / (z / y)
    else if (y <= 1.05d+75) 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+39) {
		tmp = x / (z / y);
	} else if (y <= 1.05e+75) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+39:
		tmp = x / (z / y)
	elif y <= 1.05e+75:
		tmp = (x / z) - x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+39)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 1.05e+75)
		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+39)
		tmp = x / (z / y);
	elseif (y <= 1.05e+75)
		tmp = (x / z) - x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+39], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+75], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.80000000000000059e39

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 84.3%

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

      1. associate-/l* 84.1%

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

   4. Simplified 84.1%

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

   if -5.80000000000000059e39 < y < 1.04999999999999999e75

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 99.4%

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

      1. neg-mul-1 99.4%

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

      2. +-commutative 99.4%

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

      3. unsub-neg 99.4%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 94.9%

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

   if 1.04999999999999999e75 < y

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 85.9%

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

      1. associate-/l* 69.1%

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

      2. associate-/r/ 80.2%

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

   4. Simplified 80.2%

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

      1. associate-*l/ 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-/l* 80.3%

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

   6. Applied egg-rr 80.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 12: 65.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 4100000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (- x) (if (<= z 4100000.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 4100000.0) {
		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 <= 4100000.0d0) 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 <= 4100000.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 4100000.0:
		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 <= 4100000.0)
		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 <= 4100000.0)
		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, 4100000.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 4.1e6 < z

   1. Initial program 78.2%

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

   2. Taylor expanded in z around inf 72.5%

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

      1. neg-mul-1 72.5%

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

   4. Simplified 72.5%

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

   if -1 < z < 4.1e6

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.5%

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

      1. distribute-lft-in 98.5%

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

      2. *-rgt-identity 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in y around 0 58.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 4100000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 13: 39.2% 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 89.7%

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

2. Taylor expanded in z around inf 35.7%

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

   1. neg-mul-1 35.7%

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

4. Simplified 35.7%

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

5. Final simplification 35.7%

   \[\leadsto -x \]

Developer target: 99.5% 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 2023277 
(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))