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

Percentage Accurate: 88.7% → 99.8%

Time: 7.0s

Alternatives: 11

Speedup: 1.0×

• 21.5% 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: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+40} \lor \neg \left(z \leq 5 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(1 + y\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e+40) (not (<= z 5e+32)))
   (- (/ x (/ z y)) x)
   (* (/ x z) (- (+ 1.0 y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+40) || !(z <= 5e+32)) {
		tmp = (x / (z / y)) - x;
	} else {
		tmp = (x / z) * ((1.0 + 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 <= (-2d+40)) .or. (.not. (z <= 5d+32))) then
        tmp = (x / (z / y)) - x
    else
        tmp = (x / z) * ((1.0d0 + y) - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+40) || !(z <= 5e+32)) {
		tmp = (x / (z / y)) - x;
	} else {
		tmp = (x / z) * ((1.0 + y) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e+40) or not (z <= 5e+32):
		tmp = (x / (z / y)) - x
	else:
		tmp = (x / z) * ((1.0 + y) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e+40) || !(z <= 5e+32))
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(Float64(1.0 + y) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2e+40) || ~((z <= 5e+32)))
		tmp = (x / (z / y)) - x;
	else
		tmp = (x / z) * ((1.0 + y) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e+40], N[Not[LessEqual[z, 5e+32]], $MachinePrecision]], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(N[(1.0 + y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000006e40 or 4.9999999999999997e32 < z

   1. Initial program 76.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. log1p-expm1-u 99.9%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

   6. Taylor expanded in z around 0 90.8%

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

      1. neg-mul-1 90.8%

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

      2. +-commutative 90.8%

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

      3. unsub-neg 90.8%

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

      4. *-commutative 90.8%

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

      5. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 99.9%

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

   if -2.00000000000000006e40 < z < 4.9999999999999997e32

   1. Initial program 99.3%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around 0 99.3%

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

      1. associate--l+ 99.3%

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

      2. +-commutative 99.3%

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

      3. associate-*l/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+40} \lor \neg \left(z \leq 5 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(1 + y\right) - z\right)\\ \end{array} \]

Alternative 2: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1 + y, -x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 4e+82) (fma (/ x z) (+ 1.0 y) (- x)) (/ x (/ z (+ 1.0 (- y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4e+82) {
		tmp = fma((x / z), (1.0 + y), -x);
	} else {
		tmp = x / (z / (1.0 + (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4e+82)
		tmp = fma(Float64(x / z), Float64(1.0 + y), Float64(-x));
	else
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(y - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4e+82], N[(N[(x / z), $MachinePrecision] * N[(1.0 + y), $MachinePrecision] + (-x)), $MachinePrecision], N[(x / N[(z / N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.9999999999999999e82

   1. Initial program 93.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

      1. log1p-expm1-u 96.0%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

   5. Applied egg-rr 96.0%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

   6. Taylor expanded in z around 0 96.7%

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

      1. neg-mul-1 96.7%

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

      2. +-commutative 96.7%

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

      3. unsub-neg 96.7%

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

      4. *-commutative 96.7%

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

      5. associate-/l* 96.1%

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

   8. Simplified 96.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{1 + y}} - x} \]
   9. Step-by-step derivation

      1. associate-/r/ 99.4%

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

      2. fma-neg 99.4%

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

   10. Applied egg-rr 99.4%

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

   if 3.9999999999999999e82 < z

   1. Initial program 75.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 1 + y, -x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \end{array} \]

Alternative 3: 61.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-130}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+52}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) y)))
   (if (<= y -2e+28)
     t_0
     (if (<= y -8.2e-130)
       (- x)
       (if (<= y 2.7e-113) (/ x z) (if (<= y 1.16e+52) (- x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * y;
	double tmp;
	if (y <= -2e+28) {
		tmp = t_0;
	} else if (y <= -8.2e-130) {
		tmp = -x;
	} else if (y <= 2.7e-113) {
		tmp = x / z;
	} else if (y <= 1.16e+52) {
		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 <= (-2d+28)) then
        tmp = t_0
    else if (y <= (-8.2d-130)) then
        tmp = -x
    else if (y <= 2.7d-113) then
        tmp = x / z
    else if (y <= 1.16d+52) 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 <= -2e+28) {
		tmp = t_0;
	} else if (y <= -8.2e-130) {
		tmp = -x;
	} else if (y <= 2.7e-113) {
		tmp = x / z;
	} else if (y <= 1.16e+52) {
		tmp = -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * y
	tmp = 0
	if y <= -2e+28:
		tmp = t_0
	elif y <= -8.2e-130:
		tmp = -x
	elif y <= 2.7e-113:
		tmp = x / z
	elif y <= 1.16e+52:
		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 <= -2e+28)
		tmp = t_0;
	elseif (y <= -8.2e-130)
		tmp = Float64(-x);
	elseif (y <= 2.7e-113)
		tmp = Float64(x / z);
	elseif (y <= 1.16e+52)
		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 <= -2e+28)
		tmp = t_0;
	elseif (y <= -8.2e-130)
		tmp = -x;
	elseif (y <= 2.7e-113)
		tmp = x / z;
	elseif (y <= 1.16e+52)
		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, -2e+28], t$95$0, If[LessEqual[y, -8.2e-130], (-x), If[LessEqual[y, 2.7e-113], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.16e+52], (-x), t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999992e28 or 1.1599999999999999e52 < y

   1. Initial program 90.6%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around inf 73.7%

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

      1. associate-/r/ 75.5%

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

   6. Applied egg-rr 75.5%

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

   if -1.99999999999999992e28 < y < -8.19999999999999958e-130 or 2.69999999999999996e-113 < y < 1.1599999999999999e52

   1. Initial program 86.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 59.6%

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

      1. neg-mul-1 59.6%

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

   6. Simplified 59.6%

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

   if -8.19999999999999958e-130 < y < 2.69999999999999996e-113

   1. Initial program 92.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 62.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-130}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+52}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]

Alternative 4: 97.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0046\right):\\ \;\;\;\;\frac{x}{z} \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.0046))) (- (* (/ x z) y) x) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.0046)) {
		tmp = ((x / z) * y) - x;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 0.0046d0))) then
        tmp = ((x / z) * y) - x
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.0046)) {
		tmp = ((x / z) * y) - x;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.0046):
		tmp = ((x / z) * y) - x
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.0046))
		tmp = Float64(Float64(Float64(x / z) * y) - x);
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.0046)))
		tmp = ((x / z) * y) - x;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.0046]], $MachinePrecision]], N[(N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.0045999999999999999 < y

   1. Initial program 89.6%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

      1. log1p-expm1-u 93.7%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

   5. Applied egg-rr 93.7%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

   6. Taylor expanded in z around 0 92.5%

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

      1. neg-mul-1 92.5%

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

      2. +-commutative 92.5%

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

      3. unsub-neg 92.5%

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

      4. *-commutative 92.5%

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

      5. associate-/l* 93.7%

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

   8. Simplified 93.7%

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

   9. Taylor expanded in y around inf 91.1%

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

       1. associate-*r/ 93.2%

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

   11. Simplified 93.2%

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

   if -1 < y < 0.0045999999999999999

   1. Initial program 90.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-/l* 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in z around 0 98.4%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   8. Step-by-step derivation

      1. neg-mul-1 98.4%

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

      2. +-commutative 98.4%

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

      3. unsub-neg 98.4%

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

   9. Simplified 98.4%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0046\right):\\ \;\;\;\;\frac{x}{z} \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.95) (not (<= z 1.0)))
   (- (/ x (/ z y)) x)
   (/ (* x (+ 1.0 y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.95) || !(z <= 1.0)) {
		tmp = (x / (z / y)) - x;
	} else {
		tmp = (x * (1.0 + 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 <= (-0.95d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / (z / y)) - x
    else
        tmp = (x * (1.0d0 + y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.95) || !(z <= 1.0)) {
		tmp = (x / (z / y)) - x;
	} else {
		tmp = (x * (1.0 + y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.95) or not (z <= 1.0):
		tmp = (x / (z / y)) - x
	else:
		tmp = (x * (1.0 + y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.95) || !(z <= 1.0))
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	else
		tmp = Float64(Float64(x * Float64(1.0 + y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.95) || ~((z <= 1.0)))
		tmp = (x / (z / y)) - x;
	else
		tmp = (x * (1.0 + y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.95], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(1.0 + y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.94999999999999996 or 1 < z

   1. Initial program 79.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. log1p-expm1-u 99.8%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

   6. Taylor expanded in z around 0 92.4%

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

      1. neg-mul-1 92.4%

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

      2. +-commutative 92.4%

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

      3. unsub-neg 92.4%

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

      4. *-commutative 92.4%

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

      5. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 97.8%

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

   if -0.94999999999999996 < z < 1

   1. Initial program 99.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 98.7%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + y\right)}{z}\\ \end{array} \]

Alternative 6: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+31} \lor \neg \left(y \leq 5.3 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.7e+31) (not (<= y 5.3e+50))) (* (/ x z) y) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e+31) || !(y <= 5.3e+50)) {
		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 <= (-1.7d+31)) .or. (.not. (y <= 5.3d+50))) 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 <= -1.7e+31) || !(y <= 5.3e+50)) {
		tmp = (x / z) * y;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.7e+31) or not (y <= 5.3e+50):
		tmp = (x / z) * y
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.7e+31) || !(y <= 5.3e+50))
		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 <= -1.7e+31) || ~((y <= 5.3e+50)))
		tmp = (x / z) * y;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.7e+31], N[Not[LessEqual[y, 5.3e+50]], $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 < -1.6999999999999999e31 or 5.3000000000000002e50 < y

   1. Initial program 90.6%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around inf 73.7%

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

      1. associate-/r/ 75.5%

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

   6. Applied egg-rr 75.5%

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

   if -1.6999999999999999e31 < y < 5.3000000000000002e50

   1. Initial program 89.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-/l* 94.7%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in z around 0 94.7%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.7%

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

      2. +-commutative 94.7%

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

      3. unsub-neg 94.7%

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

   9. Simplified 94.7%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+31} \lor \neg \left(y \leq 5.3 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 7: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e+27)
   (* (/ x z) y)
   (if (<= y 7.8e+49) (- (/ x z) x) (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+27) {
		tmp = (x / z) * y;
	} else if (y <= 7.8e+49) {
		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 <= (-2.9d+27)) then
        tmp = (x / z) * y
    else if (y <= 7.8d+49) 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 <= -2.9e+27) {
		tmp = (x / z) * y;
	} else if (y <= 7.8e+49) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.9e+27:
		tmp = (x / z) * y
	elif y <= 7.8e+49:
		tmp = (x / z) - x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e+27)
		tmp = Float64(Float64(x / z) * y);
	elseif (y <= 7.8e+49)
		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 <= -2.9e+27)
		tmp = (x / z) * y;
	elseif (y <= 7.8e+49)
		tmp = (x / z) - x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e+27], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 7.8e+49], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9000000000000001e27

   1. Initial program 91.6%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in y around inf 69.0%

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

      1. associate-/r/ 72.0%

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

   6. Applied egg-rr 72.0%

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

   if -2.9000000000000001e27 < y < 7.8000000000000002e49

   1. Initial program 89.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-/l* 94.7%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in z around 0 94.7%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.7%

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

      2. +-commutative 94.7%

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

      3. unsub-neg 94.7%

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

   9. Simplified 94.7%

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

   if 7.8000000000000002e49 < y

   1. Initial program 89.4%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 79.0%

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

      1. associate-/l* 79.3%

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

   6. Simplified 79.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 8: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+30)
   (/ (* x y) z)
   (if (<= y 2.95e+49) (- (/ x z) x) (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+30) {
		tmp = (x * y) / z;
	} else if (y <= 2.95e+49) {
		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 <= (-7.5d+30)) then
        tmp = (x * y) / z
    else if (y <= 2.95d+49) 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 <= -7.5e+30) {
		tmp = (x * y) / z;
	} else if (y <= 2.95e+49) {
		tmp = (x / z) - x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+30:
		tmp = (x * y) / z
	elif y <= 2.95e+49:
		tmp = (x / z) - x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+30)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 2.95e+49)
		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 <= -7.5e+30)
		tmp = (x * y) / z;
	elseif (y <= 2.95e+49)
		tmp = (x / z) - x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+30], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.95e+49], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.49999999999999973e30

   1. Initial program 91.6%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in y around inf 76.9%

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

   if -7.49999999999999973e30 < y < 2.9500000000000001e49

   1. Initial program 89.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-/l* 94.7%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in z around 0 94.7%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.7%

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

      2. +-commutative 94.7%

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

      3. unsub-neg 94.7%

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

   9. Simplified 94.7%

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

   if 2.9500000000000001e49 < y

   1. Initial program 89.4%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 79.0%

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

      1. associate-/l* 79.3%

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

   6. Simplified 79.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 9: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.0%

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

   1. associate-/l* 96.8%

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

3. Simplified 96.8%

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

   1. log1p-expm1-u 96.8%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

5. Applied egg-rr 96.8%

   \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{z}{\left(y - z\right) + 1}\right)\right)}} \]

6. Taylor expanded in z around 0 96.2%

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

   1. neg-mul-1 96.2%

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

   2. +-commutative 96.2%

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

   3. unsub-neg 96.2%

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

   4. *-commutative 96.2%

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

   5. associate-/l* 96.8%

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

8. Simplified 96.8%

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

9. Final simplification 96.8%

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

Alternative 10: 64.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 2700000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (- x) (if (<= z 2700000.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 2700000.0) {
		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 <= 2700000.0d0) 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 <= 2700000.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 2700000.0:
		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 <= 2700000.0)
		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 <= 2700000.0)
		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, 2700000.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2.7e6 < z

   1. Initial program 79.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.0%

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

      1. neg-mul-1 71.0%

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

   6. Simplified 71.0%

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

   if -1 < z < 2.7e6

   1. Initial program 99.9%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around 0 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-/l* 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in z around 0 55.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 2700000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 11: 38.7% 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 90.0%

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

   1. associate-/l* 96.8%

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

3. Simplified 96.8%

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

4. Taylor expanded in z around inf 36.0%

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

   1. neg-mul-1 36.0%

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

6. Simplified 36.0%

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

7. Final simplification 36.0%

   \[\leadsto -x \]

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 2023171 
(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))