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

Percentage Accurate: 87.8% → 99.4%

Time: 7.5s

Alternatives: 10

Speedup: 0.6×

• 21.1% 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: 87.8% 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: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+48} \lor \neg \left(z \leq 1.25 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (or (<= z -2.45e+48) (not (<= z 1.25e-132)))
     (/ x (/ z t_0))
     (* t_0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if ((z <= -2.45e+48) || !(z <= 1.25e-132)) {
		tmp = x / (z / t_0);
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y - z) + 1.0d0
    if ((z <= (-2.45d+48)) .or. (.not. (z <= 1.25d-132))) then
        tmp = x / (z / t_0)
    else
        tmp = t_0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if ((z <= -2.45e+48) || !(z <= 1.25e-132)) {
		tmp = x / (z / t_0);
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if (z <= -2.45e+48) or not (z <= 1.25e-132):
		tmp = x / (z / t_0)
	else:
		tmp = t_0 * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if ((z <= -2.45e+48) || !(z <= 1.25e-132))
		tmp = Float64(x / Float64(z / t_0));
	else
		tmp = Float64(t_0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if ((z <= -2.45e+48) || ~((z <= 1.25e-132)))
		tmp = x / (z / t_0);
	else
		tmp = t_0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[Or[LessEqual[z, -2.45e+48], N[Not[LessEqual[z, 1.25e-132]], $MachinePrecision]], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000015e48 or 1.25e-132 < 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* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -2.45000000000000015e48 < z < 1.25e-132

   1. Initial program 99.8%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-*l/ 99.8%

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

      4. +-commutative 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+48} \lor \neg \left(z \leq 1.25 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -67000000000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-235}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-113}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -67000000000000.0)
     (- x)
     (if (<= z -3.2e-235)
       t_0
       (if (<= z 1.52e-186)
         (/ x z)
         (if (<= z 9.6e-113) t_0 (if (<= z 1.0) (/ x z) (- x))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -67000000000000.0) {
		tmp = -x;
	} else if (z <= -3.2e-235) {
		tmp = t_0;
	} else if (z <= 1.52e-186) {
		tmp = x / z;
	} else if (z <= 9.6e-113) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (z <= (-67000000000000.0d0)) then
        tmp = -x
    else if (z <= (-3.2d-235)) then
        tmp = t_0
    else if (z <= 1.52d-186) then
        tmp = x / z
    else if (z <= 9.6d-113) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -67000000000000.0) {
		tmp = -x;
	} else if (z <= -3.2e-235) {
		tmp = t_0;
	} else if (z <= 1.52e-186) {
		tmp = x / z;
	} else if (z <= 9.6e-113) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -67000000000000.0:
		tmp = -x
	elif z <= -3.2e-235:
		tmp = t_0
	elif z <= 1.52e-186:
		tmp = x / z
	elif z <= 9.6e-113:
		tmp = t_0
	elif z <= 1.0:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -67000000000000.0)
		tmp = Float64(-x);
	elseif (z <= -3.2e-235)
		tmp = t_0;
	elseif (z <= 1.52e-186)
		tmp = Float64(x / z);
	elseif (z <= 9.6e-113)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -67000000000000.0)
		tmp = -x;
	elseif (z <= -3.2e-235)
		tmp = t_0;
	elseif (z <= 1.52e-186)
		tmp = x / z;
	elseif (z <= 9.6e-113)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -67000000000000.0], (-x), If[LessEqual[z, -3.2e-235], t$95$0, If[LessEqual[z, 1.52e-186], N[(x / z), $MachinePrecision], If[LessEqual[z, 9.6e-113], t$95$0, If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7e13 or 1 < z

   1. Initial program 75.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 75.7%

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

      1. mul-1-neg 75.7%

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

   7. Simplified 75.7%

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

   if -6.7e13 < z < -3.2000000000000001e-235 or 1.5200000000000001e-186 < z < 9.60000000000000049e-113

   1. Initial program 99.8%

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

      1. associate-/l* 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in y around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. associate-*r/ 68.6%

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

   7. Simplified 68.6%

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

   if -3.2000000000000001e-235 < z < 1.5200000000000001e-186 or 9.60000000000000049e-113 < 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* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in y around 0 70.5%

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

   6. Taylor expanded in z around 0 68.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -67000000000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-235}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -116000 \lor \neg \left(z \leq 6.6 \cdot 10^{-73}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -116000.0) (not (<= z 6.6e-73)))
   (* x (/ (+ (- y z) 1.0) z))
   (* (/ x z) (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -116000.0) || !(z <= 6.6e-73)) {
		tmp = x * (((y - z) + 1.0) / z);
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-116000.0d0)) .or. (.not. (z <= 6.6d-73))) then
        tmp = x * (((y - z) + 1.0d0) / z)
    else
        tmp = (x / z) * (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -116000.0) || !(z <= 6.6e-73)) {
		tmp = x * (((y - z) + 1.0) / z);
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -116000.0) or not (z <= 6.6e-73):
		tmp = x * (((y - z) + 1.0) / z)
	else:
		tmp = (x / z) * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -116000.0) || !(z <= 6.6e-73))
		tmp = Float64(x * Float64(Float64(Float64(y - z) + 1.0) / z));
	else
		tmp = Float64(Float64(x / z) * Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -116000.0) || ~((z <= 6.6e-73)))
		tmp = x * (((y - z) + 1.0) / z);
	else
		tmp = (x / z) * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -116000.0], N[Not[LessEqual[z, 6.6e-73]], $MachinePrecision]], N[(x * N[(N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -116000 or 6.60000000000000007e-73 < z

   1. Initial program 78.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -116000 < z < 6.60000000000000007e-73

   1. Initial program 99.8%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -116000 \lor \neg \left(z \leq 6.6 \cdot 10^{-73}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+48} \lor \neg \left(z \leq 2.65 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot \frac{t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (or (<= z -2.55e+48) (not (<= z 2.65e-77)))
     (* x (/ t_0 z))
     (* t_0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if ((z <= -2.55e+48) || !(z <= 2.65e-77)) {
		tmp = x * (t_0 / z);
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y - z) + 1.0d0
    if ((z <= (-2.55d+48)) .or. (.not. (z <= 2.65d-77))) then
        tmp = x * (t_0 / z)
    else
        tmp = t_0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if ((z <= -2.55e+48) || !(z <= 2.65e-77)) {
		tmp = x * (t_0 / z);
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if (z <= -2.55e+48) or not (z <= 2.65e-77):
		tmp = x * (t_0 / z)
	else:
		tmp = t_0 * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if ((z <= -2.55e+48) || !(z <= 2.65e-77))
		tmp = Float64(x * Float64(t_0 / z));
	else
		tmp = Float64(t_0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if ((z <= -2.55e+48) || ~((z <= 2.65e-77)))
		tmp = x * (t_0 / z);
	else
		tmp = t_0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[Or[LessEqual[z, -2.55e+48], N[Not[LessEqual[z, 2.65e-77]], $MachinePrecision]], N[(x * N[(t$95$0 / z), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e48 or 2.65000000000000007e-77 < z

   1. Initial program 77.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -2.5499999999999999e48 < z < 2.65000000000000007e-77

   1. Initial program 99.8%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-*l/ 99.8%

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

      4. +-commutative 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+48} \lor \neg \left(z \leq 2.65 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+88)
   (* y (/ x z))
   (if (<= y 3.6e+58) (- (/ x z) x) (* (/ x z) (+ y 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+88) {
		tmp = y * (x / z);
	} else if (y <= 3.6e+58) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.25d+88)) then
        tmp = y * (x / z)
    else if (y <= 3.6d+58) then
        tmp = (x / z) - x
    else
        tmp = (x / z) * (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+88) {
		tmp = y * (x / z);
	} else if (y <= 3.6e+58) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+88:
		tmp = y * (x / z)
	elif y <= 3.6e+58:
		tmp = (x / z) - x
	else:
		tmp = (x / z) * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+88)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 3.6e+58)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e+88)
		tmp = y * (x / z);
	elseif (y <= 3.6e+58)
		tmp = (x / z) - x;
	else
		tmp = (x / z) * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+88], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+58], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.24999999999999999e88

   1. Initial program 87.4%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*r/ 86.3%

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

   7. Simplified 86.3%

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

   if -1.24999999999999999e88 < y < 3.59999999999999996e58

   1. Initial program 87.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 81.3%

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

   6. Taylor expanded in z around inf 93.9%

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

      1. neg-mul-1 93.9%

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

      2. +-commutative 93.9%

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

      3. unsub-neg 93.9%

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

   8. Simplified 93.9%

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

   if 3.59999999999999996e58 < y

   1. Initial program 86.1%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in z around 0 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-/l* 79.4%

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

   7. Applied egg-rr 79.4%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+87)
   (* y (/ x z))
   (if (<= y 4.8e+57) (- (/ x z) x) (/ (/ x z) (/ 1.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+87) {
		tmp = y * (x / z);
	} else if (y <= 4.8e+57) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) / (1.0 / 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 <= (-4.5d+87)) then
        tmp = y * (x / z)
    else if (y <= 4.8d+57) then
        tmp = (x / z) - x
    else
        tmp = (x / z) / (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+87) {
		tmp = y * (x / z);
	} else if (y <= 4.8e+57) {
		tmp = (x / z) - x;
	} else {
		tmp = (x / z) / (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+87:
		tmp = y * (x / z)
	elif y <= 4.8e+57:
		tmp = (x / z) - x
	else:
		tmp = (x / z) / (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+87)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 4.8e+57)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x / z) / Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.5e+87)
		tmp = y * (x / z);
	elseif (y <= 4.8e+57)
		tmp = (x / z) - x;
	else
		tmp = (x / z) / (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+87], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+57], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000003e87

   1. Initial program 87.4%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*r/ 86.3%

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

   7. Simplified 86.3%

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

   if -4.5000000000000003e87 < y < 4.80000000000000009e57

   1. Initial program 87.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 81.3%

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

   6. Taylor expanded in z around inf 93.9%

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

      1. neg-mul-1 93.9%

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

      2. +-commutative 93.9%

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

      3. unsub-neg 93.9%

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

   8. Simplified 93.9%

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

   if 4.80000000000000009e57 < y

   1. Initial program 86.1%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. div-inv 87.6%

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

      4. associate-*l* 87.7%

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

   4. Applied egg-rr 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*l/ 87.8%

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

      3. *-un-lft-identity 87.8%

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

      4. associate-/r/ 87.8%

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

      5. div-inv 87.7%

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

      6. associate-/r* 87.8%

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

      7. sub-neg 87.8%

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

      8. associate-+l+ 87.8%

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

      9. +-commutative 87.8%

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

      10. sub-neg 87.8%

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

   6. Applied egg-rr 87.8%

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

   7. Taylor expanded in y around inf 79.4%

      \[\leadsto \frac{\frac{x}{z}}{\color{blue}{\frac{1}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+87} \lor \neg \left(y \leq 10^{+57}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+87) (not (<= y 1e+57))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+87) || !(y <= 1e+57)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.2d+87)) .or. (.not. (y <= 1d+57))) then
        tmp = y * (x / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+87) || !(y <= 1e+57)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+87) or not (y <= 1e+57):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+87) || !(y <= 1e+57))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.2e+87) || ~((y <= 1e+57)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e+87], N[Not[LessEqual[y, 1e+57]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e87 or 1.00000000000000005e57 < y

   1. Initial program 86.6%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in y around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*r/ 82.2%

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

   7. Simplified 82.2%

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

   if -4.2e87 < y < 1.00000000000000005e57

   1. Initial program 87.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 81.3%

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

   6. Taylor expanded in z around inf 93.9%

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

      1. neg-mul-1 93.9%

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

      2. +-commutative 93.9%

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

      3. unsub-neg 93.9%

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

   8. Simplified 93.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+87} \lor \neg \left(y \leq 10^{+57}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;x \leq 1.2 \cdot 10^{-103}:\\ \;\;\;\;\frac{x \cdot t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= x 1.2e-103) (/ (* x t_0) z) (/ x (/ z t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 1.2e-103) {
		tmp = (x * t_0) / z;
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y - z) + 1.0d0
    if (x <= 1.2d-103) then
        tmp = (x * t_0) / z
    else
        tmp = x / (z / t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 1.2e-103) {
		tmp = (x * t_0) / z;
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if x <= 1.2e-103:
		tmp = (x * t_0) / z
	else:
		tmp = x / (z / t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (x <= 1.2e-103)
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(x / Float64(z / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if (x <= 1.2e-103)
		tmp = (x * t_0) / z;
	else
		tmp = x / (z / t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, 1.2e-103], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.2000000000000001e-103

   1. Initial program 89.7%

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

   if 1.2000000000000001e-103 < x

   1. Initial program 81.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.2 \cdot 10^{-103}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 76.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 74.5%

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

      1. mul-1-neg 74.5%

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

   7. Simplified 74.5%

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

   if -1 < z < 1

   1. Initial program 99.8%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around 0 58.2%

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

   6. Taylor expanded in z around 0 56.9%

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

4. Final simplification 66.3%

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

Alternative 10: 37.7% 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 87.1%

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

   1. associate-/l* 95.7%

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

3. Simplified 95.7%

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

5. Taylor expanded in z around inf 41.3%

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

   1. mul-1-neg 41.3%

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

7. Simplified 41.3%

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

8. Final simplification 41.3%

   \[\leadsto -x \]
9. Add Preprocessing

Developer target: 99.4% accurate, 0.4× 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 2024075 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (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))