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

Percentage Accurate: 88.4% → 99.9%

Time: 10.5s

Alternatives: 12

Speedup: 1.0×

• 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: 88.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+17} \lor \neg \left(z \leq 1.62 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.12e+17) (not (<= z 1.62e+16)))
   (- (* x (/ y z)) x)
   (* (+ (- y z) 1.0) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.12e+17) || !(z <= 1.62e+16)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = ((y - z) + 1.0) * (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) :: tmp
    if ((z <= (-1.12d+17)) .or. (.not. (z <= 1.62d+16))) then
        tmp = (x * (y / z)) - x
    else
        tmp = ((y - z) + 1.0d0) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.12e+17) || !(z <= 1.62e+16)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = ((y - z) + 1.0) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.12e+17) or not (z <= 1.62e+16):
		tmp = (x * (y / z)) - x
	else:
		tmp = ((y - z) + 1.0) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.12e+17) || !(z <= 1.62e+16))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(Float64(y - z) + 1.0) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.12e+17) || ~((z <= 1.62e+16)))
		tmp = (x * (y / z)) - x;
	else
		tmp = ((y - z) + 1.0) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.12e+17], N[Not[LessEqual[z, 1.62e+16]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e17 or 1.62e16 < z

   1. Initial program 79.1%

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

      1. div-inv 79.0%

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

      2. associate-*l* 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 91.4%

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

      1. neg-mul-1 91.4%

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

      2. +-commutative 91.4%

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

      3. unsub-neg 91.4%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 94.8%

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

   6. Simplified 94.8%

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

   7. Taylor expanded in y around inf 91.4%

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

      1. associate-*r/ 99.9%

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

   9. Simplified 99.9%

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

   if -1.12e17 < z < 1.62e16

   1. Initial program 99.9%

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

      1. associate-/l* 95.7%

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

      2. associate-/r/ 99.9%

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

   3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+17} \lor \neg \left(z \leq 1.62 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;\frac{x \cdot t_0}{z} \leq -2 \cdot 10^{+47}:\\ \;\;\;\;t_0 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t_0 \cdot \frac{1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= (/ (* x t_0) z) -2e+47) (* t_0 (/ x z)) (* x (* t_0 (/ 1.0 z))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (((x * t_0) / z) <= -2e+47) {
		tmp = t_0 * (x / z);
	} else {
		tmp = x * (t_0 * (1.0 / 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 (((x * t_0) / z) <= (-2d+47)) then
        tmp = t_0 * (x / z)
    else
        tmp = x * (t_0 * (1.0d0 / 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 (((x * t_0) / z) <= -2e+47) {
		tmp = t_0 * (x / z);
	} else {
		tmp = x * (t_0 * (1.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if ((x * t_0) / z) <= -2e+47:
		tmp = t_0 * (x / z)
	else:
		tmp = x * (t_0 * (1.0 / z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (Float64(Float64(x * t_0) / z) <= -2e+47)
		tmp = Float64(t_0 * Float64(x / z));
	else
		tmp = Float64(x * Float64(t_0 * Float64(1.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if (((x * t_0) / z) <= -2e+47)
		tmp = t_0 * (x / z);
	else
		tmp = x * (t_0 * (1.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], -2e+47], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z) < -2.0000000000000001e47

   1. Initial program 83.8%

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

      1. associate-/l* 94.9%

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

      2. associate-/r/ 99.9%

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

   3. Applied egg-rr 99.9%

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

   if -2.0000000000000001e47 < (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

   1. Initial program 92.5%

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

      1. div-inv 92.4%

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

      2. associate-*l* 98.7%

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

   3. Applied egg-rr 98.7%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq -2 \cdot 10^{+47}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(\left(y - z\right) + 1\right) \cdot \frac{1}{z}\right)\\ \end{array} \]

Alternative 3: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -75000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -75000000.0)
     (- x)
     (if (<= z -7e-166)
       t_0
       (if (<= z 1.65e-284)
         (/ x z)
         (if (<= z 7.6e-185) t_0 (if (<= z 8.5e-11) (/ x z) (- x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -75000000.0) {
		tmp = -x;
	} else if (z <= -7e-166) {
		tmp = t_0;
	} else if (z <= 1.65e-284) {
		tmp = x / z;
	} else if (z <= 7.6e-185) {
		tmp = t_0;
	} else if (z <= 8.5e-11) {
		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 = x * (y / z)
    if (z <= (-75000000.0d0)) then
        tmp = -x
    else if (z <= (-7d-166)) then
        tmp = t_0
    else if (z <= 1.65d-284) then
        tmp = x / z
    else if (z <= 7.6d-185) then
        tmp = t_0
    else if (z <= 8.5d-11) 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 = x * (y / z);
	double tmp;
	if (z <= -75000000.0) {
		tmp = -x;
	} else if (z <= -7e-166) {
		tmp = t_0;
	} else if (z <= 1.65e-284) {
		tmp = x / z;
	} else if (z <= 7.6e-185) {
		tmp = t_0;
	} else if (z <= 8.5e-11) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -75000000.0:
		tmp = -x
	elif z <= -7e-166:
		tmp = t_0
	elif z <= 1.65e-284:
		tmp = x / z
	elif z <= 7.6e-185:
		tmp = t_0
	elif z <= 8.5e-11:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -75000000.0)
		tmp = Float64(-x);
	elseif (z <= -7e-166)
		tmp = t_0;
	elseif (z <= 1.65e-284)
		tmp = Float64(x / z);
	elseif (z <= 7.6e-185)
		tmp = t_0;
	elseif (z <= 8.5e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (z <= -75000000.0)
		tmp = -x;
	elseif (z <= -7e-166)
		tmp = t_0;
	elseif (z <= 1.65e-284)
		tmp = x / z;
	elseif (z <= 7.6e-185)
		tmp = t_0;
	elseif (z <= 8.5e-11)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -75000000.0], (-x), If[LessEqual[z, -7e-166], t$95$0, If[LessEqual[z, 1.65e-284], N[(x / z), $MachinePrecision], If[LessEqual[z, 7.6e-185], t$95$0, If[LessEqual[z, 8.5e-11], N[(x / z), $MachinePrecision], (-x)]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e7 or 8.50000000000000037e-11 < z

   1. Initial program 80.5%

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

   2. Taylor expanded in z around inf 77.0%

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

      1. neg-mul-1 77.0%

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

   4. Simplified 77.0%

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

   if -7.5e7 < z < -6.9999999999999998e-166 or 1.65000000000000004e-284 < z < 7.5999999999999998e-185

   1. Initial program 99.9%

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

      1. div-inv 99.6%

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

      2. associate-*l* 98.1%

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

   3. Applied egg-rr 98.1%

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

   4. Taylor expanded in y around inf 66.7%

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

      1. associate-*r/ 65.1%

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

   6. Simplified 65.1%

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

   if -6.9999999999999998e-166 < z < 1.65000000000000004e-284 or 7.5999999999999998e-185 < z < 8.50000000000000037e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 62.6%

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

      1. associate-/l* 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in z around 0 62.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -75000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 94.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -28000000 \lor \neg \left(y \leq 0.0011\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -28000000.0) (not (<= y 0.0011)))
   (- (* x (/ y z)) x)
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -28000000.0) || !(y <= 0.0011)) {
		tmp = (x * (y / z)) - 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 <= (-28000000.0d0)) .or. (.not. (y <= 0.0011d0))) then
        tmp = (x * (y / z)) - 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 <= -28000000.0) || !(y <= 0.0011)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -28000000.0) or not (y <= 0.0011):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -28000000.0) || !(y <= 0.0011))
		tmp = Float64(Float64(x * Float64(y / z)) - 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 <= -28000000.0) || ~((y <= 0.0011)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -28000000.0], N[Not[LessEqual[y, 0.0011]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e7 or 0.00110000000000000007 < y

   1. Initial program 89.1%

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

      1. div-inv 89.0%

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

      2. associate-*l* 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in z around 0 91.3%

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

      1. neg-mul-1 91.3%

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

      2. +-commutative 91.3%

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

      3. unsub-neg 91.3%

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

      4. associate-/l* 95.3%

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

      5. associate-/r/ 94.8%

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

   6. Simplified 94.8%

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

   7. Taylor expanded in y around inf 90.7%

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

      1. associate-*r/ 93.8%

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

   9. Simplified 93.8%

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

   if -2.8e7 < y < 0.00110000000000000007

   1. Initial program 90.8%

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

   2. Taylor expanded in y around 0 89.6%

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

      1. associate-/l* 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in z around 0 98.8%

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

      1. neg-mul-1 98.8%

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

      2. +-commutative 98.8%

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

      3. unsub-neg 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -28000000 \lor \neg \left(y \leq 0.0011\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 5: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -490 \lor \neg \left(z \leq 8.5 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -490.0) (not (<= z 8.5e-11)))
   (- (* x (/ y z)) x)
   (/ (* x (+ y 1.0)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -490.0) || !(z <= 8.5e-11)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x * (y + 1.0)) / 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 <= (-490.0d0)) .or. (.not. (z <= 8.5d-11))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x * (y + 1.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -490.0) || !(z <= 8.5e-11)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -490.0) or not (z <= 8.5e-11):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x * (y + 1.0)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -490.0) || !(z <= 8.5e-11))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -490.0) || ~((z <= 8.5e-11)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x * (y + 1.0)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -490.0], N[Not[LessEqual[z, 8.5e-11]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -490 or 8.50000000000000037e-11 < z

   1. Initial program 80.7%

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

      1. div-inv 80.5%

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

      2. associate-*l* 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 92.1%

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

      1. neg-mul-1 92.1%

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

      2. +-commutative 92.1%

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

      3. unsub-neg 92.1%

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

      4. associate-/l* 99.9%

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

      5. associate-/r/ 95.2%

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

   6. Simplified 95.2%

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

   7. Taylor expanded in y around inf 90.8%

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

      1. associate-*r/ 98.7%

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

   9. Simplified 98.7%

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

   if -490 < z < 8.50000000000000037e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -490 \lor \neg \left(z \leq 8.5 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]

Alternative 6: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -180000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -180000000.0)
   (- x)
   (if (<= z 2.1e-185) (* y (/ x z)) (if (<= z 8.5e-11) (/ x z) (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -180000000.0) {
		tmp = -x;
	} else if (z <= 2.1e-185) {
		tmp = y * (x / z);
	} else if (z <= 8.5e-11) {
		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 <= (-180000000.0d0)) then
        tmp = -x
    else if (z <= 2.1d-185) then
        tmp = y * (x / z)
    else if (z <= 8.5d-11) 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 <= -180000000.0) {
		tmp = -x;
	} else if (z <= 2.1e-185) {
		tmp = y * (x / z);
	} else if (z <= 8.5e-11) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -180000000.0:
		tmp = -x
	elif z <= 2.1e-185:
		tmp = y * (x / z)
	elif z <= 8.5e-11:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -180000000.0)
		tmp = Float64(-x);
	elseif (z <= 2.1e-185)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 8.5e-11)
		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 <= -180000000.0)
		tmp = -x;
	elseif (z <= 2.1e-185)
		tmp = y * (x / z);
	elseif (z <= 8.5e-11)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -180000000.0], (-x), If[LessEqual[z, 2.1e-185], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-11], N[(x / z), $MachinePrecision], (-x)]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e8 or 8.50000000000000037e-11 < z

   1. Initial program 80.5%

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

   2. Taylor expanded in z around inf 77.0%

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

      1. neg-mul-1 77.0%

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

   4. Simplified 77.0%

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

   if -1.8e8 < z < 2.1e-185

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 60.3%

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

      1. associate-/l* 56.1%

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

      2. associate-/r/ 64.7%

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

   4. Simplified 64.7%

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

   if 2.1e-185 < z < 8.50000000000000037e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.0%

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

      1. associate-/l* 63.0%

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

   4. Simplified 63.0%

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

   5. Taylor expanded in z around 0 62.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -180000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 7: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+82} \lor \neg \left(y \leq 8.3 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.7e+82) (not (<= y 8.3e+14))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+82) || !(y <= 8.3e+14)) {
		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 <= (-3.7d+82)) .or. (.not. (y <= 8.3d+14))) 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 <= -3.7e+82) || !(y <= 8.3e+14)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.7e+82) or not (y <= 8.3e+14):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.7e+82) || !(y <= 8.3e+14))
		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 <= -3.7e+82) || ~((y <= 8.3e+14)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.7e+82], N[Not[LessEqual[y, 8.3e+14]], $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 < -3.7000000000000002e82 or 8.3e14 < y

   1. Initial program 89.0%

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

   2. Taylor expanded in y around inf 77.9%

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

      1. associate-/l* 75.4%

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

      2. associate-/r/ 76.2%

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

   4. Simplified 76.2%

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

   if -3.7000000000000002e82 < y < 8.3e14

   1. Initial program 90.7%

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

   2. Taylor expanded in y around 0 84.4%

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

      1. associate-/l* 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in z around 0 93.8%

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

      1. neg-mul-1 93.8%

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

      2. +-commutative 93.8%

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

      3. unsub-neg 93.8%

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

   7. Simplified 93.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+82} \lor \neg \left(y \leq 8.3 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 8: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+82}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 46000000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.7e+82)
   (/ (* x y) z)
   (if (<= y 46000000000000.0) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+82) {
		tmp = (x * y) / z;
	} else if (y <= 46000000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (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 (y <= (-3.7d+82)) then
        tmp = (x * y) / z
    else if (y <= 46000000000000.0d0) then
        tmp = (x / z) - x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+82) {
		tmp = (x * y) / z;
	} else if (y <= 46000000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.7e+82:
		tmp = (x * y) / z
	elif y <= 46000000000000.0:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.7e+82)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 46000000000000.0)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.7e+82)
		tmp = (x * y) / z;
	elseif (y <= 46000000000000.0)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.7e+82], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 46000000000000.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7000000000000002e82

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 80.0%

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

   if -3.7000000000000002e82 < y < 4.6e13

   1. Initial program 90.7%

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

   2. Taylor expanded in y around 0 84.4%

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

      1. associate-/l* 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in z around 0 93.8%

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

      1. neg-mul-1 93.8%

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

      2. +-commutative 93.8%

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

      3. unsub-neg 93.8%

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

   7. Simplified 93.8%

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

   if 4.6e13 < y

   1. Initial program 92.8%

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

   2. Taylor expanded in y around inf 75.9%

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

      1. associate-/l* 75.6%

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

      2. associate-/r/ 77.4%

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

   4. Simplified 77.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+82}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 46000000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 9: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $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. div-inv 89.8%

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

   2. associate-*l* 97.2%

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

3. Applied egg-rr 97.2%

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

4. Taylor expanded in z around 0 95.9%

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

   1. neg-mul-1 95.9%

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

   2. +-commutative 95.9%

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

   3. unsub-neg 95.9%

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

   4. associate-/l* 97.7%

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

   5. associate-/r/ 97.5%

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

6. Simplified 97.5%

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

7. Final simplification 97.5%

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

Alternative 10: 64.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.245:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.245) (- x) (if (<= z 8.5e-11) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.245) {
		tmp = -x;
	} else if (z <= 8.5e-11) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.245d0)) then
        tmp = -x
    else if (z <= 8.5d-11) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.245) {
		tmp = -x;
	} else if (z <= 8.5e-11) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.245:
		tmp = -x
	elif z <= 8.5e-11:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.245)
		tmp = Float64(-x);
	elseif (z <= 8.5e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.245)
		tmp = -x;
	elseif (z <= 8.5e-11)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.245], (-x), If[LessEqual[z, 8.5e-11], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -0.245 or 8.50000000000000037e-11 < z

   1. Initial program 80.9%

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

   2. Taylor expanded in z around inf 75.3%

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

      1. neg-mul-1 75.3%

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

   4. Simplified 75.3%

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

   if -0.245 < z < 8.50000000000000037e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 56.7%

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

      1. associate-/l* 56.7%

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

   4. Simplified 56.7%

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

   5. Taylor expanded in z around 0 56.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.245:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 11: 38.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return -x

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 90.0%

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

2. Taylor expanded in z around inf 40.8%

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

   1. neg-mul-1 40.8%

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

4. Simplified 40.8%

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

5. Final simplification 40.8%

   \[\leadsto -x \]

Alternative 12: 3.0% accurate, 9.0× 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 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. Taylor expanded in z around inf 32.3%

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

   1. associate-*r* 32.3%

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

   2. neg-mul-1 32.3%

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

4. Simplified 32.3%

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

   1. div-inv 32.3%

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

   2. associate-*l* 40.8%

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

   3. div-inv 40.8%

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

   4. *-inverses 40.8%

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

   5. *-commutative 40.8%

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

   6. *-un-lft-identity 40.8%

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

   7. neg-sub0 40.8%

      \[\leadsto \color{blue}{0 - x} \]

   8. metadata-eval 40.8%

      \[\leadsto \color{blue}{\log 1} - x \]

   9. sub-neg 40.8%

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

   10. metadata-eval 40.8%

       \[\leadsto \color{blue}{0} + \left(-x\right) \]

   11. add-sqr-sqrt 18.4%

       \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   12. sqrt-unprod 16.7%

       \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   13. sqr-neg 16.7%

       \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   14. sqrt-unprod 2.0%

       \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   15. add-sqr-sqrt 3.4%

       \[\leadsto 0 + \color{blue}{x} \]

6. Applied egg-rr 3.4%

   \[\leadsto \color{blue}{0 + x} \]
7. Step-by-step derivation

   1. +-lft-identity 3.4%

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

8. Simplified 3.4%

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

9. Final simplification 3.4%

   \[\leadsto x \]

Developer target: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023285 
(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))