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

Percentage Accurate: 87.3% → 99.3%

Time: 8.1s

Alternatives: 13

Speedup: 0.6×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 87.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-142}:\\ \;\;\;\;t\_0 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= z -1.08e+29)
     (* x (+ (/ y z) -1.0))
     (if (<= z 4.5e-142) (* t_0 (/ x z)) (/ x (/ z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (z <= -1.08e+29) {
		tmp = x * ((y / z) + -1.0);
	} else if (z <= 4.5e-142) {
		tmp = t_0 * (x / 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 (z <= (-1.08d+29)) then
        tmp = x * ((y / z) + (-1.0d0))
    else if (z <= 4.5d-142) then
        tmp = t_0 * (x / 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 (z <= -1.08e+29) {
		tmp = x * ((y / z) + -1.0);
	} else if (z <= 4.5e-142) {
		tmp = t_0 * (x / z);
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if z <= -1.08e+29:
		tmp = x * ((y / z) + -1.0)
	elif z <= 4.5e-142:
		tmp = t_0 * (x / 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 (z <= -1.08e+29)
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	elseif (z <= 4.5e-142)
		tmp = Float64(t_0 * Float64(x / 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 (z <= -1.08e+29)
		tmp = x * ((y / z) + -1.0);
	elseif (z <= 4.5e-142)
		tmp = t_0 * (x / 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[z, -1.08e+29], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-142], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0800000000000001e29

   1. Initial program 73.9%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+r- 100.0%

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

      4. div-sub 100.0%

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

      5. *-inverses 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -1.0800000000000001e29 < z < 4.50000000000000019e-142

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   if 4.50000000000000019e-142 < 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* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. +-commutative 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-142}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.36 \cdot 10^{+44}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-234}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.0019:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -1.36e+44)
     (- x)
     (if (<= z -8.5e-13)
       t_0
       (if (<= z -4.3e-64)
         (/ x z)
         (if (<= z -1.9e-234)
           t_0
           (if (<= z 0.0019) (/ x z) (if (<= z 3.3e+86) t_0 (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -1.36e+44) {
		tmp = -x;
	} else if (z <= -8.5e-13) {
		tmp = t_0;
	} else if (z <= -4.3e-64) {
		tmp = x / z;
	} else if (z <= -1.9e-234) {
		tmp = t_0;
	} else if (z <= 0.0019) {
		tmp = x / z;
	} else if (z <= 3.3e+86) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y / z)
    if (z <= (-1.36d+44)) then
        tmp = -x
    else if (z <= (-8.5d-13)) then
        tmp = t_0
    else if (z <= (-4.3d-64)) then
        tmp = x / z
    else if (z <= (-1.9d-234)) then
        tmp = t_0
    else if (z <= 0.0019d0) then
        tmp = x / z
    else if (z <= 3.3d+86) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -1.36e+44) {
		tmp = -x;
	} else if (z <= -8.5e-13) {
		tmp = t_0;
	} else if (z <= -4.3e-64) {
		tmp = x / z;
	} else if (z <= -1.9e-234) {
		tmp = t_0;
	} else if (z <= 0.0019) {
		tmp = x / z;
	} else if (z <= 3.3e+86) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -1.36e+44:
		tmp = -x
	elif z <= -8.5e-13:
		tmp = t_0
	elif z <= -4.3e-64:
		tmp = x / z
	elif z <= -1.9e-234:
		tmp = t_0
	elif z <= 0.0019:
		tmp = x / z
	elif z <= 3.3e+86:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -1.36e+44)
		tmp = Float64(-x);
	elseif (z <= -8.5e-13)
		tmp = t_0;
	elseif (z <= -4.3e-64)
		tmp = Float64(x / z);
	elseif (z <= -1.9e-234)
		tmp = t_0;
	elseif (z <= 0.0019)
		tmp = Float64(x / z);
	elseif (z <= 3.3e+86)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (z <= -1.36e+44)
		tmp = -x;
	elseif (z <= -8.5e-13)
		tmp = t_0;
	elseif (z <= -4.3e-64)
		tmp = x / z;
	elseif (z <= -1.9e-234)
		tmp = t_0;
	elseif (z <= 0.0019)
		tmp = x / z;
	elseif (z <= 3.3e+86)
		tmp = t_0;
	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, -1.36e+44], (-x), If[LessEqual[z, -8.5e-13], t$95$0, If[LessEqual[z, -4.3e-64], N[(x / z), $MachinePrecision], If[LessEqual[z, -1.9e-234], t$95$0, If[LessEqual[z, 0.0019], N[(x / z), $MachinePrecision], If[LessEqual[z, 3.3e+86], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.36000000000000005e44 or 3.2999999999999999e86 < z

   1. Initial program 68.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 100.0%

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

      5. *-inverses 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. neg-mul-1 81.0%

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

   7. Simplified 81.0%

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

   if -1.36000000000000005e44 < z < -8.5000000000000001e-13 or -4.29999999999999973e-64 < z < -1.89999999999999992e-234 or 0.0019 < z < 3.2999999999999999e86

   1. Initial program 96.2%

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

      1. associate-/l* 95.9%

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

      2. +-commutative 95.9%

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

      3. associate-+r- 95.9%

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

      4. div-sub 95.9%

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

      5. *-inverses 95.9%

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

      6. sub-neg 95.9%

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

      7. metadata-eval 95.9%

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

      8. +-commutative 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 66.9%

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

   7. Simplified 66.9%

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

   if -8.5000000000000001e-13 < z < -4.29999999999999973e-64 or -1.89999999999999992e-234 < z < 0.0019

   1. Initial program 99.9%

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

      1. associate-/l* 89.1%

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

      2. +-commutative 89.1%

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

      3. associate-+r- 89.1%

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

      4. div-sub 89.1%

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

      5. *-inverses 89.1%

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

      6. sub-neg 89.1%

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

      7. metadata-eval 89.1%

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

      8. +-commutative 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in y around 0 68.6%

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

      1. sub-neg 68.6%

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

      2. metadata-eval 68.6%

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

      3. distribute-rgt-in 68.6%

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

      4. associate-*l/ 68.8%

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

      5. *-lft-identity 68.8%

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

      6. neg-mul-1 68.8%

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

      7. unsub-neg 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in z around 0 67.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+44}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 0.0019:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+43}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.0019:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+86}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -6.2e+43)
     (- x)
     (if (<= z -6.2e-13)
       t_0
       (if (<= z -3.5e-66)
         (/ x z)
         (if (<= z 1.18e-135)
           (* y (/ x z))
           (if (<= z 0.0019) (/ x z) (if (<= z 2.45e+86) t_0 (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -6.2e+43) {
		tmp = -x;
	} else if (z <= -6.2e-13) {
		tmp = t_0;
	} else if (z <= -3.5e-66) {
		tmp = x / z;
	} else if (z <= 1.18e-135) {
		tmp = y * (x / z);
	} else if (z <= 0.0019) {
		tmp = x / z;
	} else if (z <= 2.45e+86) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y / z)
    if (z <= (-6.2d+43)) then
        tmp = -x
    else if (z <= (-6.2d-13)) then
        tmp = t_0
    else if (z <= (-3.5d-66)) then
        tmp = x / z
    else if (z <= 1.18d-135) then
        tmp = y * (x / z)
    else if (z <= 0.0019d0) then
        tmp = x / z
    else if (z <= 2.45d+86) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -6.2e+43) {
		tmp = -x;
	} else if (z <= -6.2e-13) {
		tmp = t_0;
	} else if (z <= -3.5e-66) {
		tmp = x / z;
	} else if (z <= 1.18e-135) {
		tmp = y * (x / z);
	} else if (z <= 0.0019) {
		tmp = x / z;
	} else if (z <= 2.45e+86) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -6.2e+43:
		tmp = -x
	elif z <= -6.2e-13:
		tmp = t_0
	elif z <= -3.5e-66:
		tmp = x / z
	elif z <= 1.18e-135:
		tmp = y * (x / z)
	elif z <= 0.0019:
		tmp = x / z
	elif z <= 2.45e+86:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -6.2e+43)
		tmp = Float64(-x);
	elseif (z <= -6.2e-13)
		tmp = t_0;
	elseif (z <= -3.5e-66)
		tmp = Float64(x / z);
	elseif (z <= 1.18e-135)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 0.0019)
		tmp = Float64(x / z);
	elseif (z <= 2.45e+86)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (z <= -6.2e+43)
		tmp = -x;
	elseif (z <= -6.2e-13)
		tmp = t_0;
	elseif (z <= -3.5e-66)
		tmp = x / z;
	elseif (z <= 1.18e-135)
		tmp = y * (x / z);
	elseif (z <= 0.0019)
		tmp = x / z;
	elseif (z <= 2.45e+86)
		tmp = t_0;
	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, -6.2e+43], (-x), If[LessEqual[z, -6.2e-13], t$95$0, If[LessEqual[z, -3.5e-66], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.18e-135], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0019], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.45e+86], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2000000000000003e43 or 2.45e86 < z

   1. Initial program 68.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 100.0%

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

      5. *-inverses 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. neg-mul-1 81.0%

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

   7. Simplified 81.0%

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

   if -6.2000000000000003e43 < z < -6.1999999999999998e-13 or 0.0019 < z < 2.45e86

   1. Initial program 90.2%

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

      1. associate-/l* 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-+r- 99.4%

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

      4. div-sub 99.4%

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

      5. *-inverses 99.4%

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

      6. sub-neg 99.4%

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

      7. metadata-eval 99.4%

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

      8. +-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 60.5%

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

      1. associate-/l* 69.8%

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

   7. Simplified 69.8%

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

   if -6.1999999999999998e-13 < z < -3.5e-66 or 1.18000000000000003e-135 < z < 0.0019

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+r- 99.7%

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

      4. div-sub 99.6%

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

      5. *-inverses 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

      8. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 88.4%

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

      1. sub-neg 88.4%

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

      2. metadata-eval 88.4%

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

      3. distribute-rgt-in 88.5%

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

      4. associate-*l/ 88.8%

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

      5. *-lft-identity 88.8%

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

      6. neg-mul-1 88.8%

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

      7. unsub-neg 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in z around 0 85.8%

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

   if -3.5e-66 < z < 1.18000000000000003e-135

   1. Initial program 99.8%

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

      1. clear-num 87.6%

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

      2. un-div-inv 87.7%

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

      3. +-commutative 87.7%

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

   6. Applied egg-rr 87.7%

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

   7. Taylor expanded in y around inf 56.7%

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

      1. associate-/r/ 69.8%

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

   9. Applied egg-rr 69.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+43}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.0019:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-17} \lor \neg \left(z \leq 3.6 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y + 1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.6e-17) (not (<= z 3.6e-84)))
   (* x (+ -1.0 (/ (+ y 1.0) z)))
   (* (/ x z) (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.6e-17) || !(z <= 3.6e-84)) {
		tmp = x * (-1.0 + ((y + 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 <= (-8.6d-17)) .or. (.not. (z <= 3.6d-84))) then
        tmp = x * ((-1.0d0) + ((y + 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 <= -8.6e-17) || !(z <= 3.6e-84)) {
		tmp = x * (-1.0 + ((y + 1.0) / z));
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.6e-17) or not (z <= 3.6e-84):
		tmp = x * (-1.0 + ((y + 1.0) / z))
	else:
		tmp = (x / z) * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.6e-17) || !(z <= 3.6e-84))
		tmp = Float64(x * Float64(-1.0 + Float64(Float64(y + 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 <= -8.6e-17) || ~((z <= 3.6e-84)))
		tmp = x * (-1.0 + ((y + 1.0) / z));
	else
		tmp = (x / z) * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.6e-17], N[Not[LessEqual[z, 3.6e-84]], $MachinePrecision]], N[(x * N[(-1.0 + N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000046e-17 or 3.60000000000000003e-84 < z

   1. Initial program 77.1%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   if -8.60000000000000046e-17 < z < 3.60000000000000003e-84

   1. Initial program 99.8%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

      1. clear-num 89.3%

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

      2. un-div-inv 89.4%

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

      3. +-commutative 89.4%

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

   6. Applied egg-rr 89.4%

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

   7. Taylor expanded in z around 0 89.4%

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

   8. Taylor expanded in x around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-17} \lor \neg \left(z \leq 3.6 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y + 1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+30} \lor \neg \left(z \leq 8.8 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e+30) (not (<= z 8.8e+15)))
   (* x (+ (/ y z) -1.0))
   (* (+ (- y z) 1.0) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+30) || !(z <= 8.8e+15)) {
		tmp = x * ((y / z) + -1.0);
	} 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 <= (-2d+30)) .or. (.not. (z <= 8.8d+15))) then
        tmp = x * ((y / z) + (-1.0d0))
    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 <= -2e+30) || !(z <= 8.8e+15)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = ((y - z) + 1.0) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e+30) or not (z <= 8.8e+15):
		tmp = x * ((y / z) + -1.0)
	else:
		tmp = ((y - z) + 1.0) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e+30) || !(z <= 8.8e+15))
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	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 <= -2e+30) || ~((z <= 8.8e+15)))
		tmp = x * ((y / z) + -1.0);
	else
		tmp = ((y - z) + 1.0) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e+30], N[Not[LessEqual[z, 8.8e+15]], $MachinePrecision]], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $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 < -2e30 or 8.8e15 < z

   1. Initial program 70.7%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.9%

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

   if -2e30 < z < 8.8e15

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+30} \lor \neg \left(z \leq 8.8 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90 \lor \neg \left(y \leq 2.45 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -90.0) (not (<= y 2.45e-14)))
   (* x (+ (/ y z) -1.0))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -90.0) || !(y <= 2.45e-14)) {
		tmp = x * ((y / z) + -1.0);
	} 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 <= (-90.0d0)) .or. (.not. (y <= 2.45d-14))) then
        tmp = x * ((y / z) + (-1.0d0))
    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 <= -90.0) || !(y <= 2.45e-14)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -90.0) or not (y <= 2.45e-14):
		tmp = x * ((y / z) + -1.0)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -90.0) || !(y <= 2.45e-14))
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -90.0) || ~((y <= 2.45e-14)))
		tmp = x * ((y / z) + -1.0);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -90.0], N[Not[LessEqual[y, 2.45e-14]], $MachinePrecision]], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -90 or 2.44999999999999997e-14 < y

   1. Initial program 89.8%

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

      1. associate-/l* 91.2%

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

      2. +-commutative 91.2%

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

      3. associate-+r- 91.2%

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

      4. div-sub 91.2%

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

      5. *-inverses 91.2%

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

      6. sub-neg 91.2%

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

      7. metadata-eval 91.2%

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

      8. +-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around inf 91.1%

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

   if -90 < y < 2.44999999999999997e-14

   1. Initial program 84.5%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. distribute-rgt-in 99.8%

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

      4. associate-*l/ 100.0%

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

      5. *-lft-identity 100.0%

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

      6. neg-mul-1 100.0%

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

      7. unsub-neg 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90 \lor \neg \left(y \leq 2.45 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00025 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.00025) (not (<= z 1.0)))
   (* x (+ (/ y z) -1.0))
   (* (/ x z) (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.00025) || !(z <= 1.0)) {
		tmp = x * ((y / z) + -1.0);
	} 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 <= (-0.00025d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y / z) + (-1.0d0))
    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 <= -0.00025) || !(z <= 1.0)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x / z) * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.00025) or not (z <= 1.0):
		tmp = x * ((y / z) + -1.0)
	else:
		tmp = (x / z) * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.00025) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	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 <= -0.00025) || ~((z <= 1.0)))
		tmp = x * ((y / z) + -1.0);
	else
		tmp = (x / z) * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.00025], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000001e-4 or 1 < z

   1. Initial program 73.8%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.8%

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

   if -2.5000000000000001e-4 < 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* 90.7%

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

   3. Simplified 90.7%

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

      1. clear-num 90.7%

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

      2. un-div-inv 90.8%

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

      3. +-commutative 90.8%

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

   6. Applied egg-rr 90.8%

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

   7. Taylor expanded in z around 0 90.1%

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

   8. Taylor expanded in x around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-*l/ 99.1%

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

   10. Simplified 99.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00025 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 23000000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+20)
   (* y (/ x z))
   (if (<= y 23000000000000.0) (- (/ x z) x) (* x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+20) {
		tmp = y * (x / z);
	} else if (y <= 23000000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.8d+20)) then
        tmp = y * (x / z)
    else if (y <= 23000000000000.0d0) then
        tmp = (x / z) - x
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+20) {
		tmp = y * (x / z);
	} else if (y <= 23000000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+20:
		tmp = y * (x / z)
	elif y <= 23000000000000.0:
		tmp = (x / z) - x
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+20)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 23000000000000.0)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e+20)
		tmp = y * (x / z);
	elseif (y <= 23000000000000.0)
		tmp = (x / z) - x;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+20], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 23000000000000.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8e20

   1. Initial program 88.6%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.3%

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

      3. +-commutative 85.3%

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

   6. Applied egg-rr 85.3%

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

   7. Taylor expanded in y around inf 70.2%

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

      1. associate-/r/ 81.8%

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

   9. Applied egg-rr 81.8%

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

   if -5.8e20 < y < 2.3e13

   1. Initial program 85.3%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.0%

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

      1. sub-neg 99.0%

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

      2. metadata-eval 99.0%

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

      3. distribute-rgt-in 99.0%

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

      4. associate-*l/ 99.2%

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

      5. *-lft-identity 99.2%

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

      6. neg-mul-1 99.2%

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

      7. unsub-neg 99.2%

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

   7. Simplified 99.2%

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

   if 2.3e13 < y

   1. Initial program 90.0%

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

      1. associate-/l* 94.9%

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

      2. +-commutative 94.9%

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

      3. associate-+r- 94.9%

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

      4. div-sub 94.9%

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

      5. *-inverses 94.9%

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

      6. sub-neg 94.9%

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

      7. metadata-eval 94.9%

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

      8. +-commutative 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. associate-/l* 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 23000000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 13000000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e+26)
   (* y (/ x z))
   (if (<= y 13000000000000.0) (- (/ x z) x) (/ (* x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e+26) {
		tmp = y * (x / z);
	} else if (y <= 13000000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.8d+26)) then
        tmp = y * (x / z)
    else if (y <= 13000000000000.0d0) then
        tmp = (x / z) - x
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e+26) {
		tmp = y * (x / z);
	} else if (y <= 13000000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e+26:
		tmp = y * (x / z)
	elif y <= 13000000000000.0:
		tmp = (x / z) - x
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e+26)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 13000000000000.0)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.8e+26)
		tmp = y * (x / z);
	elseif (y <= 13000000000000.0)
		tmp = (x / z) - x;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e+26], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 13000000000000.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000009e26

   1. Initial program 88.6%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.3%

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

      3. +-commutative 85.3%

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

   6. Applied egg-rr 85.3%

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

   7. Taylor expanded in y around inf 70.2%

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

      1. associate-/r/ 81.8%

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

   9. Applied egg-rr 81.8%

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

   if -4.80000000000000009e26 < y < 1.3e13

   1. Initial program 85.3%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.0%

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

      1. sub-neg 99.0%

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

      2. metadata-eval 99.0%

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

      3. distribute-rgt-in 99.0%

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

      4. associate-*l/ 99.2%

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

      5. *-lft-identity 99.2%

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

      6. neg-mul-1 99.2%

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

      7. unsub-neg 99.2%

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

   7. Simplified 99.2%

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

   if 1.3e13 < y

   1. Initial program 90.0%

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

      1. associate-/l* 94.9%

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

      2. +-commutative 94.9%

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

      3. associate-+r- 94.9%

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

      4. div-sub 94.9%

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

      5. *-inverses 94.9%

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

      6. sub-neg 94.9%

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

      7. metadata-eval 94.9%

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

      8. +-commutative 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf 76.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 13000000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;x \leq 1.55 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= x 1.55e-54) (/ (* 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 <= 1.55e-54) {
		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 <= 1.55d-54) 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 <= 1.55e-54) {
		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 <= 1.55e-54:
		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 <= 1.55e-54)
		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 <= 1.55e-54)
		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, 1.55e-54], 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 < 1.55000000000000002e-54

   1. Initial program 91.5%

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

   if 1.55000000000000002e-54 < x

   1. Initial program 78.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

      3. +-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2000\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 2000.0))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 2000.0)) {
		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 <= 2000.0d0))) 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 <= 2000.0)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 2000.0):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 2000.0))
		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 <= 2000.0)))
		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, 2000.0]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2e3 < z

   1. Initial program 73.4%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 69.7%

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

      1. neg-mul-1 69.7%

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

   7. Simplified 69.7%

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

   if -1 < z < 2e3

   1. Initial program 99.8%

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

      1. associate-/l* 90.9%

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

      2. +-commutative 90.9%

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

      3. associate-+r- 90.9%

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

      4. div-sub 90.9%

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

      5. *-inverses 90.9%

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

      6. sub-neg 90.9%

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

      7. metadata-eval 90.9%

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

      8. +-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 57.1%

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

      1. sub-neg 57.1%

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

      2. metadata-eval 57.1%

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

      3. distribute-rgt-in 57.2%

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

      4. associate-*l/ 57.3%

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

      5. *-lft-identity 57.3%

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

      6. neg-mul-1 57.3%

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

      7. unsub-neg 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in z around 0 56.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2000\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.4% 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 87.4%

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

   1. associate-/l* 95.1%

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

   2. +-commutative 95.1%

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

   3. associate-+r- 95.1%

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

   4. div-sub 95.1%

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

   5. *-inverses 95.1%

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

   6. sub-neg 95.1%

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

   7. metadata-eval 95.1%

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

   8. +-commutative 95.1%

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

3. Simplified 95.1%

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

5. Taylor expanded in z around inf 34.3%

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

   1. neg-mul-1 34.3%

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

7. Simplified 34.3%

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

8. Final simplification 34.3%

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

Alternative 13: 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 87.4%

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

   1. *-commutative 87.4%

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

   2. associate-/l* 89.7%

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

   3. +-commutative 89.7%

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

4. Applied egg-rr 89.7%

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

   1. associate-*r/ 87.4%

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

   2. clear-num 87.3%

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

   3. *-commutative 87.3%

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

   4. +-commutative 87.3%

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

   5. associate-+l- 87.3%

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

6. Applied egg-rr 87.3%

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

7. Taylor expanded in z around inf 34.3%

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

   1. frac-2neg 34.3%

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

   2. metadata-eval 34.3%

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

   3. remove-double-div 34.3%

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

   4. neg-sub0 34.3%

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

   5. sub-neg 34.3%

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

   6. add-sqr-sqrt 16.2%

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

   7. sqrt-unprod 18.0%

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

   8. sqr-neg 18.0%

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

   9. sqrt-unprod 1.4%

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

   10. add-sqr-sqrt 3.1%

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

9. Applied egg-rr 3.1%

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

    1. +-lft-identity 3.1%

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

11. Simplified 3.1%

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

12. Final simplification 3.1%

    \[\leadsto x \]
13. 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 2024077 
(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))