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

Percentage Accurate: 88.3% → 99.4%

Time: 14.8s

Alternatives: 12

Speedup: 0.6×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.3% 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: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{elif}\;z \leq 10^{-104}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - \left(z + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y + 1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+21)
   (* x (+ (/ y z) -1.0))
   (if (<= z 1e-104)
     (* (/ x z) (- y (+ z -1.0)))
     (* x (+ -1.0 (/ (+ y 1.0) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+21) {
		tmp = x * ((y / z) + -1.0);
	} else if (z <= 1e-104) {
		tmp = (x / z) * (y - (z + -1.0));
	} else {
		tmp = x * (-1.0 + ((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 <= (-2d+21)) then
        tmp = x * ((y / z) + (-1.0d0))
    else if (z <= 1d-104) then
        tmp = (x / z) * (y - (z + (-1.0d0)))
    else
        tmp = x * ((-1.0d0) + ((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 <= -2e+21) {
		tmp = x * ((y / z) + -1.0);
	} else if (z <= 1e-104) {
		tmp = (x / z) * (y - (z + -1.0));
	} else {
		tmp = x * (-1.0 + ((y + 1.0) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+21:
		tmp = x * ((y / z) + -1.0)
	elif z <= 1e-104:
		tmp = (x / z) * (y - (z + -1.0))
	else:
		tmp = x * (-1.0 + ((y + 1.0) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+21)
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	elseif (z <= 1e-104)
		tmp = Float64(Float64(x / z) * Float64(y - Float64(z + -1.0)));
	else
		tmp = Float64(x * Float64(-1.0 + Float64(Float64(y + 1.0) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e+21)
		tmp = x * ((y / z) + -1.0);
	elseif (z <= 1e-104)
		tmp = (x / z) * (y - (z + -1.0));
	else
		tmp = x * (-1.0 + ((y + 1.0) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+21], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-104], N[(N[(x / z), $MachinePrecision] * N[(y - N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-1.0 + N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e21

   1. Initial program 85.8%

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

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

   if -2e21 < z < 9.99999999999999927e-105

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*l/ 99.9%

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

      4. associate-+l- 99.9%

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

   5. Simplified 99.9%

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

   if 9.99999999999999927e-105 < z

   1. Initial program 83.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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 99.9%

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

      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
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{elif}\;z \leq 10^{-104}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - \left(z + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y + 1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -160000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-141}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-252}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))) (t_1 (* x (/ y z))))
   (if (<= z -160000000.0)
     (- x)
     (if (<= z -1.1e-10)
       t_1
       (if (<= z -1.16e-39)
         (/ x z)
         (if (<= z -2.1e-141)
           t_0
           (if (<= z -8.8e-179)
             (/ x z)
             (if (<= z -3.3e-252)
               t_0
               (if (<= z 1.02e-305)
                 (/ x z)
                 (if (<= z 1.5e-102)
                   t_0
                   (if (<= z 1.05e-31)
                     (/ x z)
                     (if (<= z 6e+24) t_1 (- x)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -160000000.0) {
		tmp = -x;
	} else if (z <= -1.1e-10) {
		tmp = t_1;
	} else if (z <= -1.16e-39) {
		tmp = x / z;
	} else if (z <= -2.1e-141) {
		tmp = t_0;
	} else if (z <= -8.8e-179) {
		tmp = x / z;
	} else if (z <= -3.3e-252) {
		tmp = t_0;
	} else if (z <= 1.02e-305) {
		tmp = x / z;
	} else if (z <= 1.5e-102) {
		tmp = t_0;
	} else if (z <= 1.05e-31) {
		tmp = x / z;
	} else if (z <= 6e+24) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = y * (x / z)
    t_1 = x * (y / z)
    if (z <= (-160000000.0d0)) then
        tmp = -x
    else if (z <= (-1.1d-10)) then
        tmp = t_1
    else if (z <= (-1.16d-39)) then
        tmp = x / z
    else if (z <= (-2.1d-141)) then
        tmp = t_0
    else if (z <= (-8.8d-179)) then
        tmp = x / z
    else if (z <= (-3.3d-252)) then
        tmp = t_0
    else if (z <= 1.02d-305) then
        tmp = x / z
    else if (z <= 1.5d-102) then
        tmp = t_0
    else if (z <= 1.05d-31) then
        tmp = x / z
    else if (z <= 6d+24) then
        tmp = t_1
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -160000000.0) {
		tmp = -x;
	} else if (z <= -1.1e-10) {
		tmp = t_1;
	} else if (z <= -1.16e-39) {
		tmp = x / z;
	} else if (z <= -2.1e-141) {
		tmp = t_0;
	} else if (z <= -8.8e-179) {
		tmp = x / z;
	} else if (z <= -3.3e-252) {
		tmp = t_0;
	} else if (z <= 1.02e-305) {
		tmp = x / z;
	} else if (z <= 1.5e-102) {
		tmp = t_0;
	} else if (z <= 1.05e-31) {
		tmp = x / z;
	} else if (z <= 6e+24) {
		tmp = t_1;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	t_1 = x * (y / z)
	tmp = 0
	if z <= -160000000.0:
		tmp = -x
	elif z <= -1.1e-10:
		tmp = t_1
	elif z <= -1.16e-39:
		tmp = x / z
	elif z <= -2.1e-141:
		tmp = t_0
	elif z <= -8.8e-179:
		tmp = x / z
	elif z <= -3.3e-252:
		tmp = t_0
	elif z <= 1.02e-305:
		tmp = x / z
	elif z <= 1.5e-102:
		tmp = t_0
	elif z <= 1.05e-31:
		tmp = x / z
	elif z <= 6e+24:
		tmp = t_1
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -160000000.0)
		tmp = Float64(-x);
	elseif (z <= -1.1e-10)
		tmp = t_1;
	elseif (z <= -1.16e-39)
		tmp = Float64(x / z);
	elseif (z <= -2.1e-141)
		tmp = t_0;
	elseif (z <= -8.8e-179)
		tmp = Float64(x / z);
	elseif (z <= -3.3e-252)
		tmp = t_0;
	elseif (z <= 1.02e-305)
		tmp = Float64(x / z);
	elseif (z <= 1.5e-102)
		tmp = t_0;
	elseif (z <= 1.05e-31)
		tmp = Float64(x / z);
	elseif (z <= 6e+24)
		tmp = t_1;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	t_1 = x * (y / z);
	tmp = 0.0;
	if (z <= -160000000.0)
		tmp = -x;
	elseif (z <= -1.1e-10)
		tmp = t_1;
	elseif (z <= -1.16e-39)
		tmp = x / z;
	elseif (z <= -2.1e-141)
		tmp = t_0;
	elseif (z <= -8.8e-179)
		tmp = x / z;
	elseif (z <= -3.3e-252)
		tmp = t_0;
	elseif (z <= 1.02e-305)
		tmp = x / z;
	elseif (z <= 1.5e-102)
		tmp = t_0;
	elseif (z <= 1.05e-31)
		tmp = x / z;
	elseif (z <= 6e+24)
		tmp = t_1;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -160000000.0], (-x), If[LessEqual[z, -1.1e-10], t$95$1, If[LessEqual[z, -1.16e-39], N[(x / z), $MachinePrecision], If[LessEqual[z, -2.1e-141], t$95$0, If[LessEqual[z, -8.8e-179], N[(x / z), $MachinePrecision], If[LessEqual[z, -3.3e-252], t$95$0, If[LessEqual[z, 1.02e-305], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.5e-102], t$95$0, If[LessEqual[z, 1.05e-31], N[(x / z), $MachinePrecision], If[LessEqual[z, 6e+24], t$95$1, (-x)]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6e8 or 5.9999999999999999e24 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. neg-mul-1 78.7%

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

   5. Simplified 78.7%

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

   if -1.6e8 < z < -1.09999999999999995e-10 or 1.04999999999999996e-31 < z < 5.9999999999999999e24

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf 61.6%

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

      1. associate-/l* 65.4%

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

   5. Simplified 65.4%

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

   if -1.09999999999999995e-10 < z < -1.16e-39 or -2.0999999999999999e-141 < z < -8.80000000000000018e-179 or -3.30000000000000009e-252 < z < 1.01999999999999994e-305 or 1.5e-102 < z < 1.04999999999999996e-31

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 86.8%

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

   4. Taylor expanded in z around 0 85.7%

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

   if -1.16e-39 < z < -2.0999999999999999e-141 or -8.80000000000000018e-179 < z < -3.30000000000000009e-252 or 1.01999999999999994e-305 < z < 1.5e-102

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-/l* 74.2%

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

   5. Applied egg-rr 74.2%

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

Alternative 3: 63.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -160000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-134}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-245}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -160000000.0)
     (- x)
     (if (<= z -1.15e-10)
       t_0
       (if (<= z -8.8e-41)
         (/ x z)
         (if (<= z -5e-134)
           t_0
           (if (<= z -1.16e-208)
             (/ x z)
             (if (<= z -1.2e-245) t_0 (if (<= z 5.1e-8) (/ x z) (- x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -160000000.0) {
		tmp = -x;
	} else if (z <= -1.15e-10) {
		tmp = t_0;
	} else if (z <= -8.8e-41) {
		tmp = x / z;
	} else if (z <= -5e-134) {
		tmp = t_0;
	} else if (z <= -1.16e-208) {
		tmp = x / z;
	} else if (z <= -1.2e-245) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		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 <= (-160000000.0d0)) then
        tmp = -x
    else if (z <= (-1.15d-10)) then
        tmp = t_0
    else if (z <= (-8.8d-41)) then
        tmp = x / z
    else if (z <= (-5d-134)) then
        tmp = t_0
    else if (z <= (-1.16d-208)) then
        tmp = x / z
    else if (z <= (-1.2d-245)) then
        tmp = t_0
    else if (z <= 5.1d-8) 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 <= -160000000.0) {
		tmp = -x;
	} else if (z <= -1.15e-10) {
		tmp = t_0;
	} else if (z <= -8.8e-41) {
		tmp = x / z;
	} else if (z <= -5e-134) {
		tmp = t_0;
	} else if (z <= -1.16e-208) {
		tmp = x / z;
	} else if (z <= -1.2e-245) {
		tmp = t_0;
	} else if (z <= 5.1e-8) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -160000000.0:
		tmp = -x
	elif z <= -1.15e-10:
		tmp = t_0
	elif z <= -8.8e-41:
		tmp = x / z
	elif z <= -5e-134:
		tmp = t_0
	elif z <= -1.16e-208:
		tmp = x / z
	elif z <= -1.2e-245:
		tmp = t_0
	elif z <= 5.1e-8:
		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 <= -160000000.0)
		tmp = Float64(-x);
	elseif (z <= -1.15e-10)
		tmp = t_0;
	elseif (z <= -8.8e-41)
		tmp = Float64(x / z);
	elseif (z <= -5e-134)
		tmp = t_0;
	elseif (z <= -1.16e-208)
		tmp = Float64(x / z);
	elseif (z <= -1.2e-245)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		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 <= -160000000.0)
		tmp = -x;
	elseif (z <= -1.15e-10)
		tmp = t_0;
	elseif (z <= -8.8e-41)
		tmp = x / z;
	elseif (z <= -5e-134)
		tmp = t_0;
	elseif (z <= -1.16e-208)
		tmp = x / z;
	elseif (z <= -1.2e-245)
		tmp = t_0;
	elseif (z <= 5.1e-8)
		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, -160000000.0], (-x), If[LessEqual[z, -1.15e-10], t$95$0, If[LessEqual[z, -8.8e-41], N[(x / z), $MachinePrecision], If[LessEqual[z, -5e-134], t$95$0, If[LessEqual[z, -1.16e-208], N[(x / z), $MachinePrecision], If[LessEqual[z, -1.2e-245], t$95$0, If[LessEqual[z, 5.1e-8], N[(x / z), $MachinePrecision], (-x)]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e8 or 5.10000000000000001e-8 < z

   1. Initial program 81.8%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. neg-mul-1 74.9%

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

   5. Simplified 74.9%

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

   if -1.6e8 < z < -1.15000000000000004e-10 or -8.7999999999999999e-41 < z < -5.0000000000000003e-134 or -1.1600000000000001e-208 < z < -1.2e-245

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 80.4%

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

      1. associate-/l* 73.9%

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

   5. Simplified 73.9%

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

   if -1.15000000000000004e-10 < z < -8.7999999999999999e-41 or -5.0000000000000003e-134 < z < -1.1600000000000001e-208 or -1.2e-245 < z < 5.10000000000000001e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 62.4%

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

   4. Taylor expanded in z around 0 61.5%

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

Alternative 4: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{if}\;y \leq -3.1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+192}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (/ y z) -1.0))))
   (if (<= y -3.1)
     t_0
     (if (<= y 1.0) (- (/ x z) x) (if (<= y 8.8e+192) t_0 (* y (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((y / z) + -1.0);
	double tmp;
	if (y <= -3.1) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else if (y <= 8.8e+192) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * ((y / z) + (-1.0d0))
    if (y <= (-3.1d0)) then
        tmp = t_0
    else if (y <= 1.0d0) then
        tmp = (x / z) - x
    else if (y <= 8.8d+192) then
        tmp = t_0
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * ((y / z) + -1.0);
	double tmp;
	if (y <= -3.1) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else if (y <= 8.8e+192) {
		tmp = t_0;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((y / z) + -1.0)
	tmp = 0
	if y <= -3.1:
		tmp = t_0
	elif y <= 1.0:
		tmp = (x / z) - x
	elif y <= 8.8e+192:
		tmp = t_0
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(y / z) + -1.0))
	tmp = 0.0
	if (y <= -3.1)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = Float64(Float64(x / z) - x);
	elseif (y <= 8.8e+192)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((y / z) + -1.0);
	tmp = 0.0;
	if (y <= -3.1)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = (x / z) - x;
	elseif (y <= 8.8e+192)
		tmp = t_0;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1], t$95$0, If[LessEqual[y, 1.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 8.8e+192], t$95$0, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.10000000000000009 or 1 < y < 8.8000000000000003e192

   1. Initial program 86.7%

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

      1. associate-/l* 93.1%

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

      2. +-commutative 93.1%

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

      3. associate-+r- 93.1%

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

      4. div-sub 93.1%

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

      5. *-inverses 93.1%

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

      6. sub-neg 93.1%

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

      7. metadata-eval 93.1%

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

      8. +-commutative 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around inf 91.9%

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

   if -3.10000000000000009 < y < 1

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0 92.3%

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

      1. associate-/l* 97.4%

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

      2. div-sub 97.4%

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

      3. sub-neg 97.4%

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

      4. *-inverses 97.4%

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

      5. metadata-eval 97.4%

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

      6. distribute-rgt-in 97.4%

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

      7. associate-*l/ 97.6%

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

      8. *-lft-identity 97.6%

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

      9. neg-mul-1 97.6%

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

      10. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   if 8.8000000000000003e192 < y

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 92.2%

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

   5. Applied egg-rr 92.2%

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

Alternative 5: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-16} \lor \neg \left(z \leq 2 \cdot 10^{-105}\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y + 1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.15e-16) (not (<= z 2e-105)))
   (* 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 <= -1.15e-16) || !(z <= 2e-105)) {
		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 <= (-1.15d-16)) .or. (.not. (z <= 2d-105))) 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 <= -1.15e-16) || !(z <= 2e-105)) {
		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 <= -1.15e-16) or not (z <= 2e-105):
		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 <= -1.15e-16) || !(z <= 2e-105))
		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 <= -1.15e-16) || ~((z <= 2e-105)))
		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, -1.15e-16], N[Not[LessEqual[z, 2e-105]], $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 < -1.15e-16 or 1.99999999999999993e-105 < z

   1. Initial program 85.5%

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

   if -1.15e-16 < z < 1.99999999999999993e-105

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. associate-/l* 87.2%

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

      2. +-commutative 87.2%

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

      3. *-lft-identity 87.2%

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

      4. associate-*l/ 87.3%

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

      5. associate-*r* 99.7%

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

      6. *-commutative 99.7%

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

      7. associate-*l/ 99.9%

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

      8. *-lft-identity 99.9%

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

      9. +-commutative 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-16} \lor \neg \left(z \leq 2 \cdot 10^{-105}\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y + 1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -35 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -35.0) (not (<= z 5.1e-8)))
   (* x (+ (/ y z) -1.0))
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -35.0) || !(z <= 5.1e-8)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-35.0d0)) .or. (.not. (z <= 5.1d-8))) then
        tmp = x * ((y / z) + (-1.0d0))
    else
        tmp = (x + (x * y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -35.0) || !(z <= 5.1e-8)) {
		tmp = x * ((y / z) + -1.0);
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -35.0) or not (z <= 5.1e-8):
		tmp = x * ((y / z) + -1.0)
	else:
		tmp = (x + (x * y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -35.0) || !(z <= 5.1e-8))
		tmp = Float64(x * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -35.0) || ~((z <= 5.1e-8)))
		tmp = x * ((y / z) + -1.0);
	else
		tmp = (x + (x * y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -35.0], N[Not[LessEqual[z, 5.1e-8]], $MachinePrecision]], N[(x * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -35 or 5.10000000000000001e-8 < z

   1. Initial program 82.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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 99.9%

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

      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 97.8%

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

   if -35 < z < 5.10000000000000001e-8

   1. Initial program 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. *-rgt-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf 98.5%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -35 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -230 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -230.0) (not (<= z 5.1e-8)))
   (* x (+ (/ y z) -1.0))
   (* (/ x z) (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -230.0) || !(z <= 5.1e-8)) {
		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 <= (-230.0d0)) .or. (.not. (z <= 5.1d-8))) 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 <= -230.0) || !(z <= 5.1e-8)) {
		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 <= -230.0) or not (z <= 5.1e-8):
		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 <= -230.0) || !(z <= 5.1e-8))
		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 <= -230.0) || ~((z <= 5.1e-8)))
		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, -230.0], N[Not[LessEqual[z, 5.1e-8]], $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 < -230 or 5.10000000000000001e-8 < z

   1. Initial program 82.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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 99.9%

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

      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 97.8%

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

   if -230 < z < 5.10000000000000001e-8

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 98.5%

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

      1. associate-/l* 88.5%

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

      2. +-commutative 88.5%

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

      3. *-lft-identity 88.5%

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

      4. associate-*l/ 88.5%

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

      5. associate-*r* 98.4%

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

      6. *-commutative 98.4%

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

      7. associate-*l/ 98.6%

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

      8. *-lft-identity 98.6%

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

      9. +-commutative 98.6%

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

   5. Simplified 98.6%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -230 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \lor \neg \left(y \leq 3.1 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1) (not (<= y 3.1e+100))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1) || !(y <= 3.1e+100)) {
		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 <= (-3.1d0)) .or. (.not. (y <= 3.1d+100))) 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 <= -3.1) || !(y <= 3.1e+100)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1) or not (y <= 3.1e+100):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1) || !(y <= 3.1e+100))
		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 <= -3.1) || ~((y <= 3.1e+100)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1], N[Not[LessEqual[y, 3.1e+100]], $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 < -3.10000000000000009 or 3.10000000000000007e100 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/l* 80.0%

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

   5. Applied egg-rr 80.0%

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

   if -3.10000000000000009 < y < 3.10000000000000007e100

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0 85.7%

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

      1. associate-/l* 93.4%

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

      2. div-sub 93.4%

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

      3. sub-neg 93.4%

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

      4. *-inverses 93.4%

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

      5. metadata-eval 93.4%

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

      6. distribute-rgt-in 93.4%

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

      7. associate-*l/ 93.5%

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

      8. *-lft-identity 93.5%

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

      9. neg-mul-1 93.5%

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

      10. unsub-neg 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \lor \neg \left(y \leq 3.1 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - \left(z + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1e-7) (/ (* x (+ (- y z) 1.0)) z) (* (/ x z) (- y (+ z -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e-7) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (x / z) * (y - (z + -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 (x <= 1d-7) then
        tmp = (x * ((y - z) + 1.0d0)) / z
    else
        tmp = (x / z) * (y - (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e-7) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (x / z) * (y - (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1e-7:
		tmp = (x * ((y - z) + 1.0)) / z
	else:
		tmp = (x / z) * (y - (z + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e-7)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(Float64(x / z) * Float64(y - Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1e-7)
		tmp = (x * ((y - z) + 1.0)) / z;
	else
		tmp = (x / z) * (y - (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e-7], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y - N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.9999999999999995e-8

   1. Initial program 94.7%

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

   if 9.9999999999999995e-8 < x

   1. Initial program 79.8%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. associate--l+ 79.8%

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

      2. +-commutative 79.8%

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

      3. associate-*l/ 99.9%

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

      4. associate-+l- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y - \left(z + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -35 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -35.0) (not (<= z 5.1e-8))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -35.0) || !(z <= 5.1e-8)) {
		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 <= (-35.0d0)) .or. (.not. (z <= 5.1d-8))) 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 <= -35.0) || !(z <= 5.1e-8)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -35.0) or not (z <= 5.1e-8):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -35.0) || !(z <= 5.1e-8))
		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 <= -35.0) || ~((z <= 5.1e-8)))
		tmp = -x;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -35.0], N[Not[LessEqual[z, 5.1e-8]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -35 or 5.10000000000000001e-8 < z

   1. Initial program 82.5%

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

   3. Taylor expanded in z around inf 72.2%

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

      1. neg-mul-1 72.2%

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

   5. Simplified 72.2%

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

   if -35 < z < 5.10000000000000001e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 56.0%

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

   4. Taylor expanded in z around 0 54.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -35 \lor \neg \left(z \leq 5.1 \cdot 10^{-8}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.3% 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 91.5%

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

3. Taylor expanded in z around inf 36.9%

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

   1. neg-mul-1 36.9%

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

5. Simplified 36.9%

   \[\leadsto \color{blue}{-x} \]
6. Add Preprocessing

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 91.5%

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

3. Taylor expanded in z around inf 31.3%

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

   1. associate-*r* 31.3%

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

   2. neg-mul-1 31.3%

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

5. Simplified 31.3%

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

   1. associate-/l* 36.9%

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

   2. *-inverses 36.9%

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

   3. *-commutative 36.9%

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

   4. neg-sub0 36.9%

      \[\leadsto 1 \cdot \color{blue}{\left(0 - x\right)} \]

   5. *-un-lft-identity 36.9%

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

   6. sub-neg 36.9%

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

   7. add-sqr-sqrt 21.1%

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

   8. sqrt-unprod 19.5%

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

   9. sqr-neg 19.5%

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

   10. sqrt-unprod 1.3%

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

   11. add-sqr-sqrt 3.0%

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

7. Applied egg-rr 3.0%

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

   1. +-lft-identity 3.0%

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

9. Simplified 3.0%

   \[\leadsto \color{blue}{x} \]
10. 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 2024111 
(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))