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

Percentage Accurate: 88.1% → 99.9%

Time: 7.9s

Alternatives: 12

Speedup: 0.6×

• 21.7% 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: 88.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-13} \lor \neg \left(z \leq 1.22 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.85e-13) (not (<= z 1.22e-17)))
   (* x (+ (/ (+ y 1.0) z) -1.0))
   (/ (* x (+ y 1.0)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.85e-13) || !(z <= 1.22e-17)) {
		tmp = x * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.85d-13)) .or. (.not. (z <= 1.22d-17))) then
        tmp = x * (((y + 1.0d0) / z) + (-1.0d0))
    else
        tmp = (x * (y + 1.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.85e-13) || !(z <= 1.22e-17)) {
		tmp = x * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.85e-13) or not (z <= 1.22e-17):
		tmp = x * (((y + 1.0) / z) + -1.0)
	else:
		tmp = (x * (y + 1.0)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.85e-13) || !(z <= 1.22e-17))
		tmp = Float64(x * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	else
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.85e-13) || ~((z <= 1.22e-17)))
		tmp = x * (((y + 1.0) / z) + -1.0);
	else
		tmp = (x * (y + 1.0)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.85e-13], N[Not[LessEqual[z, 1.22e-17]], $MachinePrecision]], N[(x * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999994e-13 or 1.22e-17 < z

   1. Initial program 80.9%

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

   3. Taylor expanded in x around 0 80.9%

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

      1. associate--l+ 80.9%

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

      2. +-commutative 80.9%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   if -1.84999999999999994e-13 < z < 1.22e-17

   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%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-13} \lor \neg \left(z \leq 1.22 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4e-49) (/ (fma x (- y z) x) z) (* x (+ (/ (+ y 1.0) z) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e-49) {
		tmp = fma(x, (y - z), x) / z;
	} else {
		tmp = x * (((y + 1.0) / z) + -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4e-49)
		tmp = Float64(fma(x, Float64(y - z), x) / z);
	else
		tmp = Float64(x * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4e-49], N[(N[(x * N[(y - z), $MachinePrecision] + x), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.99999999999999975e-49

   1. Initial program 93.7%

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

      1. distribute-lft-in 93.7%

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

      2. fma-def 93.7%

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

      3. *-rgt-identity 93.7%

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

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}} \]
   4. Add Preprocessing

   if 3.99999999999999975e-49 < x

   1. Initial program 80.8%

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

   3. Taylor expanded in x around 0 80.8%

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

      1. associate--l+ 80.8%

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

      2. +-commutative 80.8%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4400000000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-230}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-117}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -4400000000000.0)
     (- x)
     (if (<= z 9.5e-230)
       t_0
       (if (<= z 3.8e-215)
         (/ x z)
         (if (<= z 2.75e-117)
           t_0
           (if (<= z 2.5e-65) (/ x z) (if (<= z 4.8e+42) t_0 (- x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -4400000000000.0) {
		tmp = -x;
	} else if (z <= 9.5e-230) {
		tmp = t_0;
	} else if (z <= 3.8e-215) {
		tmp = x / z;
	} else if (z <= 2.75e-117) {
		tmp = t_0;
	} else if (z <= 2.5e-65) {
		tmp = x / z;
	} else if (z <= 4.8e+42) {
		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 = y * (x / z)
    if (z <= (-4400000000000.0d0)) then
        tmp = -x
    else if (z <= 9.5d-230) then
        tmp = t_0
    else if (z <= 3.8d-215) then
        tmp = x / z
    else if (z <= 2.75d-117) then
        tmp = t_0
    else if (z <= 2.5d-65) then
        tmp = x / z
    else if (z <= 4.8d+42) 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 = y * (x / z);
	double tmp;
	if (z <= -4400000000000.0) {
		tmp = -x;
	} else if (z <= 9.5e-230) {
		tmp = t_0;
	} else if (z <= 3.8e-215) {
		tmp = x / z;
	} else if (z <= 2.75e-117) {
		tmp = t_0;
	} else if (z <= 2.5e-65) {
		tmp = x / z;
	} else if (z <= 4.8e+42) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -4400000000000.0:
		tmp = -x
	elif z <= 9.5e-230:
		tmp = t_0
	elif z <= 3.8e-215:
		tmp = x / z
	elif z <= 2.75e-117:
		tmp = t_0
	elif z <= 2.5e-65:
		tmp = x / z
	elif z <= 4.8e+42:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -4400000000000.0)
		tmp = Float64(-x);
	elseif (z <= 9.5e-230)
		tmp = t_0;
	elseif (z <= 3.8e-215)
		tmp = Float64(x / z);
	elseif (z <= 2.75e-117)
		tmp = t_0;
	elseif (z <= 2.5e-65)
		tmp = Float64(x / z);
	elseif (z <= 4.8e+42)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -4400000000000.0)
		tmp = -x;
	elseif (z <= 9.5e-230)
		tmp = t_0;
	elseif (z <= 3.8e-215)
		tmp = x / z;
	elseif (z <= 2.75e-117)
		tmp = t_0;
	elseif (z <= 2.5e-65)
		tmp = x / z;
	elseif (z <= 4.8e+42)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4400000000000.0], (-x), If[LessEqual[z, 9.5e-230], t$95$0, If[LessEqual[z, 3.8e-215], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.75e-117], t$95$0, If[LessEqual[z, 2.5e-65], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.8e+42], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4e12 or 4.7999999999999997e42 < z

   1. Initial program 78.4%

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

   3. Taylor expanded in z around inf 80.4%

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

      1. mul-1-neg 80.4%

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

   5. Simplified 80.4%

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

   if -4.4e12 < z < 9.5000000000000004e-230 or 3.79999999999999977e-215 < z < 2.75000000000000013e-117 or 2.49999999999999991e-65 < z < 4.7999999999999997e42

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 64.8%

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

      1. associate-/l* 54.7%

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

      2. associate-/r/ 71.9%

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

   5. Simplified 71.9%

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

   if 9.5000000000000004e-230 < z < 3.79999999999999977e-215 or 2.75000000000000013e-117 < z < 2.49999999999999991e-65

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in y around 0 81.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000000000:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 3.35 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 3.35e-46)))
   (* x (+ -1.0 (/ y z)))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 3.35e-46)) {
		tmp = x * (-1.0 + (y / 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 <= (-1.0d0)) .or. (.not. (y <= 3.35d-46))) then
        tmp = x * ((-1.0d0) + (y / 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 <= -1.0) || !(y <= 3.35e-46)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 3.35e-46):
		tmp = x * (-1.0 + (y / z))
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 3.35e-46))
		tmp = Float64(x * Float64(-1.0 + Float64(y / 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 <= -1.0) || ~((y <= 3.35e-46)))
		tmp = x * (-1.0 + (y / z));
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 3.35e-46]], $MachinePrecision]], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3.35e-46 < y

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0 91.1%

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

      1. associate--l+ 91.1%

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

      2. +-commutative 91.1%

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

      3. associate-*r/ 89.8%

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

      4. +-commutative 89.8%

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

      5. associate--l+ 89.8%

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

      6. div-sub 89.8%

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

      7. sub-neg 89.8%

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

      8. *-inverses 89.8%

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

      9. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in y around inf 88.8%

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

   if -1 < y < 3.35e-46

   1. Initial program 88.8%

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

   3. Taylor expanded in x around 0 88.8%

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

      1. associate--l+ 88.8%

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

      2. +-commutative 88.8%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 99.5%

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

   7. Taylor expanded in z around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. +-commutative 99.5%

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

      3. unsub-neg 99.5%

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

   9. Simplified 99.5%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 3.35 \cdot 10^{-46}\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -22000000000 \lor \neg \left(z \leq 0.007\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + 1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -22000000000.0) (not (<= z 0.007)))
   (* x (+ -1.0 (/ y z)))
   (* x (/ (+ y 1.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -22000000000.0) || !(z <= 0.007)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = x * ((y + 1.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-22000000000.0d0)) .or. (.not. (z <= 0.007d0))) then
        tmp = x * ((-1.0d0) + (y / z))
    else
        tmp = x * ((y + 1.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -22000000000.0) || !(z <= 0.007)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = x * ((y + 1.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -22000000000.0) or not (z <= 0.007):
		tmp = x * (-1.0 + (y / z))
	else:
		tmp = x * ((y + 1.0) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -22000000000.0) || !(z <= 0.007))
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	else
		tmp = Float64(x * Float64(Float64(y + 1.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -22000000000.0) || ~((z <= 0.007)))
		tmp = x * (-1.0 + (y / z));
	else
		tmp = x * ((y + 1.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -22000000000.0], N[Not[LessEqual[z, 0.007]], $MachinePrecision]], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e10 or 0.00700000000000000015 < z

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. associate--l+ 80.1%

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

      2. +-commutative 80.1%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.2%

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

   if -2.2e10 < z < 0.00700000000000000015

   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 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l/ 89.1%

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

   5. Applied egg-rr 89.1%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22000000000 \lor \neg \left(z \leq 0.007\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + 1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -22000000000 \lor \neg \left(z \leq 0.007\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -22000000000.0) (not (<= z 0.007)))
   (* x (+ -1.0 (/ y z)))
   (/ (* x (+ y 1.0)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -22000000000.0) || !(z <= 0.007)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-22000000000.0d0)) .or. (.not. (z <= 0.007d0))) then
        tmp = x * ((-1.0d0) + (y / z))
    else
        tmp = (x * (y + 1.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -22000000000.0) || !(z <= 0.007)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -22000000000.0) or not (z <= 0.007):
		tmp = x * (-1.0 + (y / z))
	else:
		tmp = (x * (y + 1.0)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -22000000000.0) || !(z <= 0.007))
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	else
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -22000000000.0) || ~((z <= 0.007)))
		tmp = x * (-1.0 + (y / z));
	else
		tmp = (x * (y + 1.0)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -22000000000.0], N[Not[LessEqual[z, 0.007]], $MachinePrecision]], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e10 or 0.00700000000000000015 < z

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. associate--l+ 80.1%

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

      2. +-commutative 80.1%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.2%

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

   if -2.2e10 < z < 0.00700000000000000015

   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 99.3%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22000000000 \lor \neg \left(z \leq 0.007\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1920000 \lor \neg \left(y \leq 0.00023\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1920000.0) (not (<= y 0.00023))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1920000.0) || !(y <= 0.00023)) {
		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 <= (-1920000.0d0)) .or. (.not. (y <= 0.00023d0))) 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 <= -1920000.0) || !(y <= 0.00023)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1920000.0) or not (y <= 0.00023):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1920000.0) || !(y <= 0.00023))
		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 <= -1920000.0) || ~((y <= 0.00023)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1920000.0], N[Not[LessEqual[y, 0.00023]], $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 < -1.92e6 or 2.3000000000000001e-4 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. associate-/l* 70.9%

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

      2. associate-/r/ 77.5%

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

   5. Simplified 77.5%

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

   if -1.92e6 < y < 2.3000000000000001e-4

   1. Initial program 88.4%

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

   3. Taylor expanded in x around 0 88.4%

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

      1. associate--l+ 88.4%

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

      2. +-commutative 88.4%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 99.5%

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

   7. Taylor expanded in z around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. +-commutative 99.5%

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

      3. unsub-neg 99.5%

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

   9. Simplified 99.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1920000 \lor \neg \left(y \leq 0.00023\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1100000 \lor \neg \left(y \leq 0.00023\right):\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1100000.0) (not (<= y 0.00023))) (/ y (/ z x)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1100000.0) || !(y <= 0.00023)) {
		tmp = y / (z / x);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1100000.0d0)) .or. (.not. (y <= 0.00023d0))) then
        tmp = y / (z / x)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1100000.0) || !(y <= 0.00023)) {
		tmp = y / (z / x);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1100000.0) or not (y <= 0.00023):
		tmp = y / (z / x)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1100000.0) || !(y <= 0.00023))
		tmp = Float64(y / Float64(z / x));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1100000.0) || ~((y <= 0.00023)))
		tmp = y / (z / x);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1100000.0], N[Not[LessEqual[y, 0.00023]], $MachinePrecision]], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e6 or 2.3000000000000001e-4 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. associate-/l* 70.9%

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

      2. associate-/r/ 77.5%

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

   5. Simplified 77.5%

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

      1. *-commutative 77.5%

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

      2. clear-num 77.4%

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

      3. un-div-inv 77.6%

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

   7. Applied egg-rr 77.6%

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

   if -1.1e6 < y < 2.3000000000000001e-4

   1. Initial program 88.4%

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

   3. Taylor expanded in x around 0 88.4%

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

      1. associate--l+ 88.4%

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

      2. +-commutative 88.4%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 99.5%

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

   7. Taylor expanded in z around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. +-commutative 99.5%

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

      3. unsub-neg 99.5%

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

   9. Simplified 99.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1100000 \lor \neg \left(y \leq 0.00023\right):\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1850000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 0.00023:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1850000.0)
   (/ y (/ z x))
   (if (<= y 0.00023) (- (/ x z) x) (/ (* x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1850000.0) {
		tmp = y / (z / x);
	} else if (y <= 0.00023) {
		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 <= (-1850000.0d0)) then
        tmp = y / (z / x)
    else if (y <= 0.00023d0) 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 <= -1850000.0) {
		tmp = y / (z / x);
	} else if (y <= 0.00023) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1850000.0:
		tmp = y / (z / x)
	elif y <= 0.00023:
		tmp = (x / z) - x
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1850000.0)
		tmp = Float64(y / Float64(z / x));
	elseif (y <= 0.00023)
		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 <= -1850000.0)
		tmp = y / (z / x);
	elseif (y <= 0.00023)
		tmp = (x / z) - x;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1850000.0], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00023], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85e6

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. associate-/l* 60.8%

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

      2. associate-/r/ 69.6%

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

   5. Simplified 69.6%

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

      1. *-commutative 69.6%

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

      2. clear-num 69.5%

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

      3. un-div-inv 69.7%

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

   7. Applied egg-rr 69.7%

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

   if -1.85e6 < y < 2.3000000000000001e-4

   1. Initial program 88.4%

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

   3. Taylor expanded in x around 0 88.4%

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

      1. associate--l+ 88.4%

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

      2. +-commutative 88.4%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 99.5%

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

   7. Taylor expanded in z around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. +-commutative 99.5%

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

      3. unsub-neg 99.5%

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

   9. Simplified 99.5%

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

   if 2.3000000000000001e-4 < y

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 84.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1850000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 0.00023:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.22 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.22e-46)
   (/ (* x (+ (- y z) 1.0)) z)
   (* x (+ (/ (+ y 1.0) z) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.22e-46) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = x * (((y + 1.0) / 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 <= 1.22d-46) then
        tmp = (x * ((y - z) + 1.0d0)) / z
    else
        tmp = x * (((y + 1.0d0) / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.22e-46) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = x * (((y + 1.0) / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.22e-46:
		tmp = (x * ((y - z) + 1.0)) / z
	else:
		tmp = x * (((y + 1.0) / z) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.22e-46)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(x * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.22e-46)
		tmp = (x * ((y - z) + 1.0)) / z;
	else
		tmp = x * (((y + 1.0) / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.22e-46], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.22e-46

   1. Initial program 93.7%

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

   if 1.22e-46 < x

   1. Initial program 80.8%

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

   3. Taylor expanded in x around 0 80.8%

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

      1. associate--l+ 80.8%

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

      2. +-commutative 80.8%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.22 \cdot 10^{-46}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 3.7 \cdot 10^{-17}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 3.7e-17))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 3.7e-17)) {
		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 <= 3.7d-17))) 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 <= 3.7e-17)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 3.7e-17):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 3.7e-17))
		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 <= 3.7e-17)))
		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, 3.7e-17]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 3.6999999999999997e-17 < z

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. mul-1-neg 72.6%

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

   5. Simplified 72.6%

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

   if -1 < z < 3.6999999999999997e-17

   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 99.4%

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

   4. Taylor expanded in y around 0 52.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 3.7 \cdot 10^{-17}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.2% accurate, 4.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.0%

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

3. Taylor expanded in z around inf 39.2%

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

   1. mul-1-neg 39.2%

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

5. Simplified 39.2%

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

6. Final simplification 39.2%

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

Developer target: 99.5% 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 2024031 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))