Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 88.2% → 99.0%

Time: 7.4s

Alternatives: 9

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-222} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-222) (not (<= t_0 0.0))) t_0 (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-222) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-222)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-222) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-222) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-222) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-222) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-222], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.00000000000000005e-222 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   if -1.00000000000000005e-222 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 20.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 92.9%

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

      1. mul-1-neg 92.9%

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

      2. associate-/l* 99.9%

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

      3. associate-/r/ 24.7%

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

      4. distribute-rgt-neg-in 24.7%

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

      5. +-commutative 24.7%

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

      6. distribute-neg-in 24.7%

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

      7. sub-neg 24.7%

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

   5. Simplified 24.7%

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

   6. Taylor expanded in y around 0 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-*l/ 100.0%

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

      3. associate-*r* 100.0%

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

      4. neg-mul-1 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-lft-out 100.0%

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

      7. distribute-neg-frac 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around 0 100.0%

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

       1. sub-neg 100.0%

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

       2. metadata-eval 100.0%

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

       3. +-commutative 100.0%

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

       4. mul-1-neg 100.0%

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

       5. sub-neg 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-222} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-173}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 8.7 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -3.2e-23)
     t_0
     (if (<= y 3.1e-173)
       (+ x y)
       (if (<= y 5.8e-157)
         (* (/ z y) (- x))
         (if (<= y 8.7e+15) (+ x y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -3.2e-23) {
		tmp = t_0;
	} else if (y <= 3.1e-173) {
		tmp = x + y;
	} else if (y <= 5.8e-157) {
		tmp = (z / y) * -x;
	} else if (y <= 8.7e+15) {
		tmp = x + y;
	} 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 = z * ((-1.0d0) - (x / y))
    if (y <= (-3.2d-23)) then
        tmp = t_0
    else if (y <= 3.1d-173) then
        tmp = x + y
    else if (y <= 5.8d-157) then
        tmp = (z / y) * -x
    else if (y <= 8.7d+15) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -3.2e-23) {
		tmp = t_0;
	} else if (y <= 3.1e-173) {
		tmp = x + y;
	} else if (y <= 5.8e-157) {
		tmp = (z / y) * -x;
	} else if (y <= 8.7e+15) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -3.2e-23:
		tmp = t_0
	elif y <= 3.1e-173:
		tmp = x + y
	elif y <= 5.8e-157:
		tmp = (z / y) * -x
	elif y <= 8.7e+15:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -3.2e-23)
		tmp = t_0;
	elseif (y <= 3.1e-173)
		tmp = Float64(x + y);
	elseif (y <= 5.8e-157)
		tmp = Float64(Float64(z / y) * Float64(-x));
	elseif (y <= 8.7e+15)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -3.2e-23)
		tmp = t_0;
	elseif (y <= 3.1e-173)
		tmp = x + y;
	elseif (y <= 5.8e-157)
		tmp = (z / y) * -x;
	elseif (y <= 8.7e+15)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e-23], t$95$0, If[LessEqual[y, 3.1e-173], N[(x + y), $MachinePrecision], If[LessEqual[y, 5.8e-157], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 8.7e+15], N[(x + y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.19999999999999976e-23 or 8.7e15 < y

   1. Initial program 79.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. associate-/l* 82.8%

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

      3. associate-/r/ 63.3%

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

      4. distribute-rgt-neg-in 63.3%

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

      5. +-commutative 63.3%

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

      6. distribute-neg-in 63.3%

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

      7. sub-neg 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in y around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-*l/ 82.8%

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

      3. associate-*r* 82.8%

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

      4. neg-mul-1 82.8%

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

      5. *-commutative 82.8%

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

      6. distribute-lft-out 82.8%

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

      7. distribute-neg-frac 82.8%

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

   8. Simplified 82.8%

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

   9. Taylor expanded in z around 0 82.8%

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

       1. sub-neg 82.8%

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

       2. metadata-eval 82.8%

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

       3. +-commutative 82.8%

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

       4. mul-1-neg 82.8%

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

       5. sub-neg 82.8%

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

   11. Simplified 82.8%

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

   if -3.19999999999999976e-23 < y < 3.10000000000000005e-173 or 5.79999999999999977e-157 < y < 8.7e15

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 73.9%

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

      1. +-commutative 73.9%

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

   5. Simplified 73.9%

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

   if 3.10000000000000005e-173 < y < 5.79999999999999977e-157

   1. Initial program 99.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. associate-/l* 80.6%

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

      3. distribute-neg-frac 80.6%

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

      4. +-commutative 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around 0 80.6%

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

      1. frac-2neg 80.6%

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

      2. associate-/r/ 99.7%

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

      3. frac-2neg 99.7%

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

   8. Applied egg-rr 99.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-173}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 8.7 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+31}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-173}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e+31)
   (- z)
   (if (<= y 3.1e-173)
     (+ x y)
     (if (<= y 5.8e-157)
       (* (/ z y) (- x))
       (if (<= y 1.45e+16) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+31) {
		tmp = -z;
	} else if (y <= 3.1e-173) {
		tmp = x + y;
	} else if (y <= 5.8e-157) {
		tmp = (z / y) * -x;
	} else if (y <= 1.45e+16) {
		tmp = x + y;
	} else {
		tmp = -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 <= (-7.2d+31)) then
        tmp = -z
    else if (y <= 3.1d-173) then
        tmp = x + y
    else if (y <= 5.8d-157) then
        tmp = (z / y) * -x
    else if (y <= 1.45d+16) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+31) {
		tmp = -z;
	} else if (y <= 3.1e-173) {
		tmp = x + y;
	} else if (y <= 5.8e-157) {
		tmp = (z / y) * -x;
	} else if (y <= 1.45e+16) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e+31:
		tmp = -z
	elif y <= 3.1e-173:
		tmp = x + y
	elif y <= 5.8e-157:
		tmp = (z / y) * -x
	elif y <= 1.45e+16:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+31)
		tmp = Float64(-z);
	elseif (y <= 3.1e-173)
		tmp = Float64(x + y);
	elseif (y <= 5.8e-157)
		tmp = Float64(Float64(z / y) * Float64(-x));
	elseif (y <= 1.45e+16)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.2e+31)
		tmp = -z;
	elseif (y <= 3.1e-173)
		tmp = x + y;
	elseif (y <= 5.8e-157)
		tmp = (z / y) * -x;
	elseif (y <= 1.45e+16)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e+31], (-z), If[LessEqual[y, 3.1e-173], N[(x + y), $MachinePrecision], If[LessEqual[y, 5.8e-157], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 1.45e+16], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.19999999999999992e31 or 1.45e16 < y

   1. Initial program 77.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.7%

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

      1. mul-1-neg 63.7%

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

   5. Simplified 63.7%

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

   if -7.19999999999999992e31 < y < 3.10000000000000005e-173 or 5.79999999999999977e-157 < y < 1.45e16

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 70.6%

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

      1. +-commutative 70.6%

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

   5. Simplified 70.6%

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

   if 3.10000000000000005e-173 < y < 5.79999999999999977e-157

   1. Initial program 99.7%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. associate-/l* 80.6%

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

      3. distribute-neg-frac 80.6%

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

      4. +-commutative 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around 0 80.6%

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

      1. frac-2neg 80.6%

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

      2. associate-/r/ 99.7%

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

      3. frac-2neg 99.7%

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

   8. Applied egg-rr 99.7%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+31}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-173}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-22} \lor \neg \left(y \leq 2.5 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e-22) (not (<= y 2.5e-20)))
   (* z (- -1.0 (/ x y)))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-22) || !(y <= 2.5e-20)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x / (1.0 - (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 <= (-1.15d-22)) .or. (.not. (y <= 2.5d-20))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-22) || !(y <= 2.5e-20)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e-22) or not (y <= 2.5e-20):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e-22) || !(y <= 2.5e-20))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.15e-22) || ~((y <= 2.5e-20)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e-22], N[Not[LessEqual[y, 2.5e-20]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e-22 or 2.4999999999999999e-20 < y

   1. Initial program 80.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-/l* 81.4%

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

      3. associate-/r/ 62.6%

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

      4. distribute-rgt-neg-in 62.6%

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

      5. +-commutative 62.6%

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

      6. distribute-neg-in 62.6%

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

      7. sub-neg 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in y around 0 74.9%

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

      1. *-commutative 74.9%

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

      2. associate-*l/ 81.4%

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

      3. associate-*r* 81.4%

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

      4. neg-mul-1 81.4%

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

      5. *-commutative 81.4%

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

      6. distribute-lft-out 81.4%

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

      7. distribute-neg-frac 81.4%

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

   8. Simplified 81.4%

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

   9. Taylor expanded in z around 0 81.4%

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

       1. sub-neg 81.4%

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

       2. metadata-eval 81.4%

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

       3. +-commutative 81.4%

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

       4. mul-1-neg 81.4%

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

       5. sub-neg 81.4%

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

   11. Simplified 81.4%

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

   if -1.1499999999999999e-22 < y < 2.4999999999999999e-20

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-22} \lor \neg \left(y \leq 2.5 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e-22)
   (/ (- z) (/ y (+ x y)))
   (if (<= y 3.2e-22) (/ x (- 1.0 (/ y z))) (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e-22) {
		tmp = -z / (y / (x + y));
	} else if (y <= 3.2e-22) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.5d-22)) then
        tmp = -z / (y / (x + y))
    else if (y <= 3.2d-22) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e-22) {
		tmp = -z / (y / (x + y));
	} else if (y <= 3.2e-22) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e-22:
		tmp = -z / (y / (x + y))
	elif y <= 3.2e-22:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e-22)
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	elseif (y <= 3.2e-22)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e-22)
		tmp = -z / (y / (x + y));
	elseif (y <= 3.2e-22)
		tmp = x / (1.0 - (y / z));
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e-22], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-22], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000043e-22

   1. Initial program 85.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate-/l* 81.5%

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

      3. distribute-neg-frac 81.5%

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

      4. +-commutative 81.5%

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

   5. Simplified 81.5%

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

   if -6.50000000000000043e-22 < y < 3.19999999999999987e-22

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.6%

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

   if 3.19999999999999987e-22 < y

   1. Initial program 73.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. associate-/l* 81.4%

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

      3. associate-/r/ 56.3%

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

      4. distribute-rgt-neg-in 56.3%

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

      5. +-commutative 56.3%

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

      6. distribute-neg-in 56.3%

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

      7. sub-neg 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in y around 0 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*l/ 81.4%

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

      3. associate-*r* 81.4%

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

      4. neg-mul-1 81.4%

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

      5. *-commutative 81.4%

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

      6. distribute-lft-out 81.4%

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

      7. distribute-neg-frac 81.4%

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

   8. Simplified 81.4%

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

   9. Taylor expanded in z around 0 81.4%

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

       1. sub-neg 81.4%

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

       2. metadata-eval 81.4%

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

       3. +-commutative 81.4%

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

       4. mul-1-neg 81.4%

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

       5. sub-neg 81.4%

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

   11. Simplified 81.4%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+29} \lor \neg \left(y \leq 1.48 \cdot 10^{+16}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+29) (not (<= y 1.48e+16))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+29) || !(y <= 1.48e+16)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.5d+29)) .or. (.not. (y <= 1.48d+16))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+29) || !(y <= 1.48e+16)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e+29) or not (y <= 1.48e+16):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e+29) || !(y <= 1.48e+16))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e+29) || ~((y <= 1.48e+16)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e+29], N[Not[LessEqual[y, 1.48e+16]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999971e29 or 1.48e16 < y

   1. Initial program 77.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.7%

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

      1. mul-1-neg 63.7%

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

   5. Simplified 63.7%

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

   if -6.49999999999999971e29 < y < 1.48e16

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.8%

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

      1. +-commutative 67.8%

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

   5. Simplified 67.8%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+29} \lor \neg \left(y \leq 1.48 \cdot 10^{+16}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-8} \lor \neg \left(y \leq 2.7 \cdot 10^{-21}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2e-8) (not (<= y 2.7e-21))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e-8) || !(y <= 2.7e-21)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2d-8)) .or. (.not. (y <= 2.7d-21))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e-8) || !(y <= 2.7e-21)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2e-8) or not (y <= 2.7e-21):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2e-8) || !(y <= 2.7e-21))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2e-8) || ~((y <= 2.7e-21)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2e-8], N[Not[LessEqual[y, 2.7e-21]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2e-8 or 2.7000000000000001e-21 < y

   1. Initial program 79.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.2%

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

      1. mul-1-neg 61.2%

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

   5. Simplified 61.2%

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

   if -2e-8 < y < 2.7000000000000001e-21

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 55.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-8} \lor \neg \left(y \leq 2.7 \cdot 10^{-21}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-179}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e-130) x (if (<= x 2.2e-179) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-130) {
		tmp = x;
	} else if (x <= 2.2e-179) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.4d-130)) then
        tmp = x
    else if (x <= 2.2d-179) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-130) {
		tmp = x;
	} else if (x <= 2.2e-179) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e-130:
		tmp = x
	elif x <= 2.2e-179:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e-130)
		tmp = x;
	elseif (x <= 2.2e-179)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4e-130)
		tmp = x;
	elseif (x <= 2.2e-179)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e-130], x, If[LessEqual[x, 2.2e-179], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.40000000000000008e-130 or 2.20000000000000005e-179 < x

   1. Initial program 87.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 30.9%

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

   if -1.40000000000000008e-130 < x < 2.20000000000000005e-179

   1. Initial program 89.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.8%

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

   4. Taylor expanded in y around 0 42.7%

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

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-179}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 87.7%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 26.9%

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

4. Final simplification 26.9%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 94.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / 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 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / 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 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024041 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

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