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

Percentage Accurate: 88.5% → 99.7%

Time: 7.0s

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: 88.5% 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-280} \lor \neg \left(t\_0 \leq 10^{-285}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-280) (not (<= t_0 1e-285)))
     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 <= -2e-280) || !(t_0 <= 1e-285)) {
		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 <= (-2d-280)) .or. (.not. (t_0 <= 1d-285))) 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 <= -2e-280) || !(t_0 <= 1e-285)) {
		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 <= -2e-280) or not (t_0 <= 1e-285):
		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 <= -2e-280) || !(t_0 <= 1e-285))
		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 <= -2e-280) || ~((t_0 <= 1e-285)))
		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, -2e-280], N[Not[LessEqual[t$95$0, 1e-285]], $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))) < -1.9999999999999999e-280 or 1.00000000000000007e-285 < (/.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 -1.9999999999999999e-280 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 1.00000000000000007e-285

   1. Initial program 16.1%

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

   3. Taylor expanded in z around 0 90.7%

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

      1. mul-1-neg 90.7%

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

      2. associate-/l* 99.8%

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

      3. distribute-neg-frac 99.8%

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

      4. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 95.6%

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

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

      3. mul-1-neg 95.6%

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

      4. associate-/l* 90.5%

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

      5. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around 0 100.0%

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

       1. neg-mul-1 100.0%

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

       2. distribute-rgt-neg-in 100.0%

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

       3. distribute-neg-in 100.0%

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

       4. metadata-eval 100.0%

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

       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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-280} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 10^{-285}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+124}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+61}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -3.4e+124)
     (/ (- z) (/ y (+ x y)))
     (if (<= y -1.35e+33)
       (/ y t_0)
       (if (<= y -4.7e-101)
         (/ x t_0)
         (if (<= y 2.6e+61)
           (* (+ x y) (+ 1.0 (/ y z)))
           (* z (- -1.0 (/ x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.4e+124) {
		tmp = -z / (y / (x + y));
	} else if (y <= -1.35e+33) {
		tmp = y / t_0;
	} else if (y <= -4.7e-101) {
		tmp = x / t_0;
	} else if (y <= 2.6e+61) {
		tmp = (x + y) * (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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (y <= (-3.4d+124)) then
        tmp = -z / (y / (x + y))
    else if (y <= (-1.35d+33)) then
        tmp = y / t_0
    else if (y <= (-4.7d-101)) then
        tmp = x / t_0
    else if (y <= 2.6d+61) then
        tmp = (x + y) * (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 t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.4e+124) {
		tmp = -z / (y / (x + y));
	} else if (y <= -1.35e+33) {
		tmp = y / t_0;
	} else if (y <= -4.7e-101) {
		tmp = x / t_0;
	} else if (y <= 2.6e+61) {
		tmp = (x + y) * (1.0 + (y / z));
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -3.4e+124:
		tmp = -z / (y / (x + y))
	elif y <= -1.35e+33:
		tmp = y / t_0
	elif y <= -4.7e-101:
		tmp = x / t_0
	elif y <= 2.6e+61:
		tmp = (x + y) * (1.0 + (y / z))
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -3.4e+124)
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	elseif (y <= -1.35e+33)
		tmp = Float64(y / t_0);
	elseif (y <= -4.7e-101)
		tmp = Float64(x / t_0);
	elseif (y <= 2.6e+61)
		tmp = Float64(Float64(x + y) * 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)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -3.4e+124)
		tmp = -z / (y / (x + y));
	elseif (y <= -1.35e+33)
		tmp = y / t_0;
	elseif (y <= -4.7e-101)
		tmp = x / t_0;
	elseif (y <= 2.6e+61)
		tmp = (x + y) * (1.0 + (y / z));
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+124], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e+33], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -4.7e-101], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 2.6e+61], N[(N[(x + y), $MachinePrecision] * 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 5 regimes

2. if y < -3.4e124

   1. Initial program 75.5%

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

   3. Taylor expanded in z around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-/l* 88.9%

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

      3. distribute-neg-frac 88.9%

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

      4. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -3.4e124 < y < -1.34999999999999996e33

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0 70.7%

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

   if -1.34999999999999996e33 < y < -4.6999999999999999e-101

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf 79.3%

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

   if -4.6999999999999999e-101 < y < 2.59999999999999973e61

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. associate-+r+ 79.8%

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

      2. *-lft-identity 79.8%

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

      3. associate-/l* 77.3%

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

      4. associate-/r/ 80.8%

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

      5. distribute-rgt-in 80.8%

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

      6. +-commutative 80.8%

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

   5. Simplified 80.8%

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

   if 2.59999999999999973e61 < y

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-/l* 72.4%

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

      3. distribute-neg-frac 72.4%

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

      4. +-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in y around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. mul-1-neg 70.7%

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

      4. associate-/l* 70.8%

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

      5. associate-/r/ 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in z around 0 72.5%

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

       1. neg-mul-1 72.5%

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

       2. distribute-rgt-neg-in 72.5%

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

       3. distribute-neg-in 72.5%

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

       4. metadata-eval 72.5%

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

       5. sub-neg 72.5%

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

   11. Simplified 72.5%

       \[\leadsto \color{blue}{z \cdot \left(-1 - \frac{x}{y}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+124}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+61}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+123} \lor \neg \left(y \leq -8 \cdot 10^{+26} \lor \neg \left(y \leq -7 \cdot 10^{-8}\right) \land y \leq 3.8 \cdot 10^{+60}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e+123)
         (not (or (<= y -8e+26) (and (not (<= y -7e-8)) (<= y 3.8e+60)))))
   (* z (- -1.0 (/ x y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e+123) || !((y <= -8e+26) || (!(y <= -7e-8) && (y <= 3.8e+60)))) {
		tmp = z * (-1.0 - (x / y));
	} 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 <= (-7.5d+123)) .or. (.not. (y <= (-8d+26)) .or. (.not. (y <= (-7d-8))) .and. (y <= 3.8d+60))) then
        tmp = z * ((-1.0d0) - (x / y))
    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 <= -7.5e+123) || !((y <= -8e+26) || (!(y <= -7e-8) && (y <= 3.8e+60)))) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e+123) or not ((y <= -8e+26) or (not (y <= -7e-8) and (y <= 3.8e+60))):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e+123) || !((y <= -8e+26) || (!(y <= -7e-8) && (y <= 3.8e+60))))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.5e+123) || ~(((y <= -8e+26) || (~((y <= -7e-8)) && (y <= 3.8e+60)))))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e+123], N[Not[Or[LessEqual[y, -8e+26], And[N[Not[LessEqual[y, -7e-8]], $MachinePrecision], LessEqual[y, 3.8e+60]]]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999999e123 or -8.00000000000000038e26 < y < -7.00000000000000048e-8 or 3.80000000000000009e60 < y

   1. Initial program 80.7%

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

   3. Taylor expanded in z around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate-/l* 80.3%

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

      3. distribute-neg-frac 80.3%

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

      4. +-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in y around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

      3. mul-1-neg 76.9%

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

      4. associate-/l* 79.4%

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

      5. associate-/r/ 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in z around 0 80.3%

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

       1. neg-mul-1 80.3%

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

       2. distribute-rgt-neg-in 80.3%

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

       3. distribute-neg-in 80.3%

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

       4. metadata-eval 80.3%

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

       5. sub-neg 80.3%

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

   11. Simplified 80.3%

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

   if -7.4999999999999999e123 < y < -8.00000000000000038e26 or -7.00000000000000048e-8 < y < 3.80000000000000009e60

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. +-commutative 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+123} \lor \neg \left(y \leq -8 \cdot 10^{+26} \lor \neg \left(y \leq -7 \cdot 10^{-8}\right) \land y \leq 3.8 \cdot 10^{+60}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* z (- -1.0 (/ x y)))))
   (if (<= y -3.2e+125)
     t_1
     (if (<= y -6.5e+33)
       (/ y t_0)
       (if (<= y -1.2e-107) (/ x t_0) (if (<= y 2.45e+58) (+ x y) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -3.2e+125) {
		tmp = t_1;
	} else if (y <= -6.5e+33) {
		tmp = y / t_0;
	} else if (y <= -1.2e-107) {
		tmp = x / t_0;
	} else if (y <= 2.45e+58) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = z * ((-1.0d0) - (x / y))
    if (y <= (-3.2d+125)) then
        tmp = t_1
    else if (y <= (-6.5d+33)) then
        tmp = y / t_0
    else if (y <= (-1.2d-107)) then
        tmp = x / t_0
    else if (y <= 2.45d+58) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -3.2e+125) {
		tmp = t_1;
	} else if (y <= -6.5e+33) {
		tmp = y / t_0;
	} else if (y <= -1.2e-107) {
		tmp = x / t_0;
	} else if (y <= 2.45e+58) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -3.2e+125:
		tmp = t_1
	elif y <= -6.5e+33:
		tmp = y / t_0
	elif y <= -1.2e-107:
		tmp = x / t_0
	elif y <= 2.45e+58:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -3.2e+125)
		tmp = t_1;
	elseif (y <= -6.5e+33)
		tmp = Float64(y / t_0);
	elseif (y <= -1.2e-107)
		tmp = Float64(x / t_0);
	elseif (y <= 2.45e+58)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -3.2e+125)
		tmp = t_1;
	elseif (y <= -6.5e+33)
		tmp = y / t_0;
	elseif (y <= -1.2e-107)
		tmp = x / t_0;
	elseif (y <= 2.45e+58)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+125], t$95$1, If[LessEqual[y, -6.5e+33], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -1.2e-107], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 2.45e+58], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.19999999999999983e125 or 2.45000000000000009e58 < y

   1. Initial program 80.1%

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

   3. Taylor expanded in z around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. associate-/l* 80.3%

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

      3. distribute-neg-frac 80.3%

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

      4. +-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

      3. mul-1-neg 76.6%

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

      4. associate-/l* 79.4%

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

      5. associate-/r/ 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in z around 0 80.2%

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

       1. neg-mul-1 80.2%

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

       2. distribute-rgt-neg-in 80.2%

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

       3. distribute-neg-in 80.2%

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

       4. metadata-eval 80.2%

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

       5. sub-neg 80.2%

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

   11. Simplified 80.2%

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

   if -3.19999999999999983e125 < y < -6.49999999999999993e33

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0 70.7%

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

   if -6.49999999999999993e33 < y < -1.19999999999999997e-107

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 79.9%

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

   if -1.19999999999999997e-107 < y < 2.45000000000000009e58

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 80.5%

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

      1. +-commutative 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+125}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+125}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -6e+125)
     (/ (- z) (/ y (+ x y)))
     (if (<= y -2.3e+33)
       (/ y t_0)
       (if (<= y -8.6e-108)
         (/ x t_0)
         (if (<= y 2.4e+61) (+ x y) (* z (- -1.0 (/ x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -6e+125) {
		tmp = -z / (y / (x + y));
	} else if (y <= -2.3e+33) {
		tmp = y / t_0;
	} else if (y <= -8.6e-108) {
		tmp = x / t_0;
	} else if (y <= 2.4e+61) {
		tmp = x + y;
	} 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 = 1.0d0 - (y / z)
    if (y <= (-6d+125)) then
        tmp = -z / (y / (x + y))
    else if (y <= (-2.3d+33)) then
        tmp = y / t_0
    else if (y <= (-8.6d-108)) then
        tmp = x / t_0
    else if (y <= 2.4d+61) then
        tmp = x + y
    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 = 1.0 - (y / z);
	double tmp;
	if (y <= -6e+125) {
		tmp = -z / (y / (x + y));
	} else if (y <= -2.3e+33) {
		tmp = y / t_0;
	} else if (y <= -8.6e-108) {
		tmp = x / t_0;
	} else if (y <= 2.4e+61) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -6e+125:
		tmp = -z / (y / (x + y))
	elif y <= -2.3e+33:
		tmp = y / t_0
	elif y <= -8.6e-108:
		tmp = x / t_0
	elif y <= 2.4e+61:
		tmp = x + y
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -6e+125)
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	elseif (y <= -2.3e+33)
		tmp = Float64(y / t_0);
	elseif (y <= -8.6e-108)
		tmp = Float64(x / t_0);
	elseif (y <= 2.4e+61)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -6e+125)
		tmp = -z / (y / (x + y));
	elseif (y <= -2.3e+33)
		tmp = y / t_0;
	elseif (y <= -8.6e-108)
		tmp = x / t_0;
	elseif (y <= 2.4e+61)
		tmp = x + y;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+125], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e+33], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -8.6e-108], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 2.4e+61], N[(x + y), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.0000000000000003e125

   1. Initial program 75.5%

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

   3. Taylor expanded in z around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-/l* 88.9%

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

      3. distribute-neg-frac 88.9%

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

      4. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -6.0000000000000003e125 < y < -2.30000000000000011e33

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0 70.7%

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

   if -2.30000000000000011e33 < y < -8.6000000000000001e-108

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 79.9%

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

   if -8.6000000000000001e-108 < y < 2.3999999999999999e61

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 80.5%

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

      1. +-commutative 80.5%

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

   5. Simplified 80.5%

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

   if 2.3999999999999999e61 < y

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-/l* 72.4%

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

      3. distribute-neg-frac 72.4%

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

      4. +-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in y around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. mul-1-neg 70.7%

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

      4. associate-/l* 70.8%

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

      5. associate-/r/ 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in z around 0 72.5%

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

       1. neg-mul-1 72.5%

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

       2. distribute-rgt-neg-in 72.5%

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

       3. distribute-neg-in 72.5%

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

       4. metadata-eval 72.5%

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

       5. sub-neg 72.5%

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

   11. Simplified 72.5%

       \[\leadsto \color{blue}{z \cdot \left(-1 - \frac{x}{y}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+125}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+126}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+43}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.12e+126)
   (- z)
   (if (<= y -1.35e+43) y (if (<= y 2.5e+62) x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.12e+126) {
		tmp = -z;
	} else if (y <= -1.35e+43) {
		tmp = y;
	} else if (y <= 2.5e+62) {
		tmp = x;
	} 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 <= (-1.12d+126)) then
        tmp = -z
    else if (y <= (-1.35d+43)) then
        tmp = y
    else if (y <= 2.5d+62) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.12e+126) {
		tmp = -z;
	} else if (y <= -1.35e+43) {
		tmp = y;
	} else if (y <= 2.5e+62) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.12e+126:
		tmp = -z
	elif y <= -1.35e+43:
		tmp = y
	elif y <= 2.5e+62:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.12e+126)
		tmp = Float64(-z);
	elseif (y <= -1.35e+43)
		tmp = y;
	elseif (y <= 2.5e+62)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.12e+126)
		tmp = -z;
	elseif (y <= -1.35e+43)
		tmp = y;
	elseif (y <= 2.5e+62)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.12e+126], (-z), If[LessEqual[y, -1.35e+43], y, If[LessEqual[y, 2.5e+62], x, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e126 or 2.50000000000000014e62 < y

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 70.2%

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

      1. mul-1-neg 70.2%

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

   5. Simplified 70.2%

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

   if -1.12e126 < y < -1.3500000000000001e43

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 66.0%

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

   4. Taylor expanded in y around 0 58.4%

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

   if -1.3500000000000001e43 < y < 2.50000000000000014e62

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 60.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+126}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+43}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+123} \lor \neg \left(y \leq 1.8 \cdot 10^{+113}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e+123) (not (<= y 1.8e+113))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e+123) || !(y <= 1.8e+113)) {
		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 <= (-7.5d+123)) .or. (.not. (y <= 1.8d+113))) 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 <= -7.5e+123) || !(y <= 1.8e+113)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e+123) or not (y <= 1.8e+113):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e+123) || !(y <= 1.8e+113))
		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 <= -7.5e+123) || ~((y <= 1.8e+113)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e+123], N[Not[LessEqual[y, 1.8e+113]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999999e123 or 1.79999999999999996e113 < y

   1. Initial program 78.1%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. mul-1-neg 74.5%

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

   5. Simplified 74.5%

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

   if -7.4999999999999999e123 < y < 1.79999999999999996e113

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 72.5%

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

      1. +-commutative 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+123} \lor \neg \left(y \leq 1.8 \cdot 10^{+113}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e-96) x (if (<= x 1.3e-52) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-96) {
		tmp = x;
	} else if (x <= 1.3e-52) {
		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 <= (-1.45d-96)) then
        tmp = x
    else if (x <= 1.3d-52) 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 <= -1.45e-96) {
		tmp = x;
	} else if (x <= 1.3e-52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e-96:
		tmp = x
	elif x <= 1.3e-52:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e-96)
		tmp = x;
	elseif (x <= 1.3e-52)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e-96)
		tmp = x;
	elseif (x <= 1.3e-52)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e-96], x, If[LessEqual[x, 1.3e-52], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999997e-96 or 1.2999999999999999e-52 < x

   1. Initial program 90.0%

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

   3. Taylor expanded in y around 0 52.5%

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

   if -1.44999999999999997e-96 < x < 1.2999999999999999e-52

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 77.1%

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

   4. Taylor expanded in y around 0 37.7%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 90.3%

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

3. Taylor expanded in y around 0 37.2%

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

4. Final simplification 37.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.9% 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 2024026 
(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))))