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

Percentage Accurate: 87.7% → 99.5%

Time: 8.9s

Alternatives: 8

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: 87.7% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-255}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;0 - z \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (<= t_0 -5e-255)
     t_0
     (if (<= t_0 0.0) (- 0.0 (* z (/ (+ x y) y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-255) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = 0.0 - (z * ((x + y) / 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 = (x + y) / (1.0d0 - (y / z))
    if (t_0 <= (-5d-255)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = 0.0d0 - (z * ((x + y) / 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 = (x + y) / (1.0 - (y / z));
	double tmp;
	if (t_0 <= -5e-255) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = 0.0 - (z * ((x + y) / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if t_0 <= -5e-255:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = 0.0 - (z * ((x + y) / y))
	else:
		tmp = t_0
	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 <= -5e-255)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(0.0 - Float64(z * Float64(Float64(x + y) / y)));
	else
		tmp = t_0;
	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 <= -5e-255)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = 0.0 - (z * ((x + y) / y));
	else
		tmp = t_0;
	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[LessEqual[t$95$0, -5e-255], t$95$0, If[LessEqual[t$95$0, 0.0], N[(0.0 - N[(z * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.9999999999999996e-255 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -4.9999999999999996e-255 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 9.2%

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

      1. div-inv N/A

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

      2. flip3-- N/A

         \[\leadsto \left(x + y\right) \cdot \frac{1}{\frac{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}}} \]

      3. clear-num N/A

         \[\leadsto \left(x + y\right) \cdot \frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{\color{blue}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}} \]

      4. *-commutative N/A

         \[\leadsto \frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}} \cdot \color{blue}{\left(x + y\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}\right), \color{blue}{\left(x + y\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}}\right), \left(\color{blue}{x} + y\right)\right) \]

      7. flip3-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{1 - \frac{y}{z}}\right), \left(x + y\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(1 - \frac{y}{z}\right)\right), \left(\color{blue}{x} + y\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \left(\frac{y}{z}\right)\right)\right), \left(x + y\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right), \left(x + y\right)\right) \]

      11. +-lowering-+.f64 9.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right) \]

   4. Applied egg-rr 9.2%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{z \cdot \left(x + y\right)}{y}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(z \cdot \color{blue}{\frac{x + y}{y}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{x + y}{y}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(x + y\right), \color{blue}{y}\right)\right)\right) \]

      7. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, y\right), y\right)\right)\right) \]

   7. Simplified 100.0%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{x + y}{y}\right)\right), \color{blue}{z}\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(\frac{x + y}{y}\right)\right), z\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(x + y\right), y\right)\right), z\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(y + x\right), y\right)\right), z\right) \]

      8. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, x\right), y\right)\right), z\right) \]

   9. Applied egg-rr 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-255}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;\frac{x + y}{1 - \frac{y}{z}} \leq 0:\\ \;\;\;\;0 - z \cdot \frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t\_0}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+275}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq -3400000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)))
   (if (<= y -1.6e+275)
     (- 0.0 z)
     (if (<= y -3400000000000.0)
       t_1
       (if (<= y 2.3e-36) (/ x t_0) (if (<= y 8.5e+162) t_1 (- 0.0 z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double tmp;
	if (y <= -1.6e+275) {
		tmp = 0.0 - z;
	} else if (y <= -3400000000000.0) {
		tmp = t_1;
	} else if (y <= 2.3e-36) {
		tmp = x / t_0;
	} else if (y <= 8.5e+162) {
		tmp = t_1;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    if (y <= (-1.6d+275)) then
        tmp = 0.0d0 - z
    else if (y <= (-3400000000000.0d0)) then
        tmp = t_1
    else if (y <= 2.3d-36) then
        tmp = x / t_0
    else if (y <= 8.5d+162) then
        tmp = t_1
    else
        tmp = 0.0d0 - z
    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 = y / t_0;
	double tmp;
	if (y <= -1.6e+275) {
		tmp = 0.0 - z;
	} else if (y <= -3400000000000.0) {
		tmp = t_1;
	} else if (y <= 2.3e-36) {
		tmp = x / t_0;
	} else if (y <= 8.5e+162) {
		tmp = t_1;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	tmp = 0
	if y <= -1.6e+275:
		tmp = 0.0 - z
	elif y <= -3400000000000.0:
		tmp = t_1
	elif y <= 2.3e-36:
		tmp = x / t_0
	elif y <= 8.5e+162:
		tmp = t_1
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(y / t_0)
	tmp = 0.0
	if (y <= -1.6e+275)
		tmp = Float64(0.0 - z);
	elseif (y <= -3400000000000.0)
		tmp = t_1;
	elseif (y <= 2.3e-36)
		tmp = Float64(x / t_0);
	elseif (y <= 8.5e+162)
		tmp = t_1;
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = y / t_0;
	tmp = 0.0;
	if (y <= -1.6e+275)
		tmp = 0.0 - z;
	elseif (y <= -3400000000000.0)
		tmp = t_1;
	elseif (y <= 2.3e-36)
		tmp = x / t_0;
	elseif (y <= 8.5e+162)
		tmp = t_1;
	else
		tmp = 0.0 - z;
	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[(y / t$95$0), $MachinePrecision]}, If[LessEqual[y, -1.6e+275], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, -3400000000000.0], t$95$1, If[LessEqual[y, 2.3e-36], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 8.5e+162], t$95$1, N[(0.0 - z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999987e275 or 8.5000000000000003e162 < y

   1. Initial program 59.6%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 76.8%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 76.8%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 76.8%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 76.8%

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

   if -1.59999999999999987e275 < y < -3.4e12 or 2.29999999999999996e-36 < y < 8.5000000000000003e162

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 65.8%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 65.8%

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

   if -3.4e12 < y < 2.29999999999999996e-36

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 79.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 79.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+275}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq -3400000000000:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0 - z \cdot \frac{x + y}{y}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 0.0 (* z (/ (+ x y) y)))))
   (if (<= y -3.5e-40)
     t_0
     (if (<= y -2.55e-135)
       (+ x y)
       (if (<= y 2.6e-50) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 0.0 - (z * ((x + y) / y));
	double tmp;
	if (y <= -3.5e-40) {
		tmp = t_0;
	} else if (y <= -2.55e-135) {
		tmp = x + y;
	} else if (y <= 2.6e-50) {
		tmp = x / (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 = 0.0d0 - (z * ((x + y) / y))
    if (y <= (-3.5d-40)) then
        tmp = t_0
    else if (y <= (-2.55d-135)) then
        tmp = x + y
    else if (y <= 2.6d-50) then
        tmp = x / (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 = 0.0 - (z * ((x + y) / y));
	double tmp;
	if (y <= -3.5e-40) {
		tmp = t_0;
	} else if (y <= -2.55e-135) {
		tmp = x + y;
	} else if (y <= 2.6e-50) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.0 - (z * ((x + y) / y))
	tmp = 0
	if y <= -3.5e-40:
		tmp = t_0
	elif y <= -2.55e-135:
		tmp = x + y
	elif y <= 2.6e-50:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.0 - Float64(z * Float64(Float64(x + y) / y)))
	tmp = 0.0
	if (y <= -3.5e-40)
		tmp = t_0;
	elseif (y <= -2.55e-135)
		tmp = Float64(x + y);
	elseif (y <= 2.6e-50)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.0 - (z * ((x + y) / y));
	tmp = 0.0;
	if (y <= -3.5e-40)
		tmp = t_0;
	elseif (y <= -2.55e-135)
		tmp = x + y;
	elseif (y <= 2.6e-50)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.0 - N[(z * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-40], t$95$0, If[LessEqual[y, -2.55e-135], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.6e-50], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000002e-40 or 2.6000000000000001e-50 < y

   1. Initial program 84.3%

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

      1. div-inv N/A

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

      2. flip3-- N/A

         \[\leadsto \left(x + y\right) \cdot \frac{1}{\frac{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}}} \]

      3. clear-num N/A

         \[\leadsto \left(x + y\right) \cdot \frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{\color{blue}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}} \]

      4. *-commutative N/A

         \[\leadsto \frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}} \cdot \color{blue}{\left(x + y\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}\right), \color{blue}{\left(x + y\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{{1}^{3} - {\left(\frac{y}{z}\right)}^{3}}{1 \cdot 1 + \left(\frac{y}{z} \cdot \frac{y}{z} + 1 \cdot \frac{y}{z}\right)}}\right), \left(\color{blue}{x} + y\right)\right) \]

      7. flip3-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{1 - \frac{y}{z}}\right), \left(x + y\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(1 - \frac{y}{z}\right)\right), \left(\color{blue}{x} + y\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \left(\frac{y}{z}\right)\right)\right), \left(x + y\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right), \left(x + y\right)\right) \]

      11. +-lowering-+.f64 84.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right) \]

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{z \cdot \left(x + y\right)}{y}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(z \cdot \color{blue}{\frac{x + y}{y}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{x + y}{y}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(x + y\right), \color{blue}{y}\right)\right)\right) \]

      7. +-lowering-+.f64 71.7%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, y\right), y\right)\right)\right) \]

   7. Simplified 71.7%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{x + y}{y}\right)\right), \color{blue}{z}\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(\frac{x + y}{y}\right)\right), z\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(x + y\right), y\right)\right), z\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(y + x\right), y\right)\right), z\right) \]

      8. +-lowering-+.f64 71.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(y, x\right), y\right)\right), z\right) \]

   9. Applied egg-rr 71.7%

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

   if -3.5000000000000002e-40 < y < -2.5500000000000001e-135

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 81.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 81.8%

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

   if -2.5500000000000001e-135 < y < 2.6000000000000001e-50

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 86.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 86.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-40}:\\ \;\;\;\;0 - z \cdot \frac{x + y}{y}\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;0 - z \cdot \frac{x + y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+130}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+130)
   (- 0.0 z)
   (if (<= y -6e-136)
     (+ x y)
     (if (<= y 6.6e+77) (/ x (- 1.0 (/ y z))) (- 0.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+130) {
		tmp = 0.0 - z;
	} else if (y <= -6e-136) {
		tmp = x + y;
	} else if (y <= 6.6e+77) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9d+130)) then
        tmp = 0.0d0 - z
    else if (y <= (-6d-136)) then
        tmp = x + y
    else if (y <= 6.6d+77) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+130) {
		tmp = 0.0 - z;
	} else if (y <= -6e-136) {
		tmp = x + y;
	} else if (y <= 6.6e+77) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+130:
		tmp = 0.0 - z
	elif y <= -6e-136:
		tmp = x + y
	elif y <= 6.6e+77:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+130)
		tmp = Float64(0.0 - z);
	elseif (y <= -6e-136)
		tmp = Float64(x + y);
	elseif (y <= 6.6e+77)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e+130)
		tmp = 0.0 - z;
	elseif (y <= -6e-136)
		tmp = x + y;
	elseif (y <= 6.6e+77)
		tmp = x / (1.0 - (y / z));
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+130], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, -6e-136], N[(x + y), $MachinePrecision], If[LessEqual[y, 6.6e+77], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000078e130 or 6.5999999999999996e77 < y

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 74.2%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 74.2%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 74.2%

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

   if -9.00000000000000078e130 < y < -5.9999999999999996e-136

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 56.2%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 56.2%

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

   if -5.9999999999999996e-136 < y < 6.5999999999999996e77

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 - \frac{y}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 77.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 77.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+130}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+132}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+132) (- 0.0 z) (if (<= y 3.4e+86) (+ x y) (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+132) {
		tmp = 0.0 - z;
	} else if (y <= 3.4e+86) {
		tmp = x + y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4d+132)) then
        tmp = 0.0d0 - z
    else if (y <= 3.4d+86) then
        tmp = x + y
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+132) {
		tmp = 0.0 - z;
	} else if (y <= 3.4e+86) {
		tmp = x + y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e+132:
		tmp = 0.0 - z
	elif y <= 3.4e+86:
		tmp = x + y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+132)
		tmp = Float64(0.0 - z);
	elseif (y <= 3.4e+86)
		tmp = Float64(x + y);
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4e+132)
		tmp = 0.0 - z;
	elseif (y <= 3.4e+86)
		tmp = x + y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+132], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 3.4e+86], N[(x + y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999996e132 or 3.3999999999999998e86 < y

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 74.2%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 74.2%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 74.2%

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

   if -3.99999999999999996e132 < y < 3.3999999999999998e86

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 66.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 66.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+132}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e-39) (- 0.0 z) (if (<= y 2.55e-52) x (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e-39) {
		tmp = 0.0 - z;
	} else if (y <= 2.55e-52) {
		tmp = x;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2d-39)) then
        tmp = 0.0d0 - z
    else if (y <= 2.55d-52) then
        tmp = x
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e-39) {
		tmp = 0.0 - z;
	} else if (y <= 2.55e-52) {
		tmp = x;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e-39:
		tmp = 0.0 - z
	elif y <= 2.55e-52:
		tmp = x
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e-39)
		tmp = Float64(0.0 - z);
	elseif (y <= 2.55e-52)
		tmp = x;
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e-39)
		tmp = 0.0 - z;
	elseif (y <= 2.55e-52)
		tmp = x;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e-39], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 2.55e-52], x, N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999986e-39 or 2.54999999999999995e-52 < y

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 52.5%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 52.5%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 52.5%

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

   if -1.99999999999999986e-39 < y < 2.54999999999999995e-52

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 65.2%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-155}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e-215) x (if (<= x 3.6e-155) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e-215) {
		tmp = x;
	} else if (x <= 3.6e-155) {
		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 <= (-1.6d-215)) then
        tmp = x
    else if (x <= 3.6d-155) 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 <= -1.6e-215) {
		tmp = x;
	} else if (x <= 3.6e-155) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e-215:
		tmp = x
	elif x <= 3.6e-155:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e-215)
		tmp = x;
	elseif (x <= 3.6e-155)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e-215)
		tmp = x;
	elseif (x <= 3.6e-155)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e-215], x, If[LessEqual[x, 3.6e-155], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e-215 or 3.59999999999999989e-155 < x

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 42.0%

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

   if -1.6000000000000001e-215 < x < 3.59999999999999989e-155

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 58.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 58.9%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 51.7%

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

Alternative 8: 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 91.3%

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

3. Taylor expanded in y around 0

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

5. Simplified 35.8%

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

Developer Target 1: 93.5% 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 2024150 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -3742931076268985600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (/ (+ y x) (- y)) z) (if (< y 3553466245608673400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z))))

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