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

Percentage Accurate: 87.6% → 99.8%

Time: 6.3s

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: 87.6% 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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-289} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-289) (not (<= t_0 0.0))) t_0 (/ (- z) (/ y (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-289) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-289)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-289) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-289) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-289) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-289) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-289], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1e-289 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1e-289 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 6.5%

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

   3. Taylor expanded in z around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-/l* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. distribute-neg-frac2 99.9%

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

      5. +-commutative 99.9%

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

   5. Simplified 99.9%

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

      1. associate-*r/ 99.8%

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

      2. distribute-frac-neg2 99.8%

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

      3. add-sqr-sqrt 52.4%

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

      4. sqrt-unprod 25.5%

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

      5. sqr-neg 25.5%

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

      6. sqrt-unprod 2.4%

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

      7. add-sqr-sqrt 5.0%

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

      8. associate-*r/ 5.0%

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

      9. clear-num 5.0%

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

      10. un-div-inv 5.0%

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

      11. add-sqr-sqrt 2.4%

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

      12. sqrt-unprod 25.4%

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

      13. sqr-neg 25.4%

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

      14. sqrt-unprod 52.5%

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

      15. add-sqr-sqrt 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-289} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{1}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* z (- -1.0 (/ x y)))))
   (if (<= y -3.8e+19)
     t_1
     (if (<= y 2.25e-51)
       (+ x y)
       (if (<= y 1.2e+17)
         (/ x t_0)
         (if (<= y 1.7e+139) (* y (/ 1.0 t_0)) 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 <= -3.8e+19) {
		tmp = t_1;
	} else if (y <= 2.25e-51) {
		tmp = x + y;
	} else if (y <= 1.2e+17) {
		tmp = x / t_0;
	} else if (y <= 1.7e+139) {
		tmp = y * (1.0 / t_0);
	} 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 <= (-3.8d+19)) then
        tmp = t_1
    else if (y <= 2.25d-51) then
        tmp = x + y
    else if (y <= 1.2d+17) then
        tmp = x / t_0
    else if (y <= 1.7d+139) then
        tmp = y * (1.0d0 / t_0)
    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 <= -3.8e+19) {
		tmp = t_1;
	} else if (y <= 2.25e-51) {
		tmp = x + y;
	} else if (y <= 1.2e+17) {
		tmp = x / t_0;
	} else if (y <= 1.7e+139) {
		tmp = y * (1.0 / t_0);
	} 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 <= -3.8e+19:
		tmp = t_1
	elif y <= 2.25e-51:
		tmp = x + y
	elif y <= 1.2e+17:
		tmp = x / t_0
	elif y <= 1.7e+139:
		tmp = y * (1.0 / t_0)
	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 <= -3.8e+19)
		tmp = t_1;
	elseif (y <= 2.25e-51)
		tmp = Float64(x + y);
	elseif (y <= 1.2e+17)
		tmp = Float64(x / t_0);
	elseif (y <= 1.7e+139)
		tmp = Float64(y * Float64(1.0 / t_0));
	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 <= -3.8e+19)
		tmp = t_1;
	elseif (y <= 2.25e-51)
		tmp = x + y;
	elseif (y <= 1.2e+17)
		tmp = x / t_0;
	elseif (y <= 1.7e+139)
		tmp = y * (1.0 / t_0);
	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, -3.8e+19], t$95$1, If[LessEqual[y, 2.25e-51], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.2e+17], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 1.7e+139], N[(y * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8e19 or 1.7000000000000001e139 < y

   1. Initial program 63.5%

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

   3. Taylor expanded in z around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. distribute-neg-frac2 88.5%

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

      5. +-commutative 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in z around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 88.5%

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

      3. +-commutative 88.5%

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

      4. distribute-rgt-neg-in 88.5%

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

      5. neg-sub0 88.5%

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

      6. *-lft-identity 88.5%

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

      7. associate-*l/ 88.3%

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

      8. distribute-rgt-in 88.3%

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

      9. rgt-mult-inverse 88.5%

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

      10. associate-*r/ 88.5%

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

      11. *-rgt-identity 88.5%

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

      12. associate--r+ 88.5%

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

      13. metadata-eval 88.5%

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

   8. Simplified 88.5%

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

   if -3.8e19 < y < 2.24999999999999987e-51

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if 2.24999999999999987e-51 < y < 1.2e17

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 76.5%

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

   if 1.2e17 < y < 1.7000000000000001e139

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 76.8%

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

      1. clear-num 76.6%

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

      2. associate-/r/ 76.8%

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

   5. Applied egg-rr 76.8%

      \[\leadsto \color{blue}{\frac{1}{1 - \frac{y}{z}} \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{1}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-52}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3600000000:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* z (- -1.0 (/ x y)))))
   (if (<= y -2e+21)
     t_1
     (if (<= y 8.2e-52)
       (+ x y)
       (if (<= y 3600000000.0)
         (/ x t_0)
         (if (<= y 1.7e+139) (/ y t_0) 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 <= -2e+21) {
		tmp = t_1;
	} else if (y <= 8.2e-52) {
		tmp = x + y;
	} else if (y <= 3600000000.0) {
		tmp = x / t_0;
	} else if (y <= 1.7e+139) {
		tmp = y / t_0;
	} 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 <= (-2d+21)) then
        tmp = t_1
    else if (y <= 8.2d-52) then
        tmp = x + y
    else if (y <= 3600000000.0d0) then
        tmp = x / t_0
    else if (y <= 1.7d+139) then
        tmp = y / t_0
    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 <= -2e+21) {
		tmp = t_1;
	} else if (y <= 8.2e-52) {
		tmp = x + y;
	} else if (y <= 3600000000.0) {
		tmp = x / t_0;
	} else if (y <= 1.7e+139) {
		tmp = y / t_0;
	} 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 <= -2e+21:
		tmp = t_1
	elif y <= 8.2e-52:
		tmp = x + y
	elif y <= 3600000000.0:
		tmp = x / t_0
	elif y <= 1.7e+139:
		tmp = y / t_0
	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 <= -2e+21)
		tmp = t_1;
	elseif (y <= 8.2e-52)
		tmp = Float64(x + y);
	elseif (y <= 3600000000.0)
		tmp = Float64(x / t_0);
	elseif (y <= 1.7e+139)
		tmp = Float64(y / t_0);
	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 <= -2e+21)
		tmp = t_1;
	elseif (y <= 8.2e-52)
		tmp = x + y;
	elseif (y <= 3600000000.0)
		tmp = x / t_0;
	elseif (y <= 1.7e+139)
		tmp = y / t_0;
	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, -2e+21], t$95$1, If[LessEqual[y, 8.2e-52], N[(x + y), $MachinePrecision], If[LessEqual[y, 3600000000.0], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 1.7e+139], N[(y / t$95$0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2e21 or 1.7000000000000001e139 < y

   1. Initial program 63.5%

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

   3. Taylor expanded in z around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. distribute-neg-frac2 88.5%

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

      5. +-commutative 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in z around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 88.5%

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

      3. +-commutative 88.5%

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

      4. distribute-rgt-neg-in 88.5%

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

      5. neg-sub0 88.5%

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

      6. *-lft-identity 88.5%

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

      7. associate-*l/ 88.3%

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

      8. distribute-rgt-in 88.3%

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

      9. rgt-mult-inverse 88.5%

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

      10. associate-*r/ 88.5%

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

      11. *-rgt-identity 88.5%

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

      12. associate--r+ 88.5%

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

      13. metadata-eval 88.5%

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

   8. Simplified 88.5%

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

   if -2e21 < y < 8.19999999999999977e-52

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   if 8.19999999999999977e-52 < y < 3.6e9

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 76.5%

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

   if 3.6e9 < y < 1.7000000000000001e139

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 76.8%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-52}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3600000000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+21} \lor \neg \left(y \leq 1.1 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.7e+21) (not (<= y 1.1e+47))) (* z (- -1.0 (/ x y))) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e+21) || !(y <= 1.1e+47)) {
		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 <= (-1.7d+21)) .or. (.not. (y <= 1.1d+47))) 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 <= -1.7e+21) || !(y <= 1.1e+47)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.7e+21) or not (y <= 1.1e+47):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.7e+21) || !(y <= 1.1e+47))
		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 <= -1.7e+21) || ~((y <= 1.1e+47)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.7e+21], N[Not[LessEqual[y, 1.1e+47]], $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 < -1.7e21 or 1.1e47 < y

   1. Initial program 69.8%

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

   3. Taylor expanded in z around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. associate-/l* 81.4%

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

      3. distribute-rgt-neg-in 81.4%

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

      4. distribute-neg-frac2 81.4%

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

      5. +-commutative 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in z around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. associate-/l* 81.4%

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

      3. +-commutative 81.4%

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

      4. distribute-rgt-neg-in 81.4%

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

      5. neg-sub0 81.4%

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

      6. *-lft-identity 81.4%

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

      7. associate-*l/ 81.3%

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

      8. distribute-rgt-in 81.3%

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

      9. rgt-mult-inverse 81.4%

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

      10. associate-*r/ 81.5%

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

      11. *-rgt-identity 81.5%

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

      12. associate--r+ 81.5%

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

      13. metadata-eval 81.5%

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

   8. Simplified 81.5%

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

   if -1.7e21 < y < 1.1e47

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.8%

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

      1. +-commutative 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+21} \lor \neg \left(y \leq 1.1 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.68:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.9) (- z) (if (<= y 0.68) x (if (<= y 1.45e+47) y (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9) {
		tmp = -z;
	} else if (y <= 0.68) {
		tmp = x;
	} else if (y <= 1.45e+47) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.9d0)) then
        tmp = -z
    else if (y <= 0.68d0) then
        tmp = x
    else if (y <= 1.45d+47) then
        tmp = y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9) {
		tmp = -z;
	} else if (y <= 0.68) {
		tmp = x;
	} else if (y <= 1.45e+47) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.9:
		tmp = -z
	elif y <= 0.68:
		tmp = x
	elif y <= 1.45e+47:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.9)
		tmp = Float64(-z);
	elseif (y <= 0.68)
		tmp = x;
	elseif (y <= 1.45e+47)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.9)
		tmp = -z;
	elseif (y <= 0.68)
		tmp = x;
	elseif (y <= 1.45e+47)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.9], (-z), If[LessEqual[y, 0.68], x, If[LessEqual[y, 1.45e+47], y, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.89999999999999991 or 1.4499999999999999e47 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 65.6%

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

      1. neg-mul-1 65.6%

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

   5. Simplified 65.6%

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

   if -3.89999999999999991 < y < 0.680000000000000049

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 58.7%

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

   if 0.680000000000000049 < y < 1.4499999999999999e47

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.8%

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

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in y around inf 64.2%

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

Alternative 6: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+21} \lor \neg \left(y \leq 1.3 \cdot 10^{+88}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+21) (not (<= y 1.3e+88))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+21) || !(y <= 1.3e+88)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.5d+21)) .or. (.not. (y <= 1.3d+88))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+21) || !(y <= 1.3e+88)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e+21) or not (y <= 1.3e+88):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e+21) || !(y <= 1.3e+88))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e+21) || ~((y <= 1.3e+88)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e+21], N[Not[LessEqual[y, 1.3e+88]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e21 or 1.3e88 < y

   1. Initial program 65.5%

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

   3. Taylor expanded in y around inf 73.1%

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

      1. neg-mul-1 73.1%

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

   5. Simplified 73.1%

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

   if -6.5e21 < y < 1.3e88

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. +-commutative 71.9%

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

   5. Simplified 71.9%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+21} \lor \neg \left(y \leq 1.3 \cdot 10^{+88}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-196}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.6e-89) x (if (<= x 1.75e-196) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.6e-89) {
		tmp = x;
	} else if (x <= 1.75e-196) {
		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 <= (-7.6d-89)) then
        tmp = x
    else if (x <= 1.75d-196) 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 <= -7.6e-89) {
		tmp = x;
	} else if (x <= 1.75e-196) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.6e-89:
		tmp = x
	elif x <= 1.75e-196:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.6e-89)
		tmp = x;
	elseif (x <= 1.75e-196)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.6e-89)
		tmp = x;
	elseif (x <= 1.75e-196)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.6e-89], x, If[LessEqual[x, 1.75e-196], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000002e-89 or 1.75000000000000002e-196 < x

   1. Initial program 86.5%

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

   3. Taylor expanded in y around 0 44.4%

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

   if -7.6000000000000002e-89 < x < 1.75000000000000002e-196

   1. Initial program 89.9%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. +-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y around inf 45.1%

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

Alternative 8: 35.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 87.5%

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

3. Taylor expanded in y around 0 35.5%

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

Developer Target 1: 93.2% 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 2024144 
(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))))