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

Percentage Accurate: 87.6% → 99.6%

Time: 6.2s

Alternatives: 12

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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-272} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-272) (not (<= t_0 0.0))) t_0 (- (- z) (/ (* x z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-272) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((x * z) / 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 <= (-5d-272)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - ((x * z) / 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 <= -5e-272) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-272) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - ((x * z) / 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 <= -5e-272) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / 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 <= -5e-272) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - ((x * z) / 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, -5e-272], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.99999999999999982e-272 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 -4.99999999999999982e-272 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 13.3%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \color{blue}{-1 \cdot z + \left(-1 \cdot \frac{x \cdot z}{y} - \frac{{z}^{2}}{y}\right)} \]

      2. associate-*r/ 100.0%

         \[\leadsto -1 \cdot z + \left(\color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{y}} - \frac{{z}^{2}}{y}\right) \]

      3. div-sub 100.0%

         \[\leadsto -1 \cdot z + \color{blue}{\frac{-1 \cdot \left(x \cdot z\right) - {z}^{2}}{y}} \]

      4. remove-double-neg 100.0%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \color{blue}{\left(-\left(-{z}^{2}\right)\right)}}{y} \]

      5. mul-1-neg 100.0%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \left(-\color{blue}{-1 \cdot {z}^{2}}\right)}{y} \]

      6. neg-mul-1 100.0%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \color{blue}{-1 \cdot \left(-1 \cdot {z}^{2}\right)}}{y} \]

      7. distribute-lft-out-- 100.0%

         \[\leadsto -1 \cdot z + \frac{\color{blue}{-1 \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}}{y} \]

      8. mul-1-neg 100.0%

         \[\leadsto -1 \cdot z + \frac{\color{blue}{-\left(x \cdot z - -1 \cdot {z}^{2}\right)}}{y} \]

      9. distribute-neg-frac 100.0%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)} \]

      10. unsub-neg 100.0%

          \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      11. mul-1-neg 100.0%

          \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z - -1 \cdot {z}^{2}}{y} \]

      12. cancel-sign-sub-inv 100.0%

          \[\leadsto \left(-z\right) - \frac{\color{blue}{x \cdot z + \left(--1\right) \cdot {z}^{2}}}{y} \]

      13. metadata-eval 100.0%

          \[\leadsto \left(-z\right) - \frac{x \cdot z + \color{blue}{1} \cdot {z}^{2}}{y} \]

      14. *-lft-identity 100.0%

          \[\leadsto \left(-z\right) - \frac{x \cdot z + \color{blue}{{z}^{2}}}{y} \]

      15. +-commutative 100.0%

          \[\leadsto \left(-z\right) - \frac{\color{blue}{{z}^{2} + x \cdot z}}{y} \]

      16. unpow2 100.0%

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

      17. distribute-rgt-out 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-272} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{y}{t\_0}\\ t_2 := \frac{x}{t\_0}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+236}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ y t_0)) (t_2 (/ x t_0)))
   (if (<= y -2.6e+236)
     (- z)
     (if (<= y -5.5e+64)
       (/ (* z (+ x y)) (- y))
       (if (<= y -1.35e-14)
         t_1
         (if (<= y -2.8e-96)
           t_2
           (if (<= y -1.55e-147) (+ x y) (if (<= y 2.1e+22) t_2 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -2.6e+236) {
		tmp = -z;
	} else if (y <= -5.5e+64) {
		tmp = (z * (x + y)) / -y;
	} else if (y <= -1.35e-14) {
		tmp = t_1;
	} else if (y <= -2.8e-96) {
		tmp = t_2;
	} else if (y <= -1.55e-147) {
		tmp = x + y;
	} else if (y <= 2.1e+22) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = y / t_0
    t_2 = x / t_0
    if (y <= (-2.6d+236)) then
        tmp = -z
    else if (y <= (-5.5d+64)) then
        tmp = (z * (x + y)) / -y
    else if (y <= (-1.35d-14)) then
        tmp = t_1
    else if (y <= (-2.8d-96)) then
        tmp = t_2
    else if (y <= (-1.55d-147)) then
        tmp = x + y
    else if (y <= 2.1d+22) then
        tmp = t_2
    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 = y / t_0;
	double t_2 = x / t_0;
	double tmp;
	if (y <= -2.6e+236) {
		tmp = -z;
	} else if (y <= -5.5e+64) {
		tmp = (z * (x + y)) / -y;
	} else if (y <= -1.35e-14) {
		tmp = t_1;
	} else if (y <= -2.8e-96) {
		tmp = t_2;
	} else if (y <= -1.55e-147) {
		tmp = x + y;
	} else if (y <= 2.1e+22) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = y / t_0
	t_2 = x / t_0
	tmp = 0
	if y <= -2.6e+236:
		tmp = -z
	elif y <= -5.5e+64:
		tmp = (z * (x + y)) / -y
	elif y <= -1.35e-14:
		tmp = t_1
	elif y <= -2.8e-96:
		tmp = t_2
	elif y <= -1.55e-147:
		tmp = x + y
	elif y <= 2.1e+22:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(y / t_0)
	t_2 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -2.6e+236)
		tmp = Float64(-z);
	elseif (y <= -5.5e+64)
		tmp = Float64(Float64(z * Float64(x + y)) / Float64(-y));
	elseif (y <= -1.35e-14)
		tmp = t_1;
	elseif (y <= -2.8e-96)
		tmp = t_2;
	elseif (y <= -1.55e-147)
		tmp = Float64(x + y);
	elseif (y <= 2.1e+22)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = y / t_0;
	t_2 = x / t_0;
	tmp = 0.0;
	if (y <= -2.6e+236)
		tmp = -z;
	elseif (y <= -5.5e+64)
		tmp = (z * (x + y)) / -y;
	elseif (y <= -1.35e-14)
		tmp = t_1;
	elseif (y <= -2.8e-96)
		tmp = t_2;
	elseif (y <= -1.55e-147)
		tmp = x + y;
	elseif (y <= 2.1e+22)
		tmp = t_2;
	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[(y / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -2.6e+236], (-z), If[LessEqual[y, -5.5e+64], N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, -1.35e-14], t$95$1, If[LessEqual[y, -2.8e-96], t$95$2, If[LessEqual[y, -1.55e-147], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.1e+22], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.6e236

   1. Initial program 57.0%

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

   3. Taylor expanded in y around inf 88.6%

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

      1. mul-1-neg 88.6%

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

   5. Simplified 88.6%

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

   if -2.6e236 < y < -5.4999999999999996e64

   1. Initial program 67.6%

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

   3. Taylor expanded in z around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. +-commutative 82.5%

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

   5. Simplified 82.5%

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

   if -5.4999999999999996e64 < y < -1.3499999999999999e-14 or 2.0999999999999998e22 < y

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 66.8%

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

   if -1.3499999999999999e-14 < y < -2.80000000000000015e-96 or -1.5500000000000001e-147 < y < 2.0999999999999998e22

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.9%

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

   if -2.80000000000000015e-96 < y < -1.5500000000000001e-147

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.6%

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

      1. +-commutative 86.6%

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

   5. Simplified 86.6%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+236}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{-y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \left(-z\right) \cdot \frac{x + y}{y}\\ t_2 := \frac{x}{t\_0}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 340:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (* (- z) (/ (+ x y) y))) (t_2 (/ x t_0)))
   (if (<= y -2.2e+62)
     t_1
     (if (<= y -4.4e-15)
       (/ y t_0)
       (if (<= y -1.8e-92)
         t_2
         (if (<= y -1.14e-147) (+ x y) (if (<= y 340.0) t_2 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = -z * ((x + y) / y);
	double t_2 = x / t_0;
	double tmp;
	if (y <= -2.2e+62) {
		tmp = t_1;
	} else if (y <= -4.4e-15) {
		tmp = y / t_0;
	} else if (y <= -1.8e-92) {
		tmp = t_2;
	} else if (y <= -1.14e-147) {
		tmp = x + y;
	} else if (y <= 340.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = -z * ((x + y) / y)
    t_2 = x / t_0
    if (y <= (-2.2d+62)) then
        tmp = t_1
    else if (y <= (-4.4d-15)) then
        tmp = y / t_0
    else if (y <= (-1.8d-92)) then
        tmp = t_2
    else if (y <= (-1.14d-147)) then
        tmp = x + y
    else if (y <= 340.0d0) then
        tmp = t_2
    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 * ((x + y) / y);
	double t_2 = x / t_0;
	double tmp;
	if (y <= -2.2e+62) {
		tmp = t_1;
	} else if (y <= -4.4e-15) {
		tmp = y / t_0;
	} else if (y <= -1.8e-92) {
		tmp = t_2;
	} else if (y <= -1.14e-147) {
		tmp = x + y;
	} else if (y <= 340.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = -z * ((x + y) / y)
	t_2 = x / t_0
	tmp = 0
	if y <= -2.2e+62:
		tmp = t_1
	elif y <= -4.4e-15:
		tmp = y / t_0
	elif y <= -1.8e-92:
		tmp = t_2
	elif y <= -1.14e-147:
		tmp = x + y
	elif y <= 340.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(Float64(-z) * Float64(Float64(x + y) / y))
	t_2 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -2.2e+62)
		tmp = t_1;
	elseif (y <= -4.4e-15)
		tmp = Float64(y / t_0);
	elseif (y <= -1.8e-92)
		tmp = t_2;
	elseif (y <= -1.14e-147)
		tmp = Float64(x + y);
	elseif (y <= 340.0)
		tmp = t_2;
	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 * ((x + y) / y);
	t_2 = x / t_0;
	tmp = 0.0;
	if (y <= -2.2e+62)
		tmp = t_1;
	elseif (y <= -4.4e-15)
		tmp = y / t_0;
	elseif (y <= -1.8e-92)
		tmp = t_2;
	elseif (y <= -1.14e-147)
		tmp = x + y;
	elseif (y <= 340.0)
		tmp = t_2;
	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[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -2.2e+62], t$95$1, If[LessEqual[y, -4.4e-15], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -1.8e-92], t$95$2, If[LessEqual[y, -1.14e-147], N[(x + y), $MachinePrecision], If[LessEqual[y, 340.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.20000000000000015e62 or 340 < y

   1. Initial program 72.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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* 77.9%

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

      3. distribute-rgt-neg-in 77.9%

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

      4. distribute-neg-frac2 77.9%

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

      5. +-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -2.20000000000000015e62 < y < -4.39999999999999971e-15

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 72.8%

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

   if -4.39999999999999971e-15 < y < -1.80000000000000008e-92 or -1.14e-147 < y < 340

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.2%

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

   if -1.80000000000000008e-92 < y < -1.14e-147

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. +-commutative 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+62}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 340:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+62}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{-1}{\frac{y}{z} + -1}\\ \mathbf{elif}\;y \leq -1.24 \cdot 10^{-147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2500:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -1.4e+62)
     (* (- z) (/ (+ x y) y))
     (if (<= y -4.3e-14)
       (/ y t_0)
       (if (<= y -9.5e-94)
         (* x (/ -1.0 (+ (/ y z) -1.0)))
         (if (<= y -1.24e-147)
           (+ x y)
           (if (<= y 2500.0) (/ x t_0) (* 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 <= -1.4e+62) {
		tmp = -z * ((x + y) / y);
	} else if (y <= -4.3e-14) {
		tmp = y / t_0;
	} else if (y <= -9.5e-94) {
		tmp = x * (-1.0 / ((y / z) + -1.0));
	} else if (y <= -1.24e-147) {
		tmp = x + y;
	} else if (y <= 2500.0) {
		tmp = x / 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 = 1.0d0 - (y / z)
    if (y <= (-1.4d+62)) then
        tmp = -z * ((x + y) / y)
    else if (y <= (-4.3d-14)) then
        tmp = y / t_0
    else if (y <= (-9.5d-94)) then
        tmp = x * ((-1.0d0) / ((y / z) + (-1.0d0)))
    else if (y <= (-1.24d-147)) then
        tmp = x + y
    else if (y <= 2500.0d0) then
        tmp = x / 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 = 1.0 - (y / z);
	double tmp;
	if (y <= -1.4e+62) {
		tmp = -z * ((x + y) / y);
	} else if (y <= -4.3e-14) {
		tmp = y / t_0;
	} else if (y <= -9.5e-94) {
		tmp = x * (-1.0 / ((y / z) + -1.0));
	} else if (y <= -1.24e-147) {
		tmp = x + y;
	} else if (y <= 2500.0) {
		tmp = x / t_0;
	} 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 <= -1.4e+62:
		tmp = -z * ((x + y) / y)
	elif y <= -4.3e-14:
		tmp = y / t_0
	elif y <= -9.5e-94:
		tmp = x * (-1.0 / ((y / z) + -1.0))
	elif y <= -1.24e-147:
		tmp = x + y
	elif y <= 2500.0:
		tmp = x / t_0
	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 <= -1.4e+62)
		tmp = Float64(Float64(-z) * Float64(Float64(x + y) / y));
	elseif (y <= -4.3e-14)
		tmp = Float64(y / t_0);
	elseif (y <= -9.5e-94)
		tmp = Float64(x * Float64(-1.0 / Float64(Float64(y / z) + -1.0)));
	elseif (y <= -1.24e-147)
		tmp = Float64(x + y);
	elseif (y <= 2500.0)
		tmp = Float64(x / 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 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -1.4e+62)
		tmp = -z * ((x + y) / y);
	elseif (y <= -4.3e-14)
		tmp = y / t_0;
	elseif (y <= -9.5e-94)
		tmp = x * (-1.0 / ((y / z) + -1.0));
	elseif (y <= -1.24e-147)
		tmp = x + y;
	elseif (y <= 2500.0)
		tmp = x / t_0;
	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, -1.4e+62], N[((-z) * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.3e-14], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -9.5e-94], N[(x * N[(-1.0 / N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.24e-147], N[(x + y), $MachinePrecision], If[LessEqual[y, 2500.0], N[(x / t$95$0), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.40000000000000007e62

   1. Initial program 63.9%

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

   3. Taylor expanded in z around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. associate-/l* 89.0%

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

      3. distribute-rgt-neg-in 89.0%

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

      4. distribute-neg-frac2 89.0%

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

      5. +-commutative 89.0%

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

   5. Simplified 89.0%

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

   if -1.40000000000000007e62 < y < -4.29999999999999998e-14

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 72.8%

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

   if -4.29999999999999998e-14 < y < -9.4999999999999997e-94

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 69.5%

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

      1. div-inv 69.5%

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

      2. *-commutative 69.5%

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

      3. frac-2neg 69.5%

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

      4. metadata-eval 69.5%

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

      5. sub-neg 69.5%

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

      6. distribute-neg-in 69.5%

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

      7. metadata-eval 69.5%

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

      8. distribute-neg-frac 69.5%

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

      9. distribute-frac-neg2 69.5%

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

      10. frac-2neg 69.5%

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

   5. Applied egg-rr 69.5%

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

   if -9.4999999999999997e-94 < y < -1.2400000000000001e-147

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. +-commutative 79.4%

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

   5. Simplified 79.4%

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

   if -1.2400000000000001e-147 < y < 2500

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 87.0%

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

   if 2500 < y

   1. Initial program 80.6%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. associate--l+ 60.9%

         \[\leadsto \color{blue}{-1 \cdot z + \left(-1 \cdot \frac{x \cdot z}{y} - \frac{{z}^{2}}{y}\right)} \]

      2. associate-*r/ 60.9%

         \[\leadsto -1 \cdot z + \left(\color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{y}} - \frac{{z}^{2}}{y}\right) \]

      3. div-sub 60.9%

         \[\leadsto -1 \cdot z + \color{blue}{\frac{-1 \cdot \left(x \cdot z\right) - {z}^{2}}{y}} \]

      4. remove-double-neg 60.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \color{blue}{\left(-\left(-{z}^{2}\right)\right)}}{y} \]

      5. mul-1-neg 60.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \left(-\color{blue}{-1 \cdot {z}^{2}}\right)}{y} \]

      6. neg-mul-1 60.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \color{blue}{-1 \cdot \left(-1 \cdot {z}^{2}\right)}}{y} \]

      7. distribute-lft-out-- 60.9%

         \[\leadsto -1 \cdot z + \frac{\color{blue}{-1 \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}}{y} \]

      8. mul-1-neg 60.9%

         \[\leadsto -1 \cdot z + \frac{\color{blue}{-\left(x \cdot z - -1 \cdot {z}^{2}\right)}}{y} \]

      9. distribute-neg-frac 60.9%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)} \]

      10. unsub-neg 60.9%

          \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      11. mul-1-neg 60.9%

          \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z - -1 \cdot {z}^{2}}{y} \]

      12. cancel-sign-sub-inv 60.9%

          \[\leadsto \left(-z\right) - \frac{\color{blue}{x \cdot z + \left(--1\right) \cdot {z}^{2}}}{y} \]

      13. metadata-eval 60.9%

          \[\leadsto \left(-z\right) - \frac{x \cdot z + \color{blue}{1} \cdot {z}^{2}}{y} \]

      14. *-lft-identity 60.9%

          \[\leadsto \left(-z\right) - \frac{x \cdot z + \color{blue}{{z}^{2}}}{y} \]

      15. +-commutative 60.9%

          \[\leadsto \left(-z\right) - \frac{\color{blue}{{z}^{2} + x \cdot z}}{y} \]

      16. unpow2 60.9%

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

      17. distribute-rgt-out 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in z around 0 67.7%

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

      1. associate-*r* 67.7%

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

      2. mul-1-neg 67.7%

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

   8. Simplified 67.7%

      \[\leadsto \color{blue}{\left(-z\right) \cdot \left(1 + \frac{x}{y}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+62}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{-1}{\frac{y}{z} + -1}\\ \mathbf{elif}\;y \leq -1.24 \cdot 10^{-147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2500:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t\_0}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+63}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 700:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= y -1.8e+63)
     (* (- z) (/ (+ x y) y))
     (if (<= y -3.5e-12)
       (/ y t_0)
       (if (<= y -1.36e-92)
         t_1
         (if (<= y -1.22e-147)
           (+ x y)
           (if (<= y 700.0) t_1 (* z (- -1.0 (/ x y))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (y <= -1.8e+63) {
		tmp = -z * ((x + y) / y);
	} else if (y <= -3.5e-12) {
		tmp = y / t_0;
	} else if (y <= -1.36e-92) {
		tmp = t_1;
	} else if (y <= -1.22e-147) {
		tmp = x + y;
	} else if (y <= 700.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (y <= (-1.8d+63)) then
        tmp = -z * ((x + y) / y)
    else if (y <= (-3.5d-12)) then
        tmp = y / t_0
    else if (y <= (-1.36d-92)) then
        tmp = t_1
    else if (y <= (-1.22d-147)) then
        tmp = x + y
    else if (y <= 700.0d0) then
        tmp = t_1
    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 t_1 = x / t_0;
	double tmp;
	if (y <= -1.8e+63) {
		tmp = -z * ((x + y) / y);
	} else if (y <= -3.5e-12) {
		tmp = y / t_0;
	} else if (y <= -1.36e-92) {
		tmp = t_1;
	} else if (y <= -1.22e-147) {
		tmp = x + y;
	} else if (y <= 700.0) {
		tmp = t_1;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if y <= -1.8e+63:
		tmp = -z * ((x + y) / y)
	elif y <= -3.5e-12:
		tmp = y / t_0
	elif y <= -1.36e-92:
		tmp = t_1
	elif y <= -1.22e-147:
		tmp = x + y
	elif y <= 700.0:
		tmp = t_1
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (y <= -1.8e+63)
		tmp = Float64(Float64(-z) * Float64(Float64(x + y) / y));
	elseif (y <= -3.5e-12)
		tmp = Float64(y / t_0);
	elseif (y <= -1.36e-92)
		tmp = t_1;
	elseif (y <= -1.22e-147)
		tmp = Float64(x + y);
	elseif (y <= 700.0)
		tmp = t_1;
	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);
	t_1 = x / t_0;
	tmp = 0.0;
	if (y <= -1.8e+63)
		tmp = -z * ((x + y) / y);
	elseif (y <= -3.5e-12)
		tmp = y / t_0;
	elseif (y <= -1.36e-92)
		tmp = t_1;
	elseif (y <= -1.22e-147)
		tmp = x + y;
	elseif (y <= 700.0)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[y, -1.8e+63], N[((-z) * N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-12], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, -1.36e-92], t$95$1, If[LessEqual[y, -1.22e-147], N[(x + y), $MachinePrecision], If[LessEqual[y, 700.0], t$95$1, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.79999999999999999e63

   1. Initial program 63.9%

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

   3. Taylor expanded in z around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. associate-/l* 89.0%

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

      3. distribute-rgt-neg-in 89.0%

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

      4. distribute-neg-frac2 89.0%

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

      5. +-commutative 89.0%

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

   5. Simplified 89.0%

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

   if -1.79999999999999999e63 < y < -3.5e-12

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 72.8%

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

   if -3.5e-12 < y < -1.36e-92 or -1.21999999999999995e-147 < y < 700

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.2%

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

   if -1.36e-92 < y < -1.21999999999999995e-147

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. +-commutative 79.4%

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

   5. Simplified 79.4%

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

   if 700 < y

   1. Initial program 80.6%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. associate--l+ 60.9%

         \[\leadsto \color{blue}{-1 \cdot z + \left(-1 \cdot \frac{x \cdot z}{y} - \frac{{z}^{2}}{y}\right)} \]

      2. associate-*r/ 60.9%

         \[\leadsto -1 \cdot z + \left(\color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{y}} - \frac{{z}^{2}}{y}\right) \]

      3. div-sub 60.9%

         \[\leadsto -1 \cdot z + \color{blue}{\frac{-1 \cdot \left(x \cdot z\right) - {z}^{2}}{y}} \]

      4. remove-double-neg 60.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \color{blue}{\left(-\left(-{z}^{2}\right)\right)}}{y} \]

      5. mul-1-neg 60.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \left(-\color{blue}{-1 \cdot {z}^{2}}\right)}{y} \]

      6. neg-mul-1 60.9%

         \[\leadsto -1 \cdot z + \frac{-1 \cdot \left(x \cdot z\right) - \color{blue}{-1 \cdot \left(-1 \cdot {z}^{2}\right)}}{y} \]

      7. distribute-lft-out-- 60.9%

         \[\leadsto -1 \cdot z + \frac{\color{blue}{-1 \cdot \left(x \cdot z - -1 \cdot {z}^{2}\right)}}{y} \]

      8. mul-1-neg 60.9%

         \[\leadsto -1 \cdot z + \frac{\color{blue}{-\left(x \cdot z - -1 \cdot {z}^{2}\right)}}{y} \]

      9. distribute-neg-frac 60.9%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z - -1 \cdot {z}^{2}}{y}\right)} \]

      10. unsub-neg 60.9%

          \[\leadsto \color{blue}{-1 \cdot z - \frac{x \cdot z - -1 \cdot {z}^{2}}{y}} \]

      11. mul-1-neg 60.9%

          \[\leadsto \color{blue}{\left(-z\right)} - \frac{x \cdot z - -1 \cdot {z}^{2}}{y} \]

      12. cancel-sign-sub-inv 60.9%

          \[\leadsto \left(-z\right) - \frac{\color{blue}{x \cdot z + \left(--1\right) \cdot {z}^{2}}}{y} \]

      13. metadata-eval 60.9%

          \[\leadsto \left(-z\right) - \frac{x \cdot z + \color{blue}{1} \cdot {z}^{2}}{y} \]

      14. *-lft-identity 60.9%

          \[\leadsto \left(-z\right) - \frac{x \cdot z + \color{blue}{{z}^{2}}}{y} \]

      15. +-commutative 60.9%

          \[\leadsto \left(-z\right) - \frac{\color{blue}{{z}^{2} + x \cdot z}}{y} \]

      16. unpow2 60.9%

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

      17. distribute-rgt-out 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in z around 0 67.7%

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

      1. associate-*r* 67.7%

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

      2. mul-1-neg 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+63}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x + y}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 700:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+52}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-148}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-177}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+52)
   (- z)
   (if (<= y -4.2e-148)
     (+ x y)
     (if (<= y -1.3e-177)
       (* (/ z y) (- x))
       (if (<= y 5.8e+69) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+52) {
		tmp = -z;
	} else if (y <= -4.2e-148) {
		tmp = x + y;
	} else if (y <= -1.3e-177) {
		tmp = (z / y) * -x;
	} else if (y <= 5.8e+69) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.25d+52)) then
        tmp = -z
    else if (y <= (-4.2d-148)) then
        tmp = x + y
    else if (y <= (-1.3d-177)) then
        tmp = (z / y) * -x
    else if (y <= 5.8d+69) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+52) {
		tmp = -z;
	} else if (y <= -4.2e-148) {
		tmp = x + y;
	} else if (y <= -1.3e-177) {
		tmp = (z / y) * -x;
	} else if (y <= 5.8e+69) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+52:
		tmp = -z
	elif y <= -4.2e-148:
		tmp = x + y
	elif y <= -1.3e-177:
		tmp = (z / y) * -x
	elif y <= 5.8e+69:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+52)
		tmp = Float64(-z);
	elseif (y <= -4.2e-148)
		tmp = Float64(x + y);
	elseif (y <= -1.3e-177)
		tmp = Float64(Float64(z / y) * Float64(-x));
	elseif (y <= 5.8e+69)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e+52)
		tmp = -z;
	elseif (y <= -4.2e-148)
		tmp = x + y;
	elseif (y <= -1.3e-177)
		tmp = (z / y) * -x;
	elseif (y <= 5.8e+69)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+52], (-z), If[LessEqual[y, -4.2e-148], N[(x + y), $MachinePrecision], If[LessEqual[y, -1.3e-177], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 5.8e+69], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e52 or 5.7999999999999997e69 < y

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. mul-1-neg 67.1%

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

   5. Simplified 67.1%

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

   if -1.25e52 < y < -4.2e-148 or -1.3e-177 < y < 5.7999999999999997e69

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 73.9%

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

      1. +-commutative 73.9%

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

   5. Simplified 73.9%

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

   if -4.2e-148 < y < -1.3e-177

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in y around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. associate-/l* 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

      4. distribute-neg-frac2 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+52}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-148}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-177}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-6} \lor \neg \left(y \leq 4.2 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -3.3e+64)
     (- z)
     (if (or (<= y -8.5e-6) (not (<= y 4.2e+22))) (/ y t_0) (/ x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.3e+64) {
		tmp = -z;
	} else if ((y <= -8.5e-6) || !(y <= 4.2e+22)) {
		tmp = y / t_0;
	} else {
		tmp = x / t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (y <= (-3.3d+64)) then
        tmp = -z
    else if ((y <= (-8.5d-6)) .or. (.not. (y <= 4.2d+22))) then
        tmp = y / t_0
    else
        tmp = x / t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.3e+64) {
		tmp = -z;
	} else if ((y <= -8.5e-6) || !(y <= 4.2e+22)) {
		tmp = y / t_0;
	} else {
		tmp = x / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -3.3e+64:
		tmp = -z
	elif (y <= -8.5e-6) or not (y <= 4.2e+22):
		tmp = y / t_0
	else:
		tmp = x / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -3.3e+64)
		tmp = Float64(-z);
	elseif ((y <= -8.5e-6) || !(y <= 4.2e+22))
		tmp = Float64(y / t_0);
	else
		tmp = Float64(x / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -3.3e+64)
		tmp = -z;
	elseif ((y <= -8.5e-6) || ~((y <= 4.2e+22)))
		tmp = y / t_0;
	else
		tmp = x / t_0;
	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, -3.3e+64], (-z), If[Or[LessEqual[y, -8.5e-6], N[Not[LessEqual[y, 4.2e+22]], $MachinePrecision]], N[(y / t$95$0), $MachinePrecision], N[(x / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.29999999999999988e64

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf 70.8%

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

      1. mul-1-neg 70.8%

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

   5. Simplified 70.8%

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

   if -3.29999999999999988e64 < y < -8.4999999999999999e-6 or 4.1999999999999996e22 < y

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0 67.6%

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

   if -8.4999999999999999e-6 < y < 4.1999999999999996e22

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-6} \lor \neg \left(y \leq 4.2 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+22} \lor \neg \left(y \leq 5.6 \cdot 10^{+22}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.4e+22) (not (<= y 5.6e+22))) (- z) (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.4e+22) || !(y <= 5.6e+22)) {
		tmp = -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.4d+22)) .or. (.not. (y <= 5.6d+22))) then
        tmp = -z
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.4e+22) || !(y <= 5.6e+22)) {
		tmp = -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.4e+22) or not (y <= 5.6e+22):
		tmp = -z
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.4e+22) || !(y <= 5.6e+22))
		tmp = Float64(-z);
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.4e+22) || ~((y <= 5.6e+22)))
		tmp = -z;
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.4e+22], N[Not[LessEqual[y, 5.6e+22]], $MachinePrecision]], (-z), N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e22 or 5.6e22 < y

   1. Initial program 74.1%

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

   3. Taylor expanded in y around inf 62.9%

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

      1. mul-1-neg 62.9%

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

   5. Simplified 62.9%

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

   if -6.4e22 < y < 5.6e22

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+22} \lor \neg \left(y \leq 5.6 \cdot 10^{+22}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-118}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 21000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+45)
   (- z)
   (if (<= y -4.7e-118) y (if (<= y 21000.0) x (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+45) {
		tmp = -z;
	} else if (y <= -4.7e-118) {
		tmp = y;
	} else if (y <= 21000.0) {
		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 <= (-1.9d+45)) then
        tmp = -z
    else if (y <= (-4.7d-118)) then
        tmp = y
    else if (y <= 21000.0d0) 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 <= -1.9e+45) {
		tmp = -z;
	} else if (y <= -4.7e-118) {
		tmp = y;
	} else if (y <= 21000.0) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+45:
		tmp = -z
	elif y <= -4.7e-118:
		tmp = y
	elif y <= 21000.0:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+45)
		tmp = Float64(-z);
	elseif (y <= -4.7e-118)
		tmp = y;
	elseif (y <= 21000.0)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+45)
		tmp = -z;
	elseif (y <= -4.7e-118)
		tmp = y;
	elseif (y <= 21000.0)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+45], (-z), If[LessEqual[y, -4.7e-118], y, If[LessEqual[y, 21000.0], x, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000001e45 or 21000 < y

   1. Initial program 73.5%

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

   3. Taylor expanded in y around inf 63.4%

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

      1. mul-1-neg 63.4%

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

   5. Simplified 63.4%

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

   if -1.9000000000000001e45 < y < -4.69999999999999991e-118

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 54.7%

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

   4. Taylor expanded in y around 0 41.2%

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

   if -4.69999999999999991e-118 < y < 21000

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 72.4%

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

Alternative 10: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+52} \lor \neg \left(y \leq 5.9 \cdot 10^{+69}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.55e+52) (not (<= y 5.9e+69))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.55e+52) || !(y <= 5.9e+69)) {
		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 <= (-1.55d+52)) .or. (.not. (y <= 5.9d+69))) 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 <= -1.55e+52) || !(y <= 5.9e+69)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.55e+52) or not (y <= 5.9e+69):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.55e+52) || !(y <= 5.9e+69))
		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 <= -1.55e+52) || ~((y <= 5.9e+69)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.55e+52], N[Not[LessEqual[y, 5.9e+69]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e52 or 5.90000000000000004e69 < y

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. mul-1-neg 67.1%

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

   5. Simplified 67.1%

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

   if -1.55e52 < y < 5.90000000000000004e69

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 71.3%

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

      1. +-commutative 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+52} \lor \neg \left(y \leq 5.9 \cdot 10^{+69}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-118}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-118) y (if (<= y 1.16e+42) x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-118) {
		tmp = y;
	} else if (y <= 1.16e+42) {
		tmp = x;
	} else {
		tmp = 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 <= (-3.8d-118)) then
        tmp = y
    else if (y <= 1.16d+42) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-118) {
		tmp = y;
	} else if (y <= 1.16e+42) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e-118:
		tmp = y
	elif y <= 1.16e+42:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e-118)
		tmp = y;
	elseif (y <= 1.16e+42)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e-118)
		tmp = y;
	elseif (y <= 1.16e+42)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e-118], y, If[LessEqual[y, 1.16e+42], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000001e-118 or 1.15999999999999995e42 < y

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 0 58.8%

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

   4. Taylor expanded in y around 0 22.6%

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

   if -3.8000000000000001e-118 < y < 1.15999999999999995e42

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 69.0%

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

Alternative 12: 34.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 87.0%

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

3. Taylor expanded in y around 0 34.4%

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

Developer target: 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 2024097 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (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))))