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

Percentage Accurate: 87.6% → 99.8%

Time: 8.0s

Alternatives: 13

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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x + y}{t\_0}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-285} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\frac{y}{t\_0} + \frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ (+ x y) t_0)))
   (if (or (<= t_1 -1e-285) (not (<= t_1 0.0)))
     (+ (/ y t_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 t_1 = (x + y) / t_0;
	double tmp;
	if ((t_1 <= -1e-285) || !(t_1 <= 0.0)) {
		tmp = (y / t_0) + (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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = (x + y) / t_0
    if ((t_1 <= (-1d-285)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = (y / t_0) + (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 t_1 = (x + y) / t_0;
	double tmp;
	if ((t_1 <= -1e-285) || !(t_1 <= 0.0)) {
		tmp = (y / t_0) + (x / t_0);
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = (x + y) / t_0
	tmp = 0
	if (t_1 <= -1e-285) or not (t_1 <= 0.0):
		tmp = (y / t_0) + (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))
	t_1 = Float64(Float64(x + y) / t_0)
	tmp = 0.0
	if ((t_1 <= -1e-285) || !(t_1 <= 0.0))
		tmp = Float64(Float64(y / t_0) + 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);
	t_1 = (x + y) / t_0;
	tmp = 0.0;
	if ((t_1 <= -1e-285) || ~((t_1 <= 0.0)))
		tmp = (y / t_0) + (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]}, Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-285], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y / t$95$0), $MachinePrecision] + N[(x / t$95$0), $MachinePrecision]), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.00000000000000007e-285 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   if -1.00000000000000007e-285 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 15.1%

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

   3. Taylor expanded in z around 0 91.4%

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

      1. mul-1-neg 91.4%

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

      2. associate-/l* 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 91.4%

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

      1. mul-1-neg 91.4%

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

      2. associate-/l* 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. *-lft-identity 100.0%

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

      6. associate-*r/ 100.0%

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

      7. associate-*l/ 99.9%

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

      8. distribute-rgt-in 99.9%

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

      9. rgt-mult-inverse 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. unsub-neg 100.0%

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

      13. associate-*r/ 100.0%

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

      14. *-rgt-identity 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-285} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}} + \frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{-y}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+52}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;-z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- y)))))
   (if (<= y -7e+52)
     (- z)
     (if (<= y -4.6e-114)
       (+ x y)
       (if (<= y -5.7e-142)
         t_0
         (if (<= y 6.2e-92)
           (+ x y)
           (if (<= y 4.8e-58)
             t_0
             (if (<= y 2.05e-36)
               (+ x y)
               (if (<= y 95000000000.0)
                 (- (* z (/ x y)))
                 (if (<= y 1.55e+119) (+ x y) (- z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / -y);
	double tmp;
	if (y <= -7e+52) {
		tmp = -z;
	} else if (y <= -4.6e-114) {
		tmp = x + y;
	} else if (y <= -5.7e-142) {
		tmp = t_0;
	} else if (y <= 6.2e-92) {
		tmp = x + y;
	} else if (y <= 4.8e-58) {
		tmp = t_0;
	} else if (y <= 2.05e-36) {
		tmp = x + y;
	} else if (y <= 95000000000.0) {
		tmp = -(z * (x / y));
	} else if (y <= 1.55e+119) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x * (z / -y)
    if (y <= (-7d+52)) then
        tmp = -z
    else if (y <= (-4.6d-114)) then
        tmp = x + y
    else if (y <= (-5.7d-142)) then
        tmp = t_0
    else if (y <= 6.2d-92) then
        tmp = x + y
    else if (y <= 4.8d-58) then
        tmp = t_0
    else if (y <= 2.05d-36) then
        tmp = x + y
    else if (y <= 95000000000.0d0) then
        tmp = -(z * (x / y))
    else if (y <= 1.55d+119) 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 t_0 = x * (z / -y);
	double tmp;
	if (y <= -7e+52) {
		tmp = -z;
	} else if (y <= -4.6e-114) {
		tmp = x + y;
	} else if (y <= -5.7e-142) {
		tmp = t_0;
	} else if (y <= 6.2e-92) {
		tmp = x + y;
	} else if (y <= 4.8e-58) {
		tmp = t_0;
	} else if (y <= 2.05e-36) {
		tmp = x + y;
	} else if (y <= 95000000000.0) {
		tmp = -(z * (x / y));
	} else if (y <= 1.55e+119) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / -y)
	tmp = 0
	if y <= -7e+52:
		tmp = -z
	elif y <= -4.6e-114:
		tmp = x + y
	elif y <= -5.7e-142:
		tmp = t_0
	elif y <= 6.2e-92:
		tmp = x + y
	elif y <= 4.8e-58:
		tmp = t_0
	elif y <= 2.05e-36:
		tmp = x + y
	elif y <= 95000000000.0:
		tmp = -(z * (x / y))
	elif y <= 1.55e+119:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(-y)))
	tmp = 0.0
	if (y <= -7e+52)
		tmp = Float64(-z);
	elseif (y <= -4.6e-114)
		tmp = Float64(x + y);
	elseif (y <= -5.7e-142)
		tmp = t_0;
	elseif (y <= 6.2e-92)
		tmp = Float64(x + y);
	elseif (y <= 4.8e-58)
		tmp = t_0;
	elseif (y <= 2.05e-36)
		tmp = Float64(x + y);
	elseif (y <= 95000000000.0)
		tmp = Float64(-Float64(z * Float64(x / y)));
	elseif (y <= 1.55e+119)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / -y);
	tmp = 0.0;
	if (y <= -7e+52)
		tmp = -z;
	elseif (y <= -4.6e-114)
		tmp = x + y;
	elseif (y <= -5.7e-142)
		tmp = t_0;
	elseif (y <= 6.2e-92)
		tmp = x + y;
	elseif (y <= 4.8e-58)
		tmp = t_0;
	elseif (y <= 2.05e-36)
		tmp = x + y;
	elseif (y <= 95000000000.0)
		tmp = -(z * (x / y));
	elseif (y <= 1.55e+119)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+52], (-z), If[LessEqual[y, -4.6e-114], N[(x + y), $MachinePrecision], If[LessEqual[y, -5.7e-142], t$95$0, If[LessEqual[y, 6.2e-92], N[(x + y), $MachinePrecision], If[LessEqual[y, 4.8e-58], t$95$0, If[LessEqual[y, 2.05e-36], N[(x + y), $MachinePrecision], If[LessEqual[y, 95000000000.0], (-N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y, 1.55e+119], N[(x + y), $MachinePrecision], (-z)]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7e52 or 1.54999999999999998e119 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. mul-1-neg 69.3%

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

   5. Simplified 69.3%

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

   if -7e52 < y < -4.5999999999999999e-114 or -5.69999999999999995e-142 < y < 6.2000000000000002e-92 or 4.8000000000000001e-58 < y < 2.05000000000000006e-36 or 9.5e10 < y < 1.54999999999999998e119

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.3%

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

      1. +-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -4.5999999999999999e-114 < y < -5.69999999999999995e-142 or 6.2000000000000002e-92 < y < 4.8000000000000001e-58

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. associate-/l* 72.0%

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

      3. distribute-lft-neg-in 72.0%

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

      4. +-commutative 72.0%

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

   5. Simplified 72.0%

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

      1. clear-num 72.0%

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

      2. inv-pow 72.0%

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

   7. Applied egg-rr 72.0%

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

   8. Taylor expanded in y around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. associate-*r/ 79.9%

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

      3. distribute-lft-neg-in 79.9%

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

   10. Simplified 79.9%

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

   if 2.05000000000000006e-36 < y < 9.5e10

   1. Initial program 91.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* 82.5%

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

      3. distribute-lft-neg-in 82.5%

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

      4. +-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in y around 0 61.4%

      \[\leadsto \left(-z\right) \cdot \color{blue}{\frac{x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+52}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-36}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;-z \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-285} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-285) (not (<= t_0 0.0))) t_0 (* z (- -1.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-285) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-285)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-285) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-285) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-285) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-285) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-285], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.00000000000000007e-285 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1.00000000000000007e-285 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 15.1%

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

   3. Taylor expanded in z around 0 91.4%

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

      1. mul-1-neg 91.4%

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

      2. associate-/l* 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 91.4%

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

      1. mul-1-neg 91.4%

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

      2. associate-/l* 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. *-lft-identity 100.0%

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

      6. associate-*r/ 100.0%

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

      7. associate-*l/ 99.9%

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

      8. distribute-rgt-in 99.9%

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

      9. rgt-mult-inverse 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. unsub-neg 100.0%

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

      13. associate-*r/ 100.0%

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

      14. *-rgt-identity 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-285} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{-y}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-142}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 255000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- y)))))
   (if (<= y -1.9e+54)
     (- z)
     (if (<= y -4.6e-114)
       (+ x y)
       (if (<= y -5.7e-142)
         t_0
         (if (<= y 6.2e-92)
           (+ x y)
           (if (<= y 255000000000.0)
             t_0
             (if (<= y 1.65e+119) (+ x y) (- z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / -y);
	double tmp;
	if (y <= -1.9e+54) {
		tmp = -z;
	} else if (y <= -4.6e-114) {
		tmp = x + y;
	} else if (y <= -5.7e-142) {
		tmp = t_0;
	} else if (y <= 6.2e-92) {
		tmp = x + y;
	} else if (y <= 255000000000.0) {
		tmp = t_0;
	} else if (y <= 1.65e+119) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x * (z / -y)
    if (y <= (-1.9d+54)) then
        tmp = -z
    else if (y <= (-4.6d-114)) then
        tmp = x + y
    else if (y <= (-5.7d-142)) then
        tmp = t_0
    else if (y <= 6.2d-92) then
        tmp = x + y
    else if (y <= 255000000000.0d0) then
        tmp = t_0
    else if (y <= 1.65d+119) 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 t_0 = x * (z / -y);
	double tmp;
	if (y <= -1.9e+54) {
		tmp = -z;
	} else if (y <= -4.6e-114) {
		tmp = x + y;
	} else if (y <= -5.7e-142) {
		tmp = t_0;
	} else if (y <= 6.2e-92) {
		tmp = x + y;
	} else if (y <= 255000000000.0) {
		tmp = t_0;
	} else if (y <= 1.65e+119) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / -y)
	tmp = 0
	if y <= -1.9e+54:
		tmp = -z
	elif y <= -4.6e-114:
		tmp = x + y
	elif y <= -5.7e-142:
		tmp = t_0
	elif y <= 6.2e-92:
		tmp = x + y
	elif y <= 255000000000.0:
		tmp = t_0
	elif y <= 1.65e+119:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(-y)))
	tmp = 0.0
	if (y <= -1.9e+54)
		tmp = Float64(-z);
	elseif (y <= -4.6e-114)
		tmp = Float64(x + y);
	elseif (y <= -5.7e-142)
		tmp = t_0;
	elseif (y <= 6.2e-92)
		tmp = Float64(x + y);
	elseif (y <= 255000000000.0)
		tmp = t_0;
	elseif (y <= 1.65e+119)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / -y);
	tmp = 0.0;
	if (y <= -1.9e+54)
		tmp = -z;
	elseif (y <= -4.6e-114)
		tmp = x + y;
	elseif (y <= -5.7e-142)
		tmp = t_0;
	elseif (y <= 6.2e-92)
		tmp = x + y;
	elseif (y <= 255000000000.0)
		tmp = t_0;
	elseif (y <= 1.65e+119)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+54], (-z), If[LessEqual[y, -4.6e-114], N[(x + y), $MachinePrecision], If[LessEqual[y, -5.7e-142], t$95$0, If[LessEqual[y, 6.2e-92], N[(x + y), $MachinePrecision], If[LessEqual[y, 255000000000.0], t$95$0, If[LessEqual[y, 1.65e+119], N[(x + y), $MachinePrecision], (-z)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000001e54 or 1.6500000000000001e119 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. mul-1-neg 69.3%

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

   5. Simplified 69.3%

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

   if -1.9000000000000001e54 < y < -4.5999999999999999e-114 or -5.69999999999999995e-142 < y < 6.2000000000000002e-92 or 2.55e11 < y < 1.6500000000000001e119

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

   if -4.5999999999999999e-114 < y < -5.69999999999999995e-142 or 6.2000000000000002e-92 < y < 2.55e11

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 67.7%

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

      3. distribute-lft-neg-in 67.7%

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

      4. +-commutative 67.7%

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

   5. Simplified 67.7%

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

      1. clear-num 67.6%

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

      2. inv-pow 67.6%

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

   7. Applied egg-rr 67.6%

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

   8. Taylor expanded in y around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. associate-*r/ 59.6%

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

      3. distribute-lft-neg-in 59.6%

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

   10. Simplified 59.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 255000000000:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 90000000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+49)
   (- z)
   (if (<= y -4.6e-114)
     (+ x y)
     (if (<= y -5.7e-142)
       (* x (/ z (- y)))
       (if (<= y 6.2e-92)
         (+ x y)
         (if (<= y 90000000000.0)
           (/ (* x (- z)) y)
           (if (<= y 2.35e+119) (+ x y) (- z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+49) {
		tmp = -z;
	} else if (y <= -4.6e-114) {
		tmp = x + y;
	} else if (y <= -5.7e-142) {
		tmp = x * (z / -y);
	} else if (y <= 6.2e-92) {
		tmp = x + y;
	} else if (y <= 90000000000.0) {
		tmp = (x * -z) / y;
	} else if (y <= 2.35e+119) {
		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 <= (-6d+49)) then
        tmp = -z
    else if (y <= (-4.6d-114)) then
        tmp = x + y
    else if (y <= (-5.7d-142)) then
        tmp = x * (z / -y)
    else if (y <= 6.2d-92) then
        tmp = x + y
    else if (y <= 90000000000.0d0) then
        tmp = (x * -z) / y
    else if (y <= 2.35d+119) 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 <= -6e+49) {
		tmp = -z;
	} else if (y <= -4.6e-114) {
		tmp = x + y;
	} else if (y <= -5.7e-142) {
		tmp = x * (z / -y);
	} else if (y <= 6.2e-92) {
		tmp = x + y;
	} else if (y <= 90000000000.0) {
		tmp = (x * -z) / y;
	} else if (y <= 2.35e+119) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+49:
		tmp = -z
	elif y <= -4.6e-114:
		tmp = x + y
	elif y <= -5.7e-142:
		tmp = x * (z / -y)
	elif y <= 6.2e-92:
		tmp = x + y
	elif y <= 90000000000.0:
		tmp = (x * -z) / y
	elif y <= 2.35e+119:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+49)
		tmp = Float64(-z);
	elseif (y <= -4.6e-114)
		tmp = Float64(x + y);
	elseif (y <= -5.7e-142)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= 6.2e-92)
		tmp = Float64(x + y);
	elseif (y <= 90000000000.0)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (y <= 2.35e+119)
		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 <= -6e+49)
		tmp = -z;
	elseif (y <= -4.6e-114)
		tmp = x + y;
	elseif (y <= -5.7e-142)
		tmp = x * (z / -y);
	elseif (y <= 6.2e-92)
		tmp = x + y;
	elseif (y <= 90000000000.0)
		tmp = (x * -z) / y;
	elseif (y <= 2.35e+119)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+49], (-z), If[LessEqual[y, -4.6e-114], N[(x + y), $MachinePrecision], If[LessEqual[y, -5.7e-142], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-92], N[(x + y), $MachinePrecision], If[LessEqual[y, 90000000000.0], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.35e+119], N[(x + y), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.0000000000000005e49 or 2.35000000000000004e119 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. mul-1-neg 69.3%

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

   5. Simplified 69.3%

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

   if -6.0000000000000005e49 < y < -4.5999999999999999e-114 or -5.69999999999999995e-142 < y < 6.2000000000000002e-92 or 9e10 < y < 2.35000000000000004e119

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

   if -4.5999999999999999e-114 < y < -5.69999999999999995e-142

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. associate-/l* 80.1%

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

      3. distribute-lft-neg-in 80.1%

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

      4. +-commutative 80.1%

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

   5. Simplified 80.1%

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

      1. clear-num 80.4%

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

      2. inv-pow 80.4%

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

   7. Applied egg-rr 80.4%

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

   8. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. associate-*r/ 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if 6.2000000000000002e-92 < y < 9e10

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 69.1%

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

      1. mul-1-neg 69.1%

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

      2. associate-/l* 65.2%

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

      3. distribute-lft-neg-in 65.2%

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

      4. +-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around 0 48.7%

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

      1. *-commutative 48.7%

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

      2. frac-2neg 48.7%

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

      3. associate-*l/ 52.6%

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

      4. add-sqr-sqrt 19.6%

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

      5. sqrt-unprod 14.0%

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

      6. sqr-neg 14.0%

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

      7. sqrt-unprod 1.8%

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

      8. add-sqr-sqrt 2.7%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 52.6%

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

      11. sqr-neg 52.6%

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

      12. sqrt-unprod 52.5%

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

      13. add-sqr-sqrt 52.6%

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

   8. Applied egg-rr 52.6%

      \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot z}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-114}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 90000000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+32}:\\ \;\;\;\;\left(-z\right) - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= z -1.2e+117)
     (+ x y)
     (if (<= z -2.6e+27)
       (/ y t_0)
       (if (<= z -8.2e-51)
         (/ x t_0)
         (if (<= z 1.26e+32) (- (- z) (* x (/ z y))) (+ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (z <= -1.2e+117) {
		tmp = x + y;
	} else if (z <= -2.6e+27) {
		tmp = y / t_0;
	} else if (z <= -8.2e-51) {
		tmp = x / t_0;
	} else if (z <= 1.26e+32) {
		tmp = -z - (x * (z / 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (z <= (-1.2d+117)) then
        tmp = x + y
    else if (z <= (-2.6d+27)) then
        tmp = y / t_0
    else if (z <= (-8.2d-51)) then
        tmp = x / t_0
    else if (z <= 1.26d+32) then
        tmp = -z - (x * (z / y))
    else
        tmp = 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 (z <= -1.2e+117) {
		tmp = x + y;
	} else if (z <= -2.6e+27) {
		tmp = y / t_0;
	} else if (z <= -8.2e-51) {
		tmp = x / t_0;
	} else if (z <= 1.26e+32) {
		tmp = -z - (x * (z / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if z <= -1.2e+117:
		tmp = x + y
	elif z <= -2.6e+27:
		tmp = y / t_0
	elif z <= -8.2e-51:
		tmp = x / t_0
	elif z <= 1.26e+32:
		tmp = -z - (x * (z / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (z <= -1.2e+117)
		tmp = Float64(x + y);
	elseif (z <= -2.6e+27)
		tmp = Float64(y / t_0);
	elseif (z <= -8.2e-51)
		tmp = Float64(x / t_0);
	elseif (z <= 1.26e+32)
		tmp = Float64(Float64(-z) - Float64(x * Float64(z / y)));
	else
		tmp = 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 (z <= -1.2e+117)
		tmp = x + y;
	elseif (z <= -2.6e+27)
		tmp = y / t_0;
	elseif (z <= -8.2e-51)
		tmp = x / t_0;
	elseif (z <= 1.26e+32)
		tmp = -z - (x * (z / y));
	else
		tmp = 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[z, -1.2e+117], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.6e+27], N[(y / t$95$0), $MachinePrecision], If[LessEqual[z, -8.2e-51], N[(x / t$95$0), $MachinePrecision], If[LessEqual[z, 1.26e+32], N[((-z) - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1999999999999999e117 or 1.26e32 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. +-commutative 87.2%

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

   5. Simplified 87.2%

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

   if -1.1999999999999999e117 < z < -2.60000000000000009e27

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 76.3%

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

   if -2.60000000000000009e27 < z < -8.19999999999999947e-51

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.2%

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

   if -8.19999999999999947e-51 < z < 1.26e32

   1. Initial program 78.6%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/l* 75.2%

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

      3. distribute-lft-neg-in 75.2%

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

      4. +-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. distribute-lft-out 75.3%

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

      2. associate-/l* 75.8%

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

   8. Simplified 75.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z + x \cdot \frac{z}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+32}:\\ \;\;\;\;\left(-z\right) - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+115} \lor \neg \left(z \leq -2.3 \cdot 10^{+28}\right) \land \left(z \leq -9 \cdot 10^{-51} \lor \neg \left(z \leq 1.26 \cdot 10^{+32}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.4e+115)
         (and (not (<= z -2.3e+28)) (or (<= z -9e-51) (not (<= z 1.26e+32)))))
   (+ x y)
   (* z (- -1.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.4e+115) || (!(z <= -2.3e+28) && ((z <= -9e-51) || !(z <= 1.26e+32)))) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7.4d+115)) .or. (.not. (z <= (-2.3d+28))) .and. (z <= (-9d-51)) .or. (.not. (z <= 1.26d+32))) then
        tmp = x + y
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.4e+115) || (!(z <= -2.3e+28) && ((z <= -9e-51) || !(z <= 1.26e+32)))) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.4e+115) or (not (z <= -2.3e+28) and ((z <= -9e-51) or not (z <= 1.26e+32))):
		tmp = x + y
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.4e+115) || (!(z <= -2.3e+28) && ((z <= -9e-51) || !(z <= 1.26e+32))))
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.4e+115) || (~((z <= -2.3e+28)) && ((z <= -9e-51) || ~((z <= 1.26e+32)))))
		tmp = x + y;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.4e+115], And[N[Not[LessEqual[z, -2.3e+28]], $MachinePrecision], Or[LessEqual[z, -9e-51], N[Not[LessEqual[z, 1.26e+32]], $MachinePrecision]]]], N[(x + y), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.40000000000000012e115 or -2.29999999999999984e28 < z < -8.99999999999999948e-51 or 1.26e32 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. +-commutative 83.8%

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

   5. Simplified 83.8%

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

   if -7.40000000000000012e115 < z < -2.29999999999999984e28 or -8.99999999999999948e-51 < z < 1.26e32

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. associate-/l* 74.1%

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

      3. distribute-lft-neg-in 74.1%

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

      4. +-commutative 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. associate-/l* 74.1%

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

      3. +-commutative 74.1%

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

      4. distribute-rgt-neg-in 74.1%

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

      5. *-lft-identity 74.1%

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

      6. associate-*r/ 74.1%

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

      7. associate-*l/ 74.1%

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

      8. distribute-rgt-in 74.1%

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

      9. rgt-mult-inverse 74.1%

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

      10. distribute-neg-in 74.1%

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

      11. metadata-eval 74.1%

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

      12. unsub-neg 74.1%

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

      13. associate-*r/ 74.1%

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

      14. *-rgt-identity 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+115} \lor \neg \left(z \leq -2.3 \cdot 10^{+28}\right) \land \left(z \leq -9 \cdot 10^{-51} \lor \neg \left(z \leq 1.26 \cdot 10^{+32}\right)\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+32}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= z -2.8e+117)
     (+ x y)
     (if (<= z -3.9e+27)
       t_0
       (if (<= z -9.5e-51)
         (/ x (- 1.0 (/ y z)))
         (if (<= z 2e+32) t_0 (+ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (z <= -2.8e+117) {
		tmp = x + y;
	} else if (z <= -3.9e+27) {
		tmp = t_0;
	} else if (z <= -9.5e-51) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 2e+32) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * ((-1.0d0) - (x / y))
    if (z <= (-2.8d+117)) then
        tmp = x + y
    else if (z <= (-3.9d+27)) then
        tmp = t_0
    else if (z <= (-9.5d-51)) then
        tmp = x / (1.0d0 - (y / z))
    else if (z <= 2d+32) then
        tmp = t_0
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (z <= -2.8e+117) {
		tmp = x + y;
	} else if (z <= -3.9e+27) {
		tmp = t_0;
	} else if (z <= -9.5e-51) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 2e+32) {
		tmp = t_0;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if z <= -2.8e+117:
		tmp = x + y
	elif z <= -3.9e+27:
		tmp = t_0
	elif z <= -9.5e-51:
		tmp = x / (1.0 - (y / z))
	elif z <= 2e+32:
		tmp = t_0
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (z <= -2.8e+117)
		tmp = Float64(x + y);
	elseif (z <= -3.9e+27)
		tmp = t_0;
	elseif (z <= -9.5e-51)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (z <= 2e+32)
		tmp = t_0;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (z <= -2.8e+117)
		tmp = x + y;
	elseif (z <= -3.9e+27)
		tmp = t_0;
	elseif (z <= -9.5e-51)
		tmp = x / (1.0 - (y / z));
	elseif (z <= 2e+32)
		tmp = t_0;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+117], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.9e+27], t$95$0, If[LessEqual[z, -9.5e-51], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+32], t$95$0, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999997e117 or 2.00000000000000011e32 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. +-commutative 87.2%

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

   5. Simplified 87.2%

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

   if -2.79999999999999997e117 < z < -3.8999999999999999e27 or -9.4999999999999998e-51 < z < 2.00000000000000011e32

   1. Initial program 81.6%

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

   3. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. associate-/l* 74.1%

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

      3. distribute-lft-neg-in 74.1%

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

      4. +-commutative 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. associate-/l* 74.1%

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

      3. +-commutative 74.1%

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

      4. distribute-rgt-neg-in 74.1%

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

      5. *-lft-identity 74.1%

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

      6. associate-*r/ 74.1%

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

      7. associate-*l/ 74.1%

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

      8. distribute-rgt-in 74.1%

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

      9. rgt-mult-inverse 74.1%

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

      10. distribute-neg-in 74.1%

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

      11. metadata-eval 74.1%

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

      12. unsub-neg 74.1%

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

      13. associate-*r/ 74.1%

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

      14. *-rgt-identity 74.1%

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

   8. Simplified 74.1%

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

   if -3.8999999999999999e27 < z < -9.4999999999999998e-51

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+115}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= z -8.2e+115)
     (+ x y)
     (if (<= z -7.6e+27)
       (/ y t_0)
       (if (<= z -1.04e-50)
         (/ x t_0)
         (if (<= z 1.3e+32) (* z (- -1.0 (/ x y))) (+ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (z <= -8.2e+115) {
		tmp = x + y;
	} else if (z <= -7.6e+27) {
		tmp = y / t_0;
	} else if (z <= -1.04e-50) {
		tmp = x / t_0;
	} else if (z <= 1.3e+32) {
		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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (z <= (-8.2d+115)) then
        tmp = x + y
    else if (z <= (-7.6d+27)) then
        tmp = y / t_0
    else if (z <= (-1.04d-50)) then
        tmp = x / t_0
    else if (z <= 1.3d+32) 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 t_0 = 1.0 - (y / z);
	double tmp;
	if (z <= -8.2e+115) {
		tmp = x + y;
	} else if (z <= -7.6e+27) {
		tmp = y / t_0;
	} else if (z <= -1.04e-50) {
		tmp = x / t_0;
	} else if (z <= 1.3e+32) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if z <= -8.2e+115:
		tmp = x + y
	elif z <= -7.6e+27:
		tmp = y / t_0
	elif z <= -1.04e-50:
		tmp = x / t_0
	elif z <= 1.3e+32:
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (z <= -8.2e+115)
		tmp = Float64(x + y);
	elseif (z <= -7.6e+27)
		tmp = Float64(y / t_0);
	elseif (z <= -1.04e-50)
		tmp = Float64(x / t_0);
	elseif (z <= 1.3e+32)
		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)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (z <= -8.2e+115)
		tmp = x + y;
	elseif (z <= -7.6e+27)
		tmp = y / t_0;
	elseif (z <= -1.04e-50)
		tmp = x / t_0;
	elseif (z <= 1.3e+32)
		tmp = z * (-1.0 - (x / y));
	else
		tmp = 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[z, -8.2e+115], N[(x + y), $MachinePrecision], If[LessEqual[z, -7.6e+27], N[(y / t$95$0), $MachinePrecision], If[LessEqual[z, -1.04e-50], N[(x / t$95$0), $MachinePrecision], If[LessEqual[z, 1.3e+32], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.19999999999999925e115 or 1.3000000000000001e32 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. +-commutative 87.2%

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

   5. Simplified 87.2%

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

   if -8.19999999999999925e115 < z < -7.60000000000000043e27

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 76.3%

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

   if -7.60000000000000043e27 < z < -1.04e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.2%

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

   if -1.04e-50 < z < 1.3000000000000001e32

   1. Initial program 78.6%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/l* 75.2%

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

      3. distribute-lft-neg-in 75.2%

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

      4. +-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in z around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/l* 75.2%

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

      3. +-commutative 75.2%

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

      4. distribute-rgt-neg-in 75.2%

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

      5. *-lft-identity 75.2%

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

      6. associate-*r/ 75.2%

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

      7. associate-*l/ 75.2%

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

      8. distribute-rgt-in 75.2%

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

      9. rgt-mult-inverse 75.2%

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

      10. distribute-neg-in 75.2%

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

      11. metadata-eval 75.2%

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

      12. unsub-neg 75.2%

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

      13. associate-*r/ 75.3%

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

      14. *-rgt-identity 75.3%

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

   8. Simplified 75.3%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+115}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+53} \lor \neg \left(y \leq 1.58 \cdot 10^{+119}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9e+53) (not (<= y 1.58e+119))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9e+53) || !(y <= 1.58e+119)) {
		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 <= (-9d+53)) .or. (.not. (y <= 1.58d+119))) 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 <= -9e+53) || !(y <= 1.58e+119)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9e+53) or not (y <= 1.58e+119):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9e+53) || !(y <= 1.58e+119))
		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 <= -9e+53) || ~((y <= 1.58e+119)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9e+53], N[Not[LessEqual[y, 1.58e+119]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000004e53 or 1.5800000000000001e119 < y

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. mul-1-neg 69.3%

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

   5. Simplified 69.3%

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

   if -9.0000000000000004e53 < y < 1.5800000000000001e119

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 65.4%

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

      1. +-commutative 65.4%

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

   5. Simplified 65.4%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+53} \lor \neg \left(y \leq 1.58 \cdot 10^{+119}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+46} \lor \neg \left(y \leq 2.05 \cdot 10^{-36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.05e+46) (not (<= y 2.05e-36))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e+46) || !(y <= 2.05e-36)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.05d+46)) .or. (.not. (y <= 2.05d-36))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e+46) || !(y <= 2.05e-36)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.05e+46) or not (y <= 2.05e-36):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.05e+46) || !(y <= 2.05e-36))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.05e+46) || ~((y <= 2.05e-36)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.05e+46], N[Not[LessEqual[y, 2.05e-36]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e46 or 2.05000000000000006e-36 < y

   1. Initial program 77.8%

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

   3. Taylor expanded in y around inf 59.5%

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

      1. mul-1-neg 59.5%

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

   5. Simplified 59.5%

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

   if -2.05e46 < y < 2.05000000000000006e-36

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 55.5%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+46} \lor \neg \left(y \leq 2.05 \cdot 10^{-36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-54}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.6e-54) y (if (<= y 2.35e-23) x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.6e-54) {
		tmp = y;
	} else if (y <= 2.35e-23) {
		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 <= (-9.6d-54)) then
        tmp = y
    else if (y <= 2.35d-23) 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 <= -9.6e-54) {
		tmp = y;
	} else if (y <= 2.35e-23) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.6e-54:
		tmp = y
	elif y <= 2.35e-23:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.6e-54)
		tmp = y;
	elseif (y <= 2.35e-23)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.6e-54)
		tmp = y;
	elseif (y <= 2.35e-23)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.6e-54], y, If[LessEqual[y, 2.35e-23], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -9.60000000000000053e-54 or 2.35e-23 < y

   1. Initial program 80.5%

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

   3. Taylor expanded in x around 0 56.9%

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

   4. Taylor expanded in y around 0 24.4%

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

   if -9.60000000000000053e-54 < y < 2.35e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 59.8%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-54}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.4% 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 89.3%

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

3. Taylor expanded in y around 0 32.5%

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

4. Final simplification 32.5%

   \[\leadsto x \]
5. 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 2024046 
(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))))