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

Percentage Accurate: 88.5% → 99.6%

Time: 7.8s

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: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) / (1.0d0 - (y / z))
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-260} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-260) (not (<= t_0 0.0))) t_0 (* z (/ (+ x y) (- 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-260) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((x + y) / -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-260)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((x + y) / -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-260) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-260) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * ((x + y) / -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-260) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-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-260) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * ((x + y) / -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-260], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -5.0000000000000003e-260 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 -5.0000000000000003e-260 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 15.5%

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

   3. Taylor expanded in z around 0 93.5%

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

      1. mul-1-neg 93.5%

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

      2. associate-/l* 99.9%

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

      3. distribute-neg-frac 99.9%

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

      4. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 93.5%

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

      1. associate-*l/ 17.9%

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

      2. associate-*r* 17.9%

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

      3. associate-*r/ 17.9%

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

      4. associate-*l/ 17.8%

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

      5. *-commutative 17.8%

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

      6. metadata-eval 17.8%

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

      7. associate-/r* 17.8%

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

      8. neg-mul-1 17.8%

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

      9. associate-*r* 99.6%

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

      10. associate-*l/ 99.9%

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

      11. *-lft-identity 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-260} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;x \leq -38000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-76}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;x \leq 5.55 \cdot 10^{+48}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= x -38000000000.0)
     t_1
     (if (<= x -2.7e-76)
       (- z)
       (if (<= x -8.2e-96)
         (+ x y)
         (if (<= x 1.65e-92) (/ y t_0) (if (<= x 5.55e+48) (+ x y) t_1)))))))

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 (x <= -38000000000.0) {
		tmp = t_1;
	} else if (x <= -2.7e-76) {
		tmp = -z;
	} else if (x <= -8.2e-96) {
		tmp = x + y;
	} else if (x <= 1.65e-92) {
		tmp = y / t_0;
	} else if (x <= 5.55e+48) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (x <= (-38000000000.0d0)) then
        tmp = t_1
    else if (x <= (-2.7d-76)) then
        tmp = -z
    else if (x <= (-8.2d-96)) then
        tmp = x + y
    else if (x <= 1.65d-92) then
        tmp = y / t_0
    else if (x <= 5.55d+48) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (x <= -38000000000.0) {
		tmp = t_1;
	} else if (x <= -2.7e-76) {
		tmp = -z;
	} else if (x <= -8.2e-96) {
		tmp = x + y;
	} else if (x <= 1.65e-92) {
		tmp = y / t_0;
	} else if (x <= 5.55e+48) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if x <= -38000000000.0:
		tmp = t_1
	elif x <= -2.7e-76:
		tmp = -z
	elif x <= -8.2e-96:
		tmp = x + y
	elif x <= 1.65e-92:
		tmp = y / t_0
	elif x <= 5.55e+48:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (x <= -38000000000.0)
		tmp = t_1;
	elseif (x <= -2.7e-76)
		tmp = Float64(-z);
	elseif (x <= -8.2e-96)
		tmp = Float64(x + y);
	elseif (x <= 1.65e-92)
		tmp = Float64(y / t_0);
	elseif (x <= 5.55e+48)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	tmp = 0.0;
	if (x <= -38000000000.0)
		tmp = t_1;
	elseif (x <= -2.7e-76)
		tmp = -z;
	elseif (x <= -8.2e-96)
		tmp = x + y;
	elseif (x <= 1.65e-92)
		tmp = y / t_0;
	elseif (x <= 5.55e+48)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[x, -38000000000.0], t$95$1, If[LessEqual[x, -2.7e-76], (-z), If[LessEqual[x, -8.2e-96], N[(x + y), $MachinePrecision], If[LessEqual[x, 1.65e-92], N[(y / t$95$0), $MachinePrecision], If[LessEqual[x, 5.55e+48], N[(x + y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.8e10 or 5.54999999999999988e48 < x

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 73.9%

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

   if -3.8e10 < x < -2.7e-76

   1. Initial program 81.2%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. mul-1-neg 66.7%

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

   5. Simplified 66.7%

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

   if -2.7e-76 < x < -8.20000000000000048e-96 or 1.64999999999999999e-92 < x < 5.54999999999999988e48

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 76.5%

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

      1. +-commutative 76.5%

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

   5. Simplified 76.5%

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

   if -8.20000000000000048e-96 < x < 1.64999999999999999e-92

   1. Initial program 92.0%

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

   3. Taylor expanded in x around 0 80.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -38000000000:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-76}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-96}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-92}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 5.55 \cdot 10^{+48}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+64} \lor \neg \left(y \leq -1.1 \cdot 10^{+38}\right) \land \left(y \leq -1.2 \cdot 10^{-76} \lor \neg \left(y \leq 4.9 \cdot 10^{-6}\right)\right):\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e+64)
         (and (not (<= y -1.1e+38)) (or (<= y -1.2e-76) (not (<= y 4.9e-6)))))
   (* z (/ (+ x y) (- y)))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+64) || (!(y <= -1.1e+38) && ((y <= -1.2e-76) || !(y <= 4.9e-6)))) {
		tmp = z * ((x + y) / -y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-5.8d+64)) .or. (.not. (y <= (-1.1d+38))) .and. (y <= (-1.2d-76)) .or. (.not. (y <= 4.9d-6))) then
        tmp = z * ((x + y) / -y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+64) || (!(y <= -1.1e+38) && ((y <= -1.2e-76) || !(y <= 4.9e-6)))) {
		tmp = z * ((x + y) / -y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e+64) or (not (y <= -1.1e+38) and ((y <= -1.2e-76) or not (y <= 4.9e-6))):
		tmp = z * ((x + y) / -y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e+64) || (!(y <= -1.1e+38) && ((y <= -1.2e-76) || !(y <= 4.9e-6))))
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.8e+64) || (~((y <= -1.1e+38)) && ((y <= -1.2e-76) || ~((y <= 4.9e-6)))))
		tmp = z * ((x + y) / -y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e+64], And[N[Not[LessEqual[y, -1.1e+38]], $MachinePrecision], Or[LessEqual[y, -1.2e-76], N[Not[LessEqual[y, 4.9e-6]], $MachinePrecision]]]], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999986e64 or -1.10000000000000003e38 < y < -1.20000000000000007e-76 or 4.89999999999999967e-6 < y

   1. Initial program 80.2%

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

   3. Taylor expanded in z around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. associate-/l* 77.8%

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

      3. distribute-neg-frac 77.8%

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

      4. +-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in z around 0 64.3%

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

      1. associate-*l/ 58.6%

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

      2. associate-*r* 58.6%

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

      3. associate-*r/ 58.6%

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

      4. associate-*l/ 58.5%

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

      5. *-commutative 58.5%

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

      6. metadata-eval 58.5%

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

      7. associate-/r* 58.5%

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

      8. neg-mul-1 58.5%

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

      9. associate-*r* 77.5%

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

      10. associate-*l/ 77.7%

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

      11. *-lft-identity 77.7%

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

   8. Simplified 77.7%

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

   if -5.79999999999999986e64 < y < -1.10000000000000003e38 or -1.20000000000000007e-76 < y < 4.89999999999999967e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. +-commutative 84.2%

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

   5. Simplified 84.2%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+64} \lor \neg \left(y \leq -1.1 \cdot 10^{+38}\right) \land \left(y \leq -1.2 \cdot 10^{-76} \lor \neg \left(y \leq 4.9 \cdot 10^{-6}\right)\right):\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -5.8e+64)
     (- z)
     (if (<= y -1.7e-116)
       t_0
       (if (<= y 6.5e-29)
         (+ x y)
         (if (<= y 1.9e+31) t_0 (if (<= y 5.8e+69) (+ x y) (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -5.8e+64) {
		tmp = -z;
	} else if (y <= -1.7e-116) {
		tmp = t_0;
	} else if (y <= 6.5e-29) {
		tmp = x + y;
	} else if (y <= 1.9e+31) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - (y / z))
    if (y <= (-5.8d+64)) then
        tmp = -z
    else if (y <= (-1.7d-116)) then
        tmp = t_0
    else if (y <= 6.5d-29) then
        tmp = x + y
    else if (y <= 1.9d+31) then
        tmp = t_0
    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 t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -5.8e+64) {
		tmp = -z;
	} else if (y <= -1.7e-116) {
		tmp = t_0;
	} else if (y <= 6.5e-29) {
		tmp = x + y;
	} else if (y <= 1.9e+31) {
		tmp = t_0;
	} else if (y <= 5.8e+69) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -5.8e+64:
		tmp = -z
	elif y <= -1.7e-116:
		tmp = t_0
	elif y <= 6.5e-29:
		tmp = x + y
	elif y <= 1.9e+31:
		tmp = t_0
	elif y <= 5.8e+69:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -5.8e+64)
		tmp = Float64(-z);
	elseif (y <= -1.7e-116)
		tmp = t_0;
	elseif (y <= 6.5e-29)
		tmp = Float64(x + y);
	elseif (y <= 1.9e+31)
		tmp = t_0;
	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)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -5.8e+64)
		tmp = -z;
	elseif (y <= -1.7e-116)
		tmp = t_0;
	elseif (y <= 6.5e-29)
		tmp = x + y;
	elseif (y <= 1.9e+31)
		tmp = t_0;
	elseif (y <= 5.8e+69)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+64], (-z), If[LessEqual[y, -1.7e-116], t$95$0, If[LessEqual[y, 6.5e-29], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.9e+31], t$95$0, If[LessEqual[y, 5.8e+69], N[(x + y), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999986e64 or 5.7999999999999997e69 < y

   1. Initial program 74.4%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. mul-1-neg 67.6%

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

   5. Simplified 67.6%

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

   if -5.79999999999999986e64 < y < -1.69999999999999996e-116 or 6.5e-29 < y < 1.9000000000000001e31

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 59.3%

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

   if -1.69999999999999996e-116 < y < 6.5e-29 or 1.9000000000000001e31 < y < 5.7999999999999997e69

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. +-commutative 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+37} \lor \neg \left(y \leq -4.3 \cdot 10^{-75}\right) \land y \leq 0.225:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+64)
   (* z (/ (+ x y) (- y)))
   (if (or (<= y -9.2e+37) (and (not (<= y -4.3e-75)) (<= y 0.225)))
     (+ x y)
     (/ (- z) (/ y (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+64) {
		tmp = z * ((x + y) / -y);
	} else if ((y <= -9.2e+37) || (!(y <= -4.3e-75) && (y <= 0.225))) {
		tmp = x + y;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.8d+64)) then
        tmp = z * ((x + y) / -y)
    else if ((y <= (-9.2d+37)) .or. (.not. (y <= (-4.3d-75))) .and. (y <= 0.225d0)) then
        tmp = x + y
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+64) {
		tmp = z * ((x + y) / -y);
	} else if ((y <= -9.2e+37) || (!(y <= -4.3e-75) && (y <= 0.225))) {
		tmp = x + y;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+64:
		tmp = z * ((x + y) / -y)
	elif (y <= -9.2e+37) or (not (y <= -4.3e-75) and (y <= 0.225)):
		tmp = x + y
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+64)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	elseif ((y <= -9.2e+37) || (!(y <= -4.3e-75) && (y <= 0.225)))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e+64)
		tmp = z * ((x + y) / -y);
	elseif ((y <= -9.2e+37) || (~((y <= -4.3e-75)) && (y <= 0.225)))
		tmp = x + y;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+64], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -9.2e+37], And[N[Not[LessEqual[y, -4.3e-75]], $MachinePrecision], LessEqual[y, 0.225]]], N[(x + y), $MachinePrecision], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999986e64

   1. Initial program 78.8%

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

   3. Taylor expanded in z around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. associate-/l* 77.3%

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

      3. distribute-neg-frac 77.3%

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

      4. +-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in z around 0 59.0%

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

      1. associate-*l/ 57.0%

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

      2. associate-*r* 57.0%

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

      3. associate-*r/ 57.0%

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

      4. associate-*l/ 56.9%

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

      5. *-commutative 56.9%

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

      6. metadata-eval 56.9%

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

      7. associate-/r* 56.9%

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

      8. neg-mul-1 56.9%

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

      9. associate-*r* 77.0%

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

      10. associate-*l/ 77.4%

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

      11. *-lft-identity 77.4%

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

   8. Simplified 77.4%

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

   if -5.79999999999999986e64 < y < -9.2000000000000001e37 or -4.2999999999999999e-75 < y < 0.225000000000000006

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. +-commutative 84.2%

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

   5. Simplified 84.2%

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

   if -9.2000000000000001e37 < y < -4.2999999999999999e-75 or 0.225000000000000006 < y

   1. Initial program 81.1%

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

   3. Taylor expanded in z around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-/l* 78.1%

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

      3. distribute-neg-frac 78.1%

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

      4. +-commutative 78.1%

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

   5. Simplified 78.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+37} \lor \neg \left(y \leq -4.3 \cdot 10^{-75}\right) \land y \leq 0.225:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-75} \lor \neg \left(y \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+64)
   (* z (/ (+ x y) (- y)))
   (if (<= y -1.3e+38)
     (* (+ x y) (+ 1.0 (/ y z)))
     (if (or (<= y -4.1e-75) (not (<= y 2.4e-5)))
       (/ (- z) (/ y (+ x y)))
       (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+64) {
		tmp = z * ((x + y) / -y);
	} else if (y <= -1.3e+38) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if ((y <= -4.1e-75) || !(y <= 2.4e-5)) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.8d+64)) then
        tmp = z * ((x + y) / -y)
    else if (y <= (-1.3d+38)) then
        tmp = (x + y) * (1.0d0 + (y / z))
    else if ((y <= (-4.1d-75)) .or. (.not. (y <= 2.4d-5))) then
        tmp = -z / (y / (x + y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+64) {
		tmp = z * ((x + y) / -y);
	} else if (y <= -1.3e+38) {
		tmp = (x + y) * (1.0 + (y / z));
	} else if ((y <= -4.1e-75) || !(y <= 2.4e-5)) {
		tmp = -z / (y / (x + y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+64:
		tmp = z * ((x + y) / -y)
	elif y <= -1.3e+38:
		tmp = (x + y) * (1.0 + (y / z))
	elif (y <= -4.1e-75) or not (y <= 2.4e-5):
		tmp = -z / (y / (x + y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+64)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	elseif (y <= -1.3e+38)
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	elseif ((y <= -4.1e-75) || !(y <= 2.4e-5))
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e+64)
		tmp = z * ((x + y) / -y);
	elseif (y <= -1.3e+38)
		tmp = (x + y) * (1.0 + (y / z));
	elseif ((y <= -4.1e-75) || ~((y <= 2.4e-5)))
		tmp = -z / (y / (x + y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+64], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e+38], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.1e-75], N[Not[LessEqual[y, 2.4e-5]], $MachinePrecision]], N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999986e64

   1. Initial program 78.8%

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

   3. Taylor expanded in z around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. associate-/l* 77.3%

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

      3. distribute-neg-frac 77.3%

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

      4. +-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in z around 0 59.0%

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

      1. associate-*l/ 57.0%

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

      2. associate-*r* 57.0%

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

      3. associate-*r/ 57.0%

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

      4. associate-*l/ 56.9%

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

      5. *-commutative 56.9%

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

      6. metadata-eval 56.9%

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

      7. associate-/r* 56.9%

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

      8. neg-mul-1 56.9%

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

      9. associate-*r* 77.0%

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

      10. associate-*l/ 77.4%

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

      11. *-lft-identity 77.4%

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

   8. Simplified 77.4%

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

   if -5.79999999999999986e64 < y < -1.3e38

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 53.3%

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

      1. associate-+r+ 53.3%

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

      2. *-lft-identity 53.3%

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

      3. associate-/l* 73.3%

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

      4. associate-/r/ 73.3%

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

      5. distribute-rgt-in 73.3%

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

      6. +-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -1.3e38 < y < -4.10000000000000002e-75 or 2.4000000000000001e-5 < y

   1. Initial program 81.1%

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

   3. Taylor expanded in z around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-/l* 78.1%

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

      3. distribute-neg-frac 78.1%

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

      4. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -4.10000000000000002e-75 < y < 2.4000000000000001e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 85.5%

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

      1. +-commutative 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-75} \lor \neg \left(y \leq 2.4 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e+79)
   (- z)
   (if (<= y -1.15e-23)
     (+ x y)
     (if (<= y -4.3e-75)
       (* (/ z y) (- x))
       (if (<= y 2.5e+69) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+79) {
		tmp = -z;
	} else if (y <= -1.15e-23) {
		tmp = x + y;
	} else if (y <= -4.3e-75) {
		tmp = (z / y) * -x;
	} else if (y <= 2.5e+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 <= (-2.9d+79)) then
        tmp = -z
    else if (y <= (-1.15d-23)) then
        tmp = x + y
    else if (y <= (-4.3d-75)) then
        tmp = (z / y) * -x
    else if (y <= 2.5d+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 <= -2.9e+79) {
		tmp = -z;
	} else if (y <= -1.15e-23) {
		tmp = x + y;
	} else if (y <= -4.3e-75) {
		tmp = (z / y) * -x;
	} else if (y <= 2.5e+69) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.9e+79:
		tmp = -z
	elif y <= -1.15e-23:
		tmp = x + y
	elif y <= -4.3e-75:
		tmp = (z / y) * -x
	elif y <= 2.5e+69:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e+79)
		tmp = Float64(-z);
	elseif (y <= -1.15e-23)
		tmp = Float64(x + y);
	elseif (y <= -4.3e-75)
		tmp = Float64(Float64(z / y) * Float64(-x));
	elseif (y <= 2.5e+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 <= -2.9e+79)
		tmp = -z;
	elseif (y <= -1.15e-23)
		tmp = x + y;
	elseif (y <= -4.3e-75)
		tmp = (z / y) * -x;
	elseif (y <= 2.5e+69)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e+79], (-z), If[LessEqual[y, -1.15e-23], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.3e-75], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 2.5e+69], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999992e79 or 2.50000000000000018e69 < y

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. mul-1-neg 70.1%

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

   5. Simplified 70.1%

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

   if -2.89999999999999992e79 < y < -1.15000000000000005e-23 or -4.2999999999999999e-75 < y < 2.50000000000000018e69

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 75.6%

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

      1. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   if -1.15000000000000005e-23 < y < -4.2999999999999999e-75

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 56.1%

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

   4. Taylor expanded in y around inf 55.9%

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

      1. associate-*r/ 55.9%

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

      2. neg-mul-1 55.9%

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

      3. distribute-rgt-neg-in 55.9%

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

   6. Simplified 55.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+80}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+80)
   (- z)
   (if (<= y -1.15e-22)
     (+ x y)
     (if (<= y -4.3e-75)
       (/ (- z) (/ y x))
       (if (<= y 1.9e+70) (+ x y) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+80) {
		tmp = -z;
	} else if (y <= -1.15e-22) {
		tmp = x + y;
	} else if (y <= -4.3e-75) {
		tmp = -z / (y / x);
	} else if (y <= 1.9e+70) {
		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+80)) then
        tmp = -z
    else if (y <= (-1.15d-22)) then
        tmp = x + y
    else if (y <= (-4.3d-75)) then
        tmp = -z / (y / x)
    else if (y <= 1.9d+70) 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+80) {
		tmp = -z;
	} else if (y <= -1.15e-22) {
		tmp = x + y;
	} else if (y <= -4.3e-75) {
		tmp = -z / (y / x);
	} else if (y <= 1.9e+70) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+80:
		tmp = -z
	elif y <= -1.15e-22:
		tmp = x + y
	elif y <= -4.3e-75:
		tmp = -z / (y / x)
	elif y <= 1.9e+70:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+80)
		tmp = Float64(-z);
	elseif (y <= -1.15e-22)
		tmp = Float64(x + y);
	elseif (y <= -4.3e-75)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (y <= 1.9e+70)
		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+80)
		tmp = -z;
	elseif (y <= -1.15e-22)
		tmp = x + y;
	elseif (y <= -4.3e-75)
		tmp = -z / (y / x);
	elseif (y <= 1.9e+70)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+80], (-z), If[LessEqual[y, -1.15e-22], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.3e-75], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+70], N[(x + y), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999974e80 or 1.8999999999999999e70 < y

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. mul-1-neg 70.1%

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

   5. Simplified 70.1%

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

   if -5.99999999999999974e80 < y < -1.1499999999999999e-22 or -4.2999999999999999e-75 < y < 1.8999999999999999e70

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 75.6%

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

      1. +-commutative 75.6%

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

   5. Simplified 75.6%

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

   if -1.1499999999999999e-22 < y < -4.2999999999999999e-75

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. associate-/l* 90.9%

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

      3. distribute-neg-frac 90.9%

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

      4. +-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in y around 0 56.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+80}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+69}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e-71) (- z) (if (<= y 1.7e-77) x (if (<= y 1.75e+69) y (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-71) {
		tmp = -z;
	} else if (y <= 1.7e-77) {
		tmp = x;
	} else if (y <= 1.75e+69) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.2d-71)) then
        tmp = -z
    else if (y <= 1.7d-77) then
        tmp = x
    else if (y <= 1.75d+69) then
        tmp = y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-71) {
		tmp = -z;
	} else if (y <= 1.7e-77) {
		tmp = x;
	} else if (y <= 1.75e+69) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e-71:
		tmp = -z
	elif y <= 1.7e-77:
		tmp = x
	elif y <= 1.75e+69:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e-71)
		tmp = Float64(-z);
	elseif (y <= 1.7e-77)
		tmp = x;
	elseif (y <= 1.75e+69)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e-71)
		tmp = -z;
	elseif (y <= 1.7e-77)
		tmp = x;
	elseif (y <= 1.75e+69)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e-71], (-z), If[LessEqual[y, 1.7e-77], x, If[LessEqual[y, 1.75e+69], y, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000002e-71 or 1.74999999999999994e69 < y

   1. Initial program 80.5%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. mul-1-neg 58.5%

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

   5. Simplified 58.5%

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

   if -4.2000000000000002e-71 < y < 1.69999999999999991e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.9%

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

   if 1.69999999999999991e-77 < y < 1.74999999999999994e69

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf 55.3%

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

      1. associate-+r+ 55.3%

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

      2. *-lft-identity 55.3%

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

      3. associate-/l* 55.3%

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

      4. associate-/r/ 55.3%

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

      5. distribute-rgt-in 55.3%

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

      6. +-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in x around 0 43.1%

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

   7. Taylor expanded in y around 0 43.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+69}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.55 \cdot 10^{+80} \lor \neg \left(y \leq 6.2 \cdot 10^{+70}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.55e+80) (not (<= y 6.2e+70))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.55e+80) || !(y <= 6.2e+70)) {
		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 <= (-4.55d+80)) .or. (.not. (y <= 6.2d+70))) 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 <= -4.55e+80) || !(y <= 6.2e+70)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.55e+80) or not (y <= 6.2e+70):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.55e+80) || !(y <= 6.2e+70))
		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 <= -4.55e+80) || ~((y <= 6.2e+70)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.55e+80], N[Not[LessEqual[y, 6.2e+70]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.55000000000000007e80 or 6.2000000000000006e70 < y

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. mul-1-neg 70.1%

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

   5. Simplified 70.1%

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

   if -4.55000000000000007e80 < y < 6.2000000000000006e70

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 71.6%

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

      1. +-commutative 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.55 \cdot 10^{+80} \lor \neg \left(y \leq 6.2 \cdot 10^{+70}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-98}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e-102) x (if (<= x 1.35e-98) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-102) {
		tmp = x;
	} else if (x <= 1.35e-98) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d-102)) then
        tmp = x
    else if (x <= 1.35d-98) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-102) {
		tmp = x;
	} else if (x <= 1.35e-98) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e-102:
		tmp = x
	elif x <= 1.35e-98:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e-102)
		tmp = x;
	elseif (x <= 1.35e-98)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e-102)
		tmp = x;
	elseif (x <= 1.35e-98)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e-102], x, If[LessEqual[x, 1.35e-98], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999993e-102 or 1.3499999999999999e-98 < x

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 45.6%

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

   if -1.44999999999999993e-102 < x < 1.3499999999999999e-98

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 50.2%

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

      1. associate-+r+ 50.2%

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

      2. *-lft-identity 50.2%

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

      3. associate-/l* 51.4%

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

      4. associate-/r/ 51.4%

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

      5. distribute-rgt-in 51.4%

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

      6. +-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in x around 0 41.7%

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

   7. Taylor expanded in y around 0 42.7%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-98}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.7% 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 90.0%

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

3. Taylor expanded in y around 0 36.2%

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

4. Final simplification 36.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 94.1% 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 2024017 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

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