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

Percentage Accurate: 87.9% → 99.5%

Time: 4.7s

Alternatives: 9

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: 87.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-261} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z \cdot \left(x + z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-261) (not (<= t_0 0.0)))
     t_0
     (- (- z) (/ (* z (+ x z)) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-261) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((z * (x + z)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-261)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z - ((z * (x + z)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-261) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z - ((z * (x + z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-261) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z - ((z * (x + z)) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-261) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(Float64(z * Float64(x + z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-261) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z - ((z * (x + z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-261], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) - N[(N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.99999999999999997e-261 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1.99999999999999997e-261 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 15.5%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-+l- 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. mul-1-neg 100.0%

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

      7. div-sub 100.0%

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

      8. mul-1-neg 100.0%

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

      9. cancel-sign-sub-inv 100.0%

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

      10. metadata-eval 100.0%

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

      11. *-lft-identity 100.0%

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

      12. +-commutative 100.0%

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

      13. unpow2 100.0%

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

      14. distribute-rgt-out 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-261} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{z \cdot \left(x + z\right)}{y}\\ \end{array} \]

Alternative 2: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-261} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-261) (not (<= t_0 0.0))) t_0 (/ (- z) (/ y (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-261) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-261)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = -z / (y / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-261) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = -z / (y / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-261) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = -z / (y / (x + y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-261) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) / Float64(y / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-261) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = -z / (y / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-261], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[((-z) / N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.99999999999999997e-261 or -0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

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

   if -1.99999999999999997e-261 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -0.0

   1. Initial program 15.5%

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

   2. Taylor expanded in z around 0 96.8%

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

      1. mul-1-neg 96.8%

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

      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%

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

   4. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-261} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x + y}}\\ \end{array} \]

Alternative 3: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+81}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-105}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.12 \cdot 10^{+40}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -4e+81)
     (- z)
     (if (<= y -8.2e+46)
       (+ x y)
       (if (<= y -3.9e+46)
         (- z)
         (if (<= y 6.2e-142)
           t_0
           (if (<= y 1.7e-105)
             (+ x y)
             (if (<= y 2.1e-31) t_0 (if (<= y 2.12e+40) (+ x y) (- z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -4e+81) {
		tmp = -z;
	} else if (y <= -8.2e+46) {
		tmp = x + y;
	} else if (y <= -3.9e+46) {
		tmp = -z;
	} else if (y <= 6.2e-142) {
		tmp = t_0;
	} else if (y <= 1.7e-105) {
		tmp = x + y;
	} else if (y <= 2.1e-31) {
		tmp = t_0;
	} else if (y <= 2.12e+40) {
		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 <= (-4d+81)) then
        tmp = -z
    else if (y <= (-8.2d+46)) then
        tmp = x + y
    else if (y <= (-3.9d+46)) then
        tmp = -z
    else if (y <= 6.2d-142) then
        tmp = t_0
    else if (y <= 1.7d-105) then
        tmp = x + y
    else if (y <= 2.1d-31) then
        tmp = t_0
    else if (y <= 2.12d+40) 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 <= -4e+81) {
		tmp = -z;
	} else if (y <= -8.2e+46) {
		tmp = x + y;
	} else if (y <= -3.9e+46) {
		tmp = -z;
	} else if (y <= 6.2e-142) {
		tmp = t_0;
	} else if (y <= 1.7e-105) {
		tmp = x + y;
	} else if (y <= 2.1e-31) {
		tmp = t_0;
	} else if (y <= 2.12e+40) {
		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 <= -4e+81:
		tmp = -z
	elif y <= -8.2e+46:
		tmp = x + y
	elif y <= -3.9e+46:
		tmp = -z
	elif y <= 6.2e-142:
		tmp = t_0
	elif y <= 1.7e-105:
		tmp = x + y
	elif y <= 2.1e-31:
		tmp = t_0
	elif y <= 2.12e+40:
		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 <= -4e+81)
		tmp = Float64(-z);
	elseif (y <= -8.2e+46)
		tmp = Float64(x + y);
	elseif (y <= -3.9e+46)
		tmp = Float64(-z);
	elseif (y <= 6.2e-142)
		tmp = t_0;
	elseif (y <= 1.7e-105)
		tmp = Float64(x + y);
	elseif (y <= 2.1e-31)
		tmp = t_0;
	elseif (y <= 2.12e+40)
		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 <= -4e+81)
		tmp = -z;
	elseif (y <= -8.2e+46)
		tmp = x + y;
	elseif (y <= -3.9e+46)
		tmp = -z;
	elseif (y <= 6.2e-142)
		tmp = t_0;
	elseif (y <= 1.7e-105)
		tmp = x + y;
	elseif (y <= 2.1e-31)
		tmp = t_0;
	elseif (y <= 2.12e+40)
		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, -4e+81], (-z), If[LessEqual[y, -8.2e+46], N[(x + y), $MachinePrecision], If[LessEqual[y, -3.9e+46], (-z), If[LessEqual[y, 6.2e-142], t$95$0, If[LessEqual[y, 1.7e-105], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.1e-31], t$95$0, If[LessEqual[y, 2.12e+40], N[(x + y), $MachinePrecision], (-z)]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999969e81 or -8.19999999999999999e46 < y < -3.89999999999999995e46 or 2.11999999999999991e40 < y

   1. Initial program 73.3%

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

   2. Taylor expanded in y around inf 70.7%

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

      1. mul-1-neg 70.7%

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

   4. Simplified 70.7%

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

   if -3.99999999999999969e81 < y < -8.19999999999999999e46 or 6.2e-142 < y < 1.69999999999999996e-105 or 2.09999999999999991e-31 < y < 2.11999999999999991e40

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf 78.2%

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

      1. +-commutative 78.2%

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

   4. Simplified 78.2%

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

   if -3.89999999999999995e46 < y < 6.2e-142 or 1.69999999999999996e-105 < y < 2.09999999999999991e-31

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 82.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+81}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-142}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-105}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.12 \cdot 10^{+40}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-52}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-148}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-42}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z (- (- y) x)) y)))
   (if (<= z -5.8e-52)
     (+ x y)
     (if (<= z 1.25e-148)
       t_0
       (if (<= z 5.8e-127)
         (/ x (- 1.0 (/ y z)))
         (if (<= z 5.2e-42) t_0 (+ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (-y - x)) / y;
	double tmp;
	if (z <= -5.8e-52) {
		tmp = x + y;
	} else if (z <= 1.25e-148) {
		tmp = t_0;
	} else if (z <= 5.8e-127) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 5.2e-42) {
		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 * (-y - x)) / y
    if (z <= (-5.8d-52)) then
        tmp = x + y
    else if (z <= 1.25d-148) then
        tmp = t_0
    else if (z <= 5.8d-127) then
        tmp = x / (1.0d0 - (y / z))
    else if (z <= 5.2d-42) 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 * (-y - x)) / y;
	double tmp;
	if (z <= -5.8e-52) {
		tmp = x + y;
	} else if (z <= 1.25e-148) {
		tmp = t_0;
	} else if (z <= 5.8e-127) {
		tmp = x / (1.0 - (y / z));
	} else if (z <= 5.2e-42) {
		tmp = t_0;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (-y - x)) / y
	tmp = 0
	if z <= -5.8e-52:
		tmp = x + y
	elif z <= 1.25e-148:
		tmp = t_0
	elif z <= 5.8e-127:
		tmp = x / (1.0 - (y / z))
	elif z <= 5.2e-42:
		tmp = t_0
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(Float64(-y) - x)) / y)
	tmp = 0.0
	if (z <= -5.8e-52)
		tmp = Float64(x + y);
	elseif (z <= 1.25e-148)
		tmp = t_0;
	elseif (z <= 5.8e-127)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (z <= 5.2e-42)
		tmp = t_0;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (-y - x)) / y;
	tmp = 0.0;
	if (z <= -5.8e-52)
		tmp = x + y;
	elseif (z <= 1.25e-148)
		tmp = t_0;
	elseif (z <= 5.8e-127)
		tmp = x / (1.0 - (y / z));
	elseif (z <= 5.2e-42)
		tmp = t_0;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -5.8e-52], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.25e-148], t$95$0, If[LessEqual[z, 5.8e-127], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-42], t$95$0, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000003e-52 or 5.2e-42 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.6%

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

      1. +-commutative 77.6%

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

   4. Simplified 77.6%

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

   if -5.8000000000000003e-52 < z < 1.25e-148 or 5.8000000000000001e-127 < z < 5.2e-42

   1. Initial program 72.8%

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

   2. Taylor expanded in z around 0 87.5%

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

      1. mul-1-neg 87.5%

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

      2. +-commutative 87.5%

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

   4. Simplified 87.5%

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

   if 1.25e-148 < z < 5.8000000000000001e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-52}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-148}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-26} \lor \neg \left(x \leq 7.2 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (or (<= x -8.5e-26) (not (<= x 7.2e+21))) (/ x t_0) (/ y t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if ((x <= -8.5e-26) || !(x <= 7.2e+21)) {
		tmp = x / t_0;
	} else {
		tmp = y / t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if ((x <= (-8.5d-26)) .or. (.not. (x <= 7.2d+21))) then
        tmp = x / t_0
    else
        tmp = y / t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if ((x <= -8.5e-26) || !(x <= 7.2e+21)) {
		tmp = x / t_0;
	} else {
		tmp = y / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if (x <= -8.5e-26) or not (x <= 7.2e+21):
		tmp = x / t_0
	else:
		tmp = y / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if ((x <= -8.5e-26) || !(x <= 7.2e+21))
		tmp = Float64(x / t_0);
	else
		tmp = Float64(y / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if ((x <= -8.5e-26) || ~((x <= 7.2e+21)))
		tmp = x / t_0;
	else
		tmp = y / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -8.5e-26], N[Not[LessEqual[x, 7.2e+21]], $MachinePrecision]], N[(x / t$95$0), $MachinePrecision], N[(y / t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000004e-26 or 7.2e21 < x

   1. Initial program 88.0%

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

   2. Taylor expanded in x around inf 78.1%

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

   if -8.50000000000000004e-26 < x < 7.2e21

   1. Initial program 91.5%

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

   2. Taylor expanded in x around 0 72.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-26} \lor \neg \left(x \leq 7.2 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 6: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+40}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.8e+77) (- z) (if (<= y 1.65e+40) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.8e+77) {
		tmp = -z;
	} else if (y <= 1.65e+40) {
		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 <= (-8.8d+77)) then
        tmp = -z
    else if (y <= 1.65d+40) 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 <= -8.8e+77) {
		tmp = -z;
	} else if (y <= 1.65e+40) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.8e+77:
		tmp = -z
	elif y <= 1.65e+40:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.8e+77)
		tmp = Float64(-z);
	elseif (y <= 1.65e+40)
		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 <= -8.8e+77)
		tmp = -z;
	elseif (y <= 1.65e+40)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.8e+77], (-z), If[LessEqual[y, 1.65e+40], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8000000000000002e77 or 1.6499999999999999e40 < y

   1. Initial program 72.8%

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

   2. Taylor expanded in y around inf 70.1%

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

      1. mul-1-neg 70.1%

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

   4. Simplified 70.1%

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

   if -8.8000000000000002e77 < y < 1.6499999999999999e40

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 70.0%

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

      1. +-commutative 70.0%

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

   4. Simplified 70.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+40}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 58.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+53}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.00014:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+53) (- z) (if (<= y 0.00014) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+53) {
		tmp = -z;
	} else if (y <= 0.00014) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.3d+53)) then
        tmp = -z
    else if (y <= 0.00014d0) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+53) {
		tmp = -z;
	} else if (y <= 0.00014) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+53:
		tmp = -z
	elif y <= 0.00014:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+53)
		tmp = Float64(-z);
	elseif (y <= 0.00014)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+53)
		tmp = -z;
	elseif (y <= 0.00014)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+53], (-z), If[LessEqual[y, 0.00014], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3000000000000002e53 or 1.3999999999999999e-4 < y

   1. Initial program 76.5%

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

   2. Taylor expanded in y around inf 62.3%

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

      1. mul-1-neg 62.3%

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

   4. Simplified 62.3%

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

   if -2.3000000000000002e53 < y < 1.3999999999999999e-4

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 55.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+53}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.00014:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-171}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e-26) x (if (<= x 1.76e-171) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e-26) {
		tmp = x;
	} else if (x <= 1.76e-171) {
		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 <= (-8.2d-26)) then
        tmp = x
    else if (x <= 1.76d-171) 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 <= -8.2e-26) {
		tmp = x;
	} else if (x <= 1.76e-171) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.2e-26:
		tmp = x
	elif x <= 1.76e-171:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e-26)
		tmp = x;
	elseif (x <= 1.76e-171)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.2e-26)
		tmp = x;
	elseif (x <= 1.76e-171)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e-26], x, If[LessEqual[x, 1.76e-171], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999997e-26 or 1.76000000000000007e-171 < x

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 46.2%

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

   if -8.1999999999999997e-26 < x < 1.76000000000000007e-171

   1. Initial program 91.2%

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

   2. Taylor expanded in x around 0 77.9%

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

   3. Taylor expanded in y around 0 42.2%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-171}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 35.0% 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 89.6%

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

2. Taylor expanded in y around 0 35.2%

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

3. Final simplification 35.2%

   \[\leadsto x \]

Developer target: 93.8% accurate, 0.7× 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 2023293 
(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))))