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

Percentage Accurate: 88.3% → 99.1%

Time: 7.2s

Alternatives: 8

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.3% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-258} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-258) (not (<= t_0 0.0))) t_0 (/ (* z (- (- y) x)) y))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-258) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (z * (-y - x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-1d-258)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = (z * (-y - x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -1e-258) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = (z * (-y - x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -1e-258) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = (z * (-y - x)) / y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -1e-258) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(z * Float64(Float64(-y) - x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -1e-258) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = (z * (-y - x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-258], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -9.99999999999999954e-259 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.8%

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

   if -9.99999999999999954e-259 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 9.1%

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

   2. Taylor expanded in z around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. +-commutative 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-258} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \end{array} \]

Alternative 2: 69.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -3.2e+171)
     (- z)
     (if (<= y -1.55e+41)
       (/ y t_0)
       (if (<= y 8e+36) (/ x t_0) (/ (* z (- (- y) x)) y))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.2e+171) {
		tmp = -z;
	} else if (y <= -1.55e+41) {
		tmp = y / t_0;
	} else if (y <= 8e+36) {
		tmp = x / 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 = 1.0d0 - (y / z)
    if (y <= (-3.2d+171)) then
        tmp = -z
    else if (y <= (-1.55d+41)) then
        tmp = y / t_0
    else if (y <= 8d+36) then
        tmp = x / 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 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.2e+171) {
		tmp = -z;
	} else if (y <= -1.55e+41) {
		tmp = y / t_0;
	} else if (y <= 8e+36) {
		tmp = x / t_0;
	} else {
		tmp = (z * (-y - x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -3.2e+171:
		tmp = -z
	elif y <= -1.55e+41:
		tmp = y / t_0
	elif y <= 8e+36:
		tmp = x / t_0
	else:
		tmp = (z * (-y - x)) / y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -3.2e+171)
		tmp = Float64(-z);
	elseif (y <= -1.55e+41)
		tmp = Float64(y / t_0);
	elseif (y <= 8e+36)
		tmp = Float64(x / t_0);
	else
		tmp = Float64(Float64(z * Float64(Float64(-y) - x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -3.2e+171)
		tmp = -z;
	elseif (y <= -1.55e+41)
		tmp = y / t_0;
	elseif (y <= 8e+36)
		tmp = x / t_0;
	else
		tmp = (z * (-y - x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+171], (-z), If[LessEqual[y, -1.55e+41], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 8e+36], N[(x / t$95$0), $MachinePrecision], N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.20000000000000011e171

   1. Initial program 68.8%

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

   2. Taylor expanded in y around inf 93.3%

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

      1. mul-1-neg 93.3%

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

   4. Simplified 93.3%

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

   if -3.20000000000000011e171 < y < -1.55e41

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 65.8%

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

   if -1.55e41 < y < 8.00000000000000034e36

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 77.4%

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

   if 8.00000000000000034e36 < y

   1. Initial program 65.1%

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

   2. Taylor expanded in z around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. +-commutative 71.1%

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

   4. Simplified 71.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \end{array} \]

Alternative 3: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+185}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -3.7e+185)
     (- z)
     (if (<= y -6e+40) (/ y t_0) (if (<= y 9.6e+75) (/ x t_0) (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.7e+185) {
		tmp = -z;
	} else if (y <= -6e+40) {
		tmp = y / t_0;
	} else if (y <= 9.6e+75) {
		tmp = x / t_0;
	} 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 = 1.0d0 - (y / z)
    if (y <= (-3.7d+185)) then
        tmp = -z
    else if (y <= (-6d+40)) then
        tmp = y / t_0
    else if (y <= 9.6d+75) then
        tmp = x / t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.7e+185) {
		tmp = -z;
	} else if (y <= -6e+40) {
		tmp = y / t_0;
	} else if (y <= 9.6e+75) {
		tmp = x / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -3.7e+185:
		tmp = -z
	elif y <= -6e+40:
		tmp = y / t_0
	elif y <= 9.6e+75:
		tmp = x / t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -3.7e+185)
		tmp = Float64(-z);
	elseif (y <= -6e+40)
		tmp = Float64(y / t_0);
	elseif (y <= 9.6e+75)
		tmp = Float64(x / t_0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -3.7e+185)
		tmp = -z;
	elseif (y <= -6e+40)
		tmp = y / t_0;
	elseif (y <= 9.6e+75)
		tmp = x / t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+185], (-z), If[LessEqual[y, -6e+40], N[(y / t$95$0), $MachinePrecision], If[LessEqual[y, 9.6e+75], N[(x / t$95$0), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6999999999999997e185 or 9.5999999999999999e75 < y

   1. Initial program 65.6%

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

   2. Taylor expanded in y around inf 78.9%

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

      1. mul-1-neg 78.9%

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

   4. Simplified 78.9%

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

   if -3.6999999999999997e185 < y < -6.0000000000000004e40

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 65.8%

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

   if -6.0000000000000004e40 < y < 9.5999999999999999e75

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 76.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+185}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+40}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 68.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.7e+49) (- z) (if (<= y 2.25e+76) (/ x (- 1.0 (/ y z))) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+49) {
		tmp = -z;
	} else if (y <= 2.25e+76) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.7d+49)) then
        tmp = -z
    else if (y <= 2.25d+76) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+49) {
		tmp = -z;
	} else if (y <= 2.25e+76) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.7e+49:
		tmp = -z
	elif y <= 2.25e+76:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.7e+49)
		tmp = Float64(-z);
	elseif (y <= 2.25e+76)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.7e+49)
		tmp = -z;
	elseif (y <= 2.25e+76)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.7e+49], (-z), If[LessEqual[y, 2.25e+76], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000018e49 or 2.2499999999999999e76 < y

   1. Initial program 70.5%

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

   2. Taylor expanded in y around inf 69.1%

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

      1. mul-1-neg 69.1%

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

   4. Simplified 69.1%

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

   if -3.70000000000000018e49 < y < 2.2499999999999999e76

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 76.8%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 67.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+115}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e+115) (- z) (if (<= y 7.8e+37) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e+115) {
		tmp = -z;
	} else if (y <= 7.8e+37) {
		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 <= (-5d+115)) then
        tmp = -z
    else if (y <= 7.8d+37) 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 <= -5e+115) {
		tmp = -z;
	} else if (y <= 7.8e+37) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e+115:
		tmp = -z
	elif y <= 7.8e+37:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e+115)
		tmp = Float64(-z);
	elseif (y <= 7.8e+37)
		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 <= -5e+115)
		tmp = -z;
	elseif (y <= 7.8e+37)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e+115], (-z), If[LessEqual[y, 7.8e+37], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000008e115 or 7.7999999999999997e37 < y

   1. Initial program 68.2%

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

   2. Taylor expanded in y around inf 76.2%

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

      1. mul-1-neg 76.2%

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

   4. Simplified 76.2%

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

   if -5.00000000000000008e115 < y < 7.7999999999999997e37

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 60.6%

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

      1. +-commutative 60.6%

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

   4. Simplified 60.6%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+115}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+37}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 58.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4200:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4200.0) (- z) (if (<= y 1.22e-58) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4200.0) {
		tmp = -z;
	} else if (y <= 1.22e-58) {
		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 <= (-4200.0d0)) then
        tmp = -z
    else if (y <= 1.22d-58) 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 <= -4200.0) {
		tmp = -z;
	} else if (y <= 1.22e-58) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4200.0:
		tmp = -z
	elif y <= 1.22e-58:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4200.0)
		tmp = Float64(-z);
	elseif (y <= 1.22e-58)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4200.0)
		tmp = -z;
	elseif (y <= 1.22e-58)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4200.0], (-z), If[LessEqual[y, 1.22e-58], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -4200 or 1.2199999999999999e-58 < y

   1. Initial program 75.5%

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

   2. Taylor expanded in y around inf 61.6%

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

      1. mul-1-neg 61.6%

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

   4. Simplified 61.6%

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

   if -4200 < y < 1.2199999999999999e-58

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 59.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4200:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 36.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y -1.3e+56) y x))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+56) {
		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 (y <= (-1.3d+56)) 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 (y <= -1.3e+56) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e+56:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e+56)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e+56)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e+56], y, x]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000005e56

   1. Initial program 74.9%

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

   2. Taylor expanded in x around 0 66.3%

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

   3. Taylor expanded in y around 0 22.4%

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

   if -1.30000000000000005e56 < y

   1. Initial program 91.4%

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

   2. Taylor expanded in y around 0 43.6%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 34.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 87.8%

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

2. Taylor expanded in y around 0 36.0%

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

3. Final simplification 36.0%

   \[\leadsto x \]

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 2023287 
(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))))