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

Percentage Accurate: 87.5% → 99.8%

Time: 5.3s

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: 87.5% 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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-288} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1e-288) (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-288) || !(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-288)) .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-288) || !(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-288) 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-288) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(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-288) || ~((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-288], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -1.00000000000000006e-288 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 -1.00000000000000006e-288 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 6.1%

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

   2. Taylor expanded in z around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. associate-/l* 6.1%

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

      3. +-commutative 6.1%

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

      4. associate-/r/ 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. +-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1 \cdot 10^{-288} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \end{array} \]

Alternative 2: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-128}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.9e-29)
   (+ x y)
   (if (<= z 7.2e-128) (/ (* z (- (- y) x)) y) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.9e-29) {
		tmp = x + y;
	} else if (z <= 7.2e-128) {
		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 (z <= (-3.9d-29)) then
        tmp = x + y
    else if (z <= 7.2d-128) 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 (z <= -3.9e-29) {
		tmp = x + y;
	} else if (z <= 7.2e-128) {
		tmp = (z * (-y - x)) / y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.9e-29:
		tmp = x + y
	elif z <= 7.2e-128:
		tmp = (z * (-y - x)) / y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.9e-29)
		tmp = Float64(x + y);
	elseif (z <= 7.2e-128)
		tmp = Float64(Float64(z * Float64(Float64(-y) - x)) / y);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.9e-29)
		tmp = x + y;
	elseif (z <= 7.2e-128)
		tmp = (z * (-y - x)) / y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.9e-29], N[(x + y), $MachinePrecision], If[LessEqual[z, 7.2e-128], N[(N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999998e-29 or 7.20000000000000049e-128 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 81.2%

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

   if -3.8999999999999998e-29 < z < 7.20000000000000049e-128

   1. Initial program 60.7%

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

   2. Taylor expanded in z around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. +-commutative 80.2%

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

      3. *-commutative 80.2%

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

      4. +-commutative 80.2%

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

   4. Simplified 80.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-29}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-128}:\\ \;\;\;\;\frac{z \cdot \left(\left(-y\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 71.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.8e-16)
   (+ x y)
   (if (<= z 3.05e-127) (* z (/ (- (- y) x) y)) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e-16) {
		tmp = x + y;
	} else if (z <= 3.05e-127) {
		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 (z <= (-3.8d-16)) then
        tmp = x + y
    else if (z <= 3.05d-127) 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 (z <= -3.8e-16) {
		tmp = x + y;
	} else if (z <= 3.05e-127) {
		tmp = z * ((-y - x) / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.8e-16:
		tmp = x + y
	elif z <= 3.05e-127:
		tmp = z * ((-y - x) / y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.8e-16)
		tmp = Float64(x + y);
	elseif (z <= 3.05e-127)
		tmp = Float64(z * Float64(Float64(Float64(-y) - x) / y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.8e-16)
		tmp = x + y;
	elseif (z <= 3.05e-127)
		tmp = z * ((-y - x) / y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.8e-16], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.05e-127], N[(z * N[(N[((-y) - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000012e-16 or 3.0499999999999999e-127 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 81.2%

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

   if -3.80000000000000012e-16 < z < 3.0499999999999999e-127

   1. Initial program 60.7%

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

   2. Taylor expanded in z around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. associate-/l* 45.7%

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

      3. +-commutative 45.7%

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

      4. associate-/r/ 80.7%

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

      5. distribute-rgt-neg-in 80.7%

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

      6. +-commutative 80.7%

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

   4. Simplified 80.7%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \frac{\left(-y\right) - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+71}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.15e+79)
   (- z)
   (if (<= y -6.2e-135)
     (/ x (- 1.0 (/ y z)))
     (if (<= y 3e+71) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+79) {
		tmp = -z;
	} else if (y <= -6.2e-135) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 3e+71) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.15d+79)) then
        tmp = -z
    else if (y <= (-6.2d-135)) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 3d+71) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+79) {
		tmp = -z;
	} else if (y <= -6.2e-135) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 3e+71) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.15e+79:
		tmp = -z
	elif y <= -6.2e-135:
		tmp = x / (1.0 - (y / z))
	elif y <= 3e+71:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.15e+79)
		tmp = Float64(-z);
	elseif (y <= -6.2e-135)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 3e+71)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.15e+79)
		tmp = -z;
	elseif (y <= -6.2e-135)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 3e+71)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.15e+79], (-z), If[LessEqual[y, -6.2e-135], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+71], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e79 or 3.00000000000000013e71 < y

   1. Initial program 51.3%

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

   2. Taylor expanded in y around inf 81.5%

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

      1. mul-1-neg 81.5%

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

   4. Simplified 81.5%

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

   if -1.15e79 < y < -6.2000000000000001e-135

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.5%

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

   if -6.2000000000000001e-135 < y < 3.00000000000000013e71

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 82.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+71}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.6e+79) (- z) (if (<= y 1.4e+69) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.6e+79) {
		tmp = -z;
	} else if (y <= 1.4e+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 <= (-7.6d+79)) then
        tmp = -z
    else if (y <= 1.4d+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 <= -7.6e+79) {
		tmp = -z;
	} else if (y <= 1.4e+69) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.6e+79:
		tmp = -z
	elif y <= 1.4e+69:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.6e+79)
		tmp = Float64(-z);
	elseif (y <= 1.4e+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 <= -7.6e+79)
		tmp = -z;
	elseif (y <= 1.4e+69)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.6e+79], (-z), If[LessEqual[y, 1.4e+69], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -7.6000000000000005e79 or 1.39999999999999991e69 < y

   1. Initial program 51.3%

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

   2. Taylor expanded in y around inf 81.5%

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

      1. mul-1-neg 81.5%

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

   4. Simplified 81.5%

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

   if -7.6000000000000005e79 < y < 1.39999999999999991e69

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 75.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 6: 57.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+79) (- z) (if (<= y 1.8e+19) x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+79) {
		tmp = -z;
	} else if (y <= 1.8e+19) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.9d+79)) then
        tmp = -z
    else if (y <= 1.8d+19) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+79) {
		tmp = -z;
	} else if (y <= 1.8e+19) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+79:
		tmp = -z
	elif y <= 1.8e+19:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+79)
		tmp = Float64(-z);
	elseif (y <= 1.8e+19)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+79)
		tmp = -z;
	elseif (y <= 1.8e+19)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+79], (-z), If[LessEqual[y, 1.8e+19], x, (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e79 or 1.8e19 < y

   1. Initial program 55.5%

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

   2. Taylor expanded in y around inf 76.1%

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

      1. mul-1-neg 76.1%

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

   4. Simplified 76.1%

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

   if -1.9000000000000001e79 < y < 1.8e19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 60.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 39.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.9e-200) x (if (<= x 3e-17) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.9e-200) {
		tmp = x;
	} else if (x <= 3e-17) {
		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 <= (-3.9d-200)) then
        tmp = x
    else if (x <= 3d-17) 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 <= -3.9e-200) {
		tmp = x;
	} else if (x <= 3e-17) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.9e-200:
		tmp = x
	elif x <= 3e-17:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.9e-200)
		tmp = x;
	elseif (x <= 3e-17)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.9e-200)
		tmp = x;
	elseif (x <= 3e-17)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.9e-200], x, If[LessEqual[x, 3e-17], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.89999999999999999e-200 or 3.00000000000000006e-17 < x

   1. Initial program 83.2%

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

   2. Taylor expanded in y around 0 54.2%

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

   if -3.89999999999999999e-200 < x < 3.00000000000000006e-17

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0 66.7%

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

   3. Taylor expanded in y around 0 40.0%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-17}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 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 83.8%

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

2. Taylor expanded in y around 0 40.8%

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

3. Final simplification 40.8%

   \[\leadsto x \]

Developer target: 93.6% 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 2023181 
(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))))