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

Percentage Accurate: 88.1% → 99.8%

Time: 8.3s

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: 88.1% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-296} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y} - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-296) (not (<= t_0 0.0))) t_0 (- (/ (* z (- x)) y) z))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -5e-296) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((z * -x) / y) - 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 + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-5d-296)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = ((z * -x) / y) - z
    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-296) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = ((z * -x) / y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-296) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = ((z * -x) / y) - z
	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-296) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(z * Float64(-x)) / y) - z);
	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-296) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = ((z * -x) / y) - z;
	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-296], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -5.0000000000000003e-296 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

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

   if -5.0000000000000003e-296 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 6.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-*r/ 100.0%

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

      4. div-sub 100.0%

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

      5. sub-neg 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-neg-out 100.0%

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

      8. *-lft-identity 100.0%

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

      9. metadata-eval 100.0%

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

      10. cancel-sign-sub-inv 100.0%

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

      11. distribute-neg-frac 100.0%

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

      12. mul-1-neg 100.0%

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

      13. neg-mul-1 100.0%

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

      14. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-296} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y} - z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-12}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+229}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e-12)
   (- z)
   (if (<= y 2.9e+70)
     (+ x y)
     (if (<= y 2.4e+229) (/ y (- 1.0 (/ y z))) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e-12) {
		tmp = -z;
	} else if (y <= 2.9e+70) {
		tmp = x + y;
	} else if (y <= 2.4e+229) {
		tmp = y / (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 <= (-7.5d-12)) then
        tmp = -z
    else if (y <= 2.9d+70) then
        tmp = x + y
    else if (y <= 2.4d+229) then
        tmp = y / (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 <= -7.5e-12) {
		tmp = -z;
	} else if (y <= 2.9e+70) {
		tmp = x + y;
	} else if (y <= 2.4e+229) {
		tmp = y / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e-12:
		tmp = -z
	elif y <= 2.9e+70:
		tmp = x + y
	elif y <= 2.4e+229:
		tmp = y / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e-12)
		tmp = Float64(-z);
	elseif (y <= 2.9e+70)
		tmp = Float64(x + y);
	elseif (y <= 2.4e+229)
		tmp = Float64(y / 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 <= -7.5e-12)
		tmp = -z;
	elseif (y <= 2.9e+70)
		tmp = x + y;
	elseif (y <= 2.4e+229)
		tmp = y / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e-12], (-z), If[LessEqual[y, 2.9e+70], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.4e+229], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5e-12 or 2.4000000000000001e229 < y

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. neg-mul-1 76.2%

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

   5. Simplified 76.2%

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

   if -7.5e-12 < y < 2.8999999999999998e70

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. +-commutative 80.3%

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

   5. Simplified 80.3%

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

   if 2.8999999999999998e70 < y < 2.4000000000000001e229

   1. Initial program 87.9%

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

   3. Taylor expanded in x around 0 77.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-12}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+229}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{-12} \lor \neg \left(y \leq 1.75 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{z}{\frac{z}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.35e-12) (not (<= y 1.75e+70)))
   (/ z (+ (/ z y) -1.0))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.35e-12) || !(y <= 1.75e+70)) {
		tmp = z / ((z / y) + -1.0);
	} 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) :: tmp
    if ((y <= (-3.35d-12)) .or. (.not. (y <= 1.75d+70))) then
        tmp = z / ((z / y) + (-1.0d0))
    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 <= -3.35e-12) || !(y <= 1.75e+70)) {
		tmp = z / ((z / y) + -1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.35e-12) or not (y <= 1.75e+70):
		tmp = z / ((z / y) + -1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.35e-12) || !(y <= 1.75e+70))
		tmp = Float64(z / Float64(Float64(z / y) + -1.0));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.35e-12) || ~((y <= 1.75e+70)))
		tmp = z / ((z / y) + -1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.35e-12], N[Not[LessEqual[y, 1.75e+70]], $MachinePrecision]], N[(z / N[(N[(z / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3500000000000001e-12 or 1.75000000000000001e70 < y

   1. Initial program 76.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 76.6%

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

      2. associate-/r/ 76.7%

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

   4. Applied egg-rr 76.7%

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

      1. associate-*l/ 76.9%

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

      2. *-un-lft-identity 76.9%

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

      3. clear-num 76.6%

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

      4. +-commutative 76.6%

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

   6. Applied egg-rr 76.6%

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

   7. Taylor expanded in z around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. mul-1-neg 99.7%

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

      3. unsub-neg 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 85.8%

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

   if -3.3500000000000001e-12 < y < 1.75000000000000001e70

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. +-commutative 80.3%

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

   5. Simplified 80.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{-12} \lor \neg \left(y \leq 1.75 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{z}{\frac{z}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(-\frac{x + y}{y}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.65e-12)
   (* z (- (/ (+ x y) y)))
   (if (<= y 7e+70) (+ x y) (/ z (+ (/ z y) -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.65e-12) {
		tmp = z * -((x + y) / y);
	} else if (y <= 7e+70) {
		tmp = x + y;
	} else {
		tmp = z / ((z / y) + -1.0);
	}
	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) :: tmp
    if (y <= (-2.65d-12)) then
        tmp = z * -((x + y) / y)
    else if (y <= 7d+70) then
        tmp = x + y
    else
        tmp = z / ((z / y) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.65e-12) {
		tmp = z * -((x + y) / y);
	} else if (y <= 7e+70) {
		tmp = x + y;
	} else {
		tmp = z / ((z / y) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.65e-12:
		tmp = z * -((x + y) / y)
	elif y <= 7e+70:
		tmp = x + y
	else:
		tmp = z / ((z / y) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.65e-12)
		tmp = Float64(z * Float64(-Float64(Float64(x + y) / y)));
	elseif (y <= 7e+70)
		tmp = Float64(x + y);
	else
		tmp = Float64(z / Float64(Float64(z / y) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.65e-12)
		tmp = z * -((x + y) / y);
	elseif (y <= 7e+70)
		tmp = x + y;
	else
		tmp = z / ((z / y) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.65e-12], N[(z * (-N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 7e+70], N[(x + y), $MachinePrecision], N[(z / N[(N[(z / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.64999999999999982e-12

   1. Initial program 75.4%

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

   3. Taylor expanded in z around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. associate-/l* 84.4%

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

      3. distribute-rgt-neg-in 84.4%

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

      4. distribute-neg-frac2 84.4%

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

      5. +-commutative 84.4%

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

   5. Simplified 84.4%

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

   if -2.64999999999999982e-12 < y < 7.00000000000000005e70

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. +-commutative 80.3%

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

   5. Simplified 80.3%

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

   if 7.00000000000000005e70 < y

   1. Initial program 79.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 79.1%

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

      2. associate-/r/ 78.8%

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

   4. Applied egg-rr 78.8%

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

      1. associate-*l/ 79.1%

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

      2. *-un-lft-identity 79.1%

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

      3. clear-num 79.1%

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

      4. +-commutative 79.1%

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

   6. Applied egg-rr 79.1%

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

   7. Taylor expanded in z around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   9. Simplified 99.8%

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

   10. Taylor expanded in x around 0 90.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(-\frac{x + y}{y}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{-12} \lor \neg \left(y \leq 4.8 \cdot 10^{+72}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.1e-12) (not (<= y 4.8e+72))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.1e-12) || !(y <= 4.8e+72)) {
		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 <= (-7.1d-12)) .or. (.not. (y <= 4.8d+72))) 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 <= -7.1e-12) || !(y <= 4.8e+72)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.1e-12) or not (y <= 4.8e+72):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.1e-12) || !(y <= 4.8e+72))
		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 <= -7.1e-12) || ~((y <= 4.8e+72)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.1e-12], N[Not[LessEqual[y, 4.8e+72]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.1e-12 or 4.8000000000000002e72 < y

   1. Initial program 76.9%

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

   3. Taylor expanded in y around inf 70.8%

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

      1. neg-mul-1 70.8%

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

   5. Simplified 70.8%

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

   if -7.1e-12 < y < 4.8000000000000002e72

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. +-commutative 80.3%

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

   5. Simplified 80.3%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{-12} \lor \neg \left(y \leq 4.8 \cdot 10^{+72}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-12} \lor \neg \left(y \leq 1.25 \cdot 10^{+70}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.6e-12) (not (<= y 1.25e+70))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6e-12) || !(y <= 1.25e+70)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.6d-12)) .or. (.not. (y <= 1.25d+70))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6e-12) || !(y <= 1.25e+70)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.6e-12) or not (y <= 1.25e+70):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.6e-12) || !(y <= 1.25e+70))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.6e-12) || ~((y <= 1.25e+70)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.6e-12], N[Not[LessEqual[y, 1.25e+70]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999983e-12 or 1.2500000000000001e70 < y

   1. Initial program 76.9%

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

   3. Taylor expanded in y around inf 70.8%

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

      1. neg-mul-1 70.8%

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

   5. Simplified 70.8%

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

   if -2.59999999999999983e-12 < y < 1.2500000000000001e70

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 58.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-12} \lor \neg \left(y \leq 1.25 \cdot 10^{+70}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-202}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.95e-72) x (if (<= x 6.8e-202) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e-72) {
		tmp = x;
	} else if (x <= 6.8e-202) {
		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 <= (-1.95d-72)) then
        tmp = x
    else if (x <= 6.8d-202) 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 <= -1.95e-72) {
		tmp = x;
	} else if (x <= 6.8e-202) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.95e-72:
		tmp = x
	elif x <= 6.8e-202:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.95e-72)
		tmp = x;
	elseif (x <= 6.8e-202)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.95e-72)
		tmp = x;
	elseif (x <= 6.8e-202)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.95e-72], x, If[LessEqual[x, 6.8e-202], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95e-72 or 6.80000000000000025e-202 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in y around 0 44.5%

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

   if -1.95e-72 < x < 6.80000000000000025e-202

   1. Initial program 91.1%

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

   3. Taylor expanded in z around inf 53.4%

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

      1. +-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in y around inf 42.6%

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

Alternative 8: 34.2% 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. Add Preprocessing

3. Taylor expanded in y around 0 35.4%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 93.9% 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 2024170 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -3742931076268985600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (/ (+ y x) (- y)) z) (if (< y 3553466245608673400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z))))

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