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

Percentage Accurate: 87.7% → 99.5%

Time: 6.5s

Alternatives: 7

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: 87.7% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-255} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -5e-255) (not (<= t_0 0.0))) t_0 (* z (- -1.0 (/ 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 <= -5e-255) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (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 <= (-5d-255)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-1.0d0) - (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 <= -5e-255) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -5e-255) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * (-1.0 - (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 <= -5e-255) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-1.0 - 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 <= -5e-255) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * (-1.0 - (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, -5e-255], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -4.9999999999999996e-255 or 0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -4.9999999999999996e-255 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 0.0

   1. Initial program 9.2%

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

      1. flip-- 0.3%

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

      2. associate-/r/ 0.3%

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

      3. metadata-eval 0.3%

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

      4. pow2 0.3%

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

   4. Applied egg-rr 0.3%

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

      1. associate-*l/ 0.3%

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

      2. +-commutative 0.3%

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

   6. Simplified 0.3%

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

      1. unpow2 0.3%

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

      2. clear-num 0.3%

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

      3. un-div-inv 0.3%

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

   8. Applied egg-rr 0.3%

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

   9. Taylor expanded in z around 0 96.0%

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

       1. mul-1-neg 96.0%

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

       2. associate-/l* 100.0%

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

       3. +-commutative 100.0%

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

       4. distribute-rgt-neg-in 100.0%

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

       5. neg-sub0 100.0%

          \[\leadsto z \cdot \color{blue}{\left(0 - \frac{y + x}{y}\right)} \]

       6. *-lft-identity 100.0%

          \[\leadsto z \cdot \left(0 - \frac{\color{blue}{1 \cdot \left(y + x\right)}}{y}\right) \]

       7. associate-*l/ 99.8%

          \[\leadsto z \cdot \left(0 - \color{blue}{\frac{1}{y} \cdot \left(y + x\right)}\right) \]

       8. distribute-rgt-in 99.8%

          \[\leadsto z \cdot \left(0 - \color{blue}{\left(y \cdot \frac{1}{y} + x \cdot \frac{1}{y}\right)}\right) \]

       9. rgt-mult-inverse 99.9%

          \[\leadsto z \cdot \left(0 - \left(\color{blue}{1} + x \cdot \frac{1}{y}\right)\right) \]

       10. associate--r+ 99.9%

           \[\leadsto z \cdot \color{blue}{\left(\left(0 - 1\right) - x \cdot \frac{1}{y}\right)} \]

       11. metadata-eval 99.9%

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

       12. associate-*r/ 100.0%

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

       13. *-rgt-identity 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -5 \cdot 10^{-255} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- -1.0 (/ x y)))))
   (if (<= y -3.5e-40)
     t_0
     (if (<= y -2.55e-135)
       (+ x y)
       (if (<= y 2.6e-50) (/ x (- 1.0 (/ y z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -3.5e-40) {
		tmp = t_0;
	} else if (y <= -2.55e-135) {
		tmp = x + y;
	} else if (y <= 2.6e-50) {
		tmp = x / (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 = z * ((-1.0d0) - (x / y))
    if (y <= (-3.5d-40)) then
        tmp = t_0
    else if (y <= (-2.55d-135)) then
        tmp = x + y
    else if (y <= 2.6d-50) then
        tmp = x / (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 = z * (-1.0 - (x / y));
	double tmp;
	if (y <= -3.5e-40) {
		tmp = t_0;
	} else if (y <= -2.55e-135) {
		tmp = x + y;
	} else if (y <= 2.6e-50) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-1.0 - (x / y))
	tmp = 0
	if y <= -3.5e-40:
		tmp = t_0
	elif y <= -2.55e-135:
		tmp = x + y
	elif y <= 2.6e-50:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -3.5e-40)
		tmp = t_0;
	elseif (y <= -2.55e-135)
		tmp = Float64(x + y);
	elseif (y <= 2.6e-50)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-1.0 - (x / y));
	tmp = 0.0;
	if (y <= -3.5e-40)
		tmp = t_0;
	elseif (y <= -2.55e-135)
		tmp = x + y;
	elseif (y <= 2.6e-50)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-40], t$95$0, If[LessEqual[y, -2.55e-135], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.6e-50], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000002e-40 or 2.6000000000000001e-50 < y

   1. Initial program 84.3%

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

      1. flip-- 58.8%

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

      2. associate-/r/ 58.7%

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

      3. metadata-eval 58.7%

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

      4. pow2 58.7%

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

   4. Applied egg-rr 58.7%

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

      1. associate-*l/ 47.2%

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

      2. +-commutative 47.2%

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

   6. Simplified 47.2%

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

      1. unpow2 47.2%

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

      2. clear-num 47.2%

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

      3. un-div-inv 47.2%

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

   8. Applied egg-rr 47.2%

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

   9. Taylor expanded in z around 0 57.8%

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

       1. mul-1-neg 57.8%

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

       2. associate-/l* 71.7%

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

       3. +-commutative 71.7%

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

       4. distribute-rgt-neg-in 71.7%

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

       5. neg-sub0 71.7%

          \[\leadsto z \cdot \color{blue}{\left(0 - \frac{y + x}{y}\right)} \]

       6. *-lft-identity 71.7%

          \[\leadsto z \cdot \left(0 - \frac{\color{blue}{1 \cdot \left(y + x\right)}}{y}\right) \]

       7. associate-*l/ 71.5%

          \[\leadsto z \cdot \left(0 - \color{blue}{\frac{1}{y} \cdot \left(y + x\right)}\right) \]

       8. distribute-rgt-in 71.6%

          \[\leadsto z \cdot \left(0 - \color{blue}{\left(y \cdot \frac{1}{y} + x \cdot \frac{1}{y}\right)}\right) \]

       9. rgt-mult-inverse 71.7%

          \[\leadsto z \cdot \left(0 - \left(\color{blue}{1} + x \cdot \frac{1}{y}\right)\right) \]

       10. associate--r+ 71.7%

           \[\leadsto z \cdot \color{blue}{\left(\left(0 - 1\right) - x \cdot \frac{1}{y}\right)} \]

       11. metadata-eval 71.7%

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

       12. associate-*r/ 71.7%

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

       13. *-rgt-identity 71.7%

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

   11. Simplified 71.7%

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

   if -3.5000000000000002e-40 < y < -2.5500000000000001e-135

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 81.8%

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

      1. +-commutative 81.8%

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

   5. Simplified 81.8%

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

   if -2.5500000000000001e-135 < y < 2.6000000000000001e-50

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 86.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-135}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-70} \lor \neg \left(z \leq 8.5 \cdot 10^{+89}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e-70) (not (<= z 8.5e+89))) (+ x y) (* z (- -1.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e-70) || !(z <= 8.5e+89)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (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 <= (-1.8d-70)) .or. (.not. (z <= 8.5d+89))) then
        tmp = x + y
    else
        tmp = z * ((-1.0d0) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e-70) || !(z <= 8.5e+89)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e-70) or not (z <= 8.5e+89):
		tmp = x + y
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e-70) || !(z <= 8.5e+89))
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e-70) || ~((z <= 8.5e+89)))
		tmp = x + y;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e-70], N[Not[LessEqual[z, 8.5e+89]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e-70 or 8.50000000000000045e89 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 77.9%

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

      1. +-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -1.8000000000000001e-70 < z < 8.50000000000000045e89

   1. Initial program 83.5%

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

      1. flip-- 55.2%

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

      2. associate-/r/ 53.7%

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

      3. metadata-eval 53.7%

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

      4. pow2 53.7%

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

   4. Applied egg-rr 53.7%

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

      1. associate-*l/ 51.3%

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

      2. +-commutative 51.3%

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

   6. Simplified 51.3%

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

      1. unpow2 51.3%

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

      2. clear-num 51.3%

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

      3. un-div-inv 51.2%

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

   8. Applied egg-rr 51.2%

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

   9. Taylor expanded in z around 0 69.9%

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

       1. mul-1-neg 69.9%

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

       2. associate-/l* 74.1%

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

       3. +-commutative 74.1%

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

       4. distribute-rgt-neg-in 74.1%

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

       5. neg-sub0 74.1%

          \[\leadsto z \cdot \color{blue}{\left(0 - \frac{y + x}{y}\right)} \]

       6. *-lft-identity 74.1%

          \[\leadsto z \cdot \left(0 - \frac{\color{blue}{1 \cdot \left(y + x\right)}}{y}\right) \]

       7. associate-*l/ 73.9%

          \[\leadsto z \cdot \left(0 - \color{blue}{\frac{1}{y} \cdot \left(y + x\right)}\right) \]

       8. distribute-rgt-in 73.9%

          \[\leadsto z \cdot \left(0 - \color{blue}{\left(y \cdot \frac{1}{y} + x \cdot \frac{1}{y}\right)}\right) \]

       9. rgt-mult-inverse 74.0%

          \[\leadsto z \cdot \left(0 - \left(\color{blue}{1} + x \cdot \frac{1}{y}\right)\right) \]

       10. associate--r+ 74.0%

           \[\leadsto z \cdot \color{blue}{\left(\left(0 - 1\right) - x \cdot \frac{1}{y}\right)} \]

       11. metadata-eval 74.0%

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

       12. associate-*r/ 74.1%

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

       13. *-rgt-identity 74.1%

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

   11. Simplified 74.1%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-70} \lor \neg \left(z \leq 8.5 \cdot 10^{+89}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+134} \lor \neg \left(y \leq 2.36 \cdot 10^{+83}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e+134) (not (<= y 2.36e+83))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+134) || !(y <= 2.36e+83)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.8d+134)) .or. (.not. (y <= 2.36d+83))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+134) || !(y <= 2.36e+83)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e+134) or not (y <= 2.36e+83):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e+134) || !(y <= 2.36e+83))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.8e+134) || ~((y <= 2.36e+83)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e+134], N[Not[LessEqual[y, 2.36e+83]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000011e134 or 2.3599999999999999e83 < y

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf 74.2%

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

      1. neg-mul-1 74.2%

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

   5. Simplified 74.2%

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

   if -4.80000000000000011e134 < y < 2.3599999999999999e83

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 66.4%

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

      1. +-commutative 66.4%

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

   5. Simplified 66.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+134} \lor \neg \left(y \leq 2.36 \cdot 10^{+83}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-40} \lor \neg \left(y \leq 2.9 \cdot 10^{-50}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e-40) (not (<= y 2.9e-50))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e-40) || !(y <= 2.9e-50)) {
		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 <= (-2.9d-40)) .or. (.not. (y <= 2.9d-50))) 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 <= -2.9e-40) || !(y <= 2.9e-50)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.9e-40) or not (y <= 2.9e-50):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.9e-40) || !(y <= 2.9e-50))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.9e-40) || ~((y <= 2.9e-50)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.9e-40], N[Not[LessEqual[y, 2.9e-50]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999999e-40 or 2.90000000000000008e-50 < y

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. neg-mul-1 52.5%

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

   5. Simplified 52.5%

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

   if -2.8999999999999999e-40 < y < 2.90000000000000008e-50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.2%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-40} \lor \neg \left(y \leq 2.9 \cdot 10^{-50}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-155}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e-215) x (if (<= x 9e-155) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-215) {
		tmp = x;
	} else if (x <= 9e-155) {
		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 <= (-4.2d-215)) then
        tmp = x
    else if (x <= 9d-155) 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 <= -4.2e-215) {
		tmp = x;
	} else if (x <= 9e-155) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e-215:
		tmp = x
	elif x <= 9e-155:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e-215)
		tmp = x;
	elseif (x <= 9e-155)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.2e-215)
		tmp = x;
	elseif (x <= 9e-155)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e-215], x, If[LessEqual[x, 9e-155], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e-215 or 9.0000000000000007e-155 < x

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0 42.0%

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

   if -4.2e-215 < x < 9.0000000000000007e-155

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 58.9%

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

      1. +-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y around inf 51.7%

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

Alternative 7: 35.3% 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 91.3%

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

3. Taylor expanded in y around 0 35.8%

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

Developer Target 1: 93.5% 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 2024150 
(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))))