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

Percentage Accurate: 87.9% → 99.5%

Time: 7.4s

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: 87.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-243} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-243) (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 <= -2e-243) || !(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 <= (-2d-243)) .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 <= -2e-243) || !(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 <= -2e-243) 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 <= -2e-243) || !(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 <= -2e-243) || ~((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, -2e-243], 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 1 (/.f64 y z))) < -1.99999999999999999e-243 or 0.0 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.8%

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

   if -1.99999999999999999e-243 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 0.0

   1. Initial program 8.4%

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

   3. Taylor expanded in z around 0 97.3%

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

      1. mul-1-neg 97.3%

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

      2. associate-/l* 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. distribute-neg-frac2 99.8%

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

      5. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 97.3%

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

      1. mul-1-neg 97.3%

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

      2. associate-/l* 99.8%

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

      3. +-commutative 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. neg-mul-1 99.8%

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

      6. *-commutative 99.8%

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

      7. *-lft-identity 99.8%

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

      8. associate-*r/ 99.8%

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

      9. associate-*l/ 99.7%

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

      10. +-commutative 99.7%

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

      11. distribute-rgt-in 99.7%

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

      12. rgt-mult-inverse 99.8%

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

      13. associate-*r/ 99.9%

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

      14. *-rgt-identity 99.9%

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

      15. distribute-lft1-in 99.9%

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

      16. *-commutative 99.9%

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

      17. +-commutative 99.9%

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

      18. mul-1-neg 99.9%

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

      19. sub-neg 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-243} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-59}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ x y) (+ 1.0 (/ y z)))))
   (if (<= z -1.2e+79)
     t_0
     (if (<= z -9.6e+64)
       (* z (- -1.0 (/ x y)))
       (if (<= z -3e-14)
         t_0
         (if (<= z 3.8e-59) (- (- z) (/ (* x 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 (z <= -1.2e+79) {
		tmp = t_0;
	} else if (z <= -9.6e+64) {
		tmp = z * (-1.0 - (x / y));
	} else if (z <= -3e-14) {
		tmp = t_0;
	} else if (z <= 3.8e-59) {
		tmp = -z - ((x * z) / 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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) * (1.0d0 + (y / z))
    if (z <= (-1.2d+79)) then
        tmp = t_0
    else if (z <= (-9.6d+64)) then
        tmp = z * ((-1.0d0) - (x / y))
    else if (z <= (-3d-14)) then
        tmp = t_0
    else if (z <= 3.8d-59) then
        tmp = -z - ((x * z) / y)
    else
        tmp = 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 (z <= -1.2e+79) {
		tmp = t_0;
	} else if (z <= -9.6e+64) {
		tmp = z * (-1.0 - (x / y));
	} else if (z <= -3e-14) {
		tmp = t_0;
	} else if (z <= 3.8e-59) {
		tmp = -z - ((x * z) / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) * (1.0 + (y / z))
	tmp = 0
	if z <= -1.2e+79:
		tmp = t_0
	elif z <= -9.6e+64:
		tmp = z * (-1.0 - (x / y))
	elif z <= -3e-14:
		tmp = t_0
	elif z <= 3.8e-59:
		tmp = -z - ((x * z) / y)
	else:
		tmp = 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 (z <= -1.2e+79)
		tmp = t_0;
	elseif (z <= -9.6e+64)
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	elseif (z <= -3e-14)
		tmp = t_0;
	elseif (z <= 3.8e-59)
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	else
		tmp = 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 (z <= -1.2e+79)
		tmp = t_0;
	elseif (z <= -9.6e+64)
		tmp = z * (-1.0 - (x / y));
	elseif (z <= -3e-14)
		tmp = t_0;
	elseif (z <= 3.8e-59)
		tmp = -z - ((x * z) / y);
	else
		tmp = 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[LessEqual[z, -1.2e+79], t$95$0, If[LessEqual[z, -9.6e+64], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-14], t$95$0, If[LessEqual[z, 3.8e-59], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.19999999999999993e79 or -9.59999999999999997e64 < z < -2.9999999999999998e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.5%

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

      1. associate-+r+ 75.5%

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

      2. *-rgt-identity 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-/l* 79.0%

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

      5. distribute-lft-in 79.0%

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

      6. +-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -1.19999999999999993e79 < z < -9.59999999999999997e64

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. associate-/l* 84.0%

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

      3. distribute-rgt-neg-in 84.0%

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

      4. distribute-neg-frac2 84.0%

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

      5. +-commutative 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around 0 36.2%

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

      1. mul-1-neg 36.2%

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

      2. associate-/l* 84.0%

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

      3. +-commutative 84.0%

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

      4. distribute-rgt-neg-in 84.0%

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

      5. neg-mul-1 84.0%

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

      6. *-commutative 84.0%

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

      7. *-lft-identity 84.0%

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

      8. associate-*r/ 84.0%

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

      9. associate-*l/ 83.7%

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

      10. +-commutative 83.7%

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

      11. distribute-rgt-in 83.7%

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

      12. rgt-mult-inverse 84.0%

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

      13. associate-*r/ 84.0%

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

      14. *-rgt-identity 84.0%

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

      15. distribute-lft1-in 84.0%

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

      16. *-commutative 84.0%

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

      17. +-commutative 84.0%

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

      18. mul-1-neg 84.0%

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

      19. sub-neg 84.0%

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

   8. Simplified 84.0%

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

   if -2.9999999999999998e-14 < z < 3.79999999999999983e-59

   1. Initial program 72.4%

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

   3. Taylor expanded in z around 0 77.7%

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

   4. Taylor expanded in x around 0 80.8%

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

   if 3.79999999999999983e-59 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. +-commutative 74.9%

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

   5. Simplified 74.9%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+79}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-14}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-59}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+164} \lor \neg \left(y \leq -4.3 \cdot 10^{+108}\right) \land \left(y \leq -2.8 \cdot 10^{-38} \lor \neg \left(y \leq 1.9 \cdot 10^{+129}\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+164)
         (and (not (<= y -4.3e+108))
              (or (<= y -2.8e-38) (not (<= y 1.9e+129)))))
   (- z)
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+164) || (!(y <= -4.3e+108) && ((y <= -2.8e-38) || !(y <= 1.9e+129)))) {
		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 <= (-1d+164)) .or. (.not. (y <= (-4.3d+108))) .and. (y <= (-2.8d-38)) .or. (.not. (y <= 1.9d+129))) 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 <= -1e+164) || (!(y <= -4.3e+108) && ((y <= -2.8e-38) || !(y <= 1.9e+129)))) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+164) or (not (y <= -4.3e+108) and ((y <= -2.8e-38) or not (y <= 1.9e+129))):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+164) || (!(y <= -4.3e+108) && ((y <= -2.8e-38) || !(y <= 1.9e+129))))
		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 <= -1e+164) || (~((y <= -4.3e+108)) && ((y <= -2.8e-38) || ~((y <= 1.9e+129)))))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+164], And[N[Not[LessEqual[y, -4.3e+108]], $MachinePrecision], Or[LessEqual[y, -2.8e-38], N[Not[LessEqual[y, 1.9e+129]], $MachinePrecision]]]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e164 or -4.29999999999999996e108 < y < -2.8e-38 or 1.90000000000000003e129 < y

   1. Initial program 66.7%

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

   3. Taylor expanded in y around inf 63.9%

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

      1. mul-1-neg 63.9%

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

   5. Simplified 63.9%

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

   if -1e164 < y < -4.29999999999999996e108 or -2.8e-38 < y < 1.90000000000000003e129

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. +-commutative 69.7%

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

   5. Simplified 69.7%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+164} \lor \neg \left(y \leq -4.3 \cdot 10^{+108}\right) \land \left(y \leq -2.8 \cdot 10^{-38} \lor \neg \left(y \leq 1.9 \cdot 10^{+129}\right)\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-15} \lor \neg \left(z \leq 3.8 \cdot 10^{-59}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4e-15) (not (<= z 3.8e-59)))
   (+ x y)
   (- (- z) (/ (* x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e-15) || !(z <= 3.8e-59)) {
		tmp = x + y;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.4d-15)) .or. (.not. (z <= 3.8d-59))) then
        tmp = x + y
    else
        tmp = -z - ((x * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e-15) || !(z <= 3.8e-59)) {
		tmp = x + y;
	} else {
		tmp = -z - ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4e-15) or not (z <= 3.8e-59):
		tmp = x + y
	else:
		tmp = -z - ((x * z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.4e-15) || !(z <= 3.8e-59))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(-z) - Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.4e-15) || ~((z <= 3.8e-59)))
		tmp = x + y;
	else
		tmp = -z - ((x * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4e-15], N[Not[LessEqual[z, 3.8e-59]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[((-z) - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.40000000000000018e-15 or 3.79999999999999983e-59 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 73.8%

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

      1. +-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -5.40000000000000018e-15 < z < 3.79999999999999983e-59

   1. Initial program 72.4%

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

   3. Taylor expanded in z around 0 77.7%

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

   4. Taylor expanded in x around 0 80.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-15} \lor \neg \left(z \leq 3.8 \cdot 10^{-59}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - \frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-21} \lor \neg \left(z \leq 2.3 \cdot 10^{-59}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-21) (not (<= z 2.3e-59))) (+ x y) (* z (- -1.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-21) || !(z <= 2.3e-59)) {
		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 <= (-4.8d-21)) .or. (.not. (z <= 2.3d-59))) 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 <= -4.8e-21) || !(z <= 2.3e-59)) {
		tmp = x + y;
	} else {
		tmp = z * (-1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-21) or not (z <= 2.3e-59):
		tmp = x + y
	else:
		tmp = z * (-1.0 - (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-21) || !(z <= 2.3e-59))
		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 <= -4.8e-21) || ~((z <= 2.3e-59)))
		tmp = x + y;
	else
		tmp = z * (-1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-21], N[Not[LessEqual[z, 2.3e-59]], $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 < -4.7999999999999999e-21 or 2.29999999999999979e-59 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 73.8%

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

      1. +-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -4.7999999999999999e-21 < z < 2.29999999999999979e-59

   1. Initial program 72.4%

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

   3. Taylor expanded in z around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. associate-/l* 80.5%

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

      3. distribute-rgt-neg-in 80.5%

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

      4. distribute-neg-frac2 80.5%

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

      5. +-commutative 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in z around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. associate-/l* 80.5%

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

      3. +-commutative 80.5%

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

      4. distribute-rgt-neg-in 80.5%

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

      5. neg-mul-1 80.5%

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

      6. *-commutative 80.5%

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

      7. *-lft-identity 80.5%

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

      8. associate-*r/ 80.5%

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

      9. associate-*l/ 80.4%

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

      10. +-commutative 80.4%

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

      11. distribute-rgt-in 80.4%

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

      12. rgt-mult-inverse 80.5%

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

      13. associate-*r/ 80.6%

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

      14. *-rgt-identity 80.6%

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

      15. distribute-lft1-in 80.6%

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

      16. *-commutative 80.6%

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

      17. +-commutative 80.6%

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

      18. mul-1-neg 80.6%

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

      19. sub-neg 80.6%

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

   8. Simplified 80.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-21} \lor \neg \left(z \leq 2.3 \cdot 10^{-59}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-39} \lor \neg \left(y \leq 1.8 \cdot 10^{+27}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e-39) (not (<= y 1.8e+27))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-39) || !(y <= 1.8e+27)) {
		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 <= (-2.3d-39)) .or. (.not. (y <= 1.8d+27))) 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 <= -2.3e-39) || !(y <= 1.8e+27)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.3e-39) or not (y <= 1.8e+27):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e-39) || !(y <= 1.8e+27))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.3e-39) || ~((y <= 1.8e+27)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e-39], N[Not[LessEqual[y, 1.8e+27]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2.30000000000000008e-39 or 1.79999999999999991e27 < y

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

   5. Simplified 56.8%

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

   if -2.30000000000000008e-39 < y < 1.79999999999999991e27

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 54.1%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-39} \lor \neg \left(y \leq 1.8 \cdot 10^{+27}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e-131) x (if (<= x 1.65e-113) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e-131) {
		tmp = x;
	} else if (x <= 1.65e-113) {
		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 <= (-1.6d-131)) then
        tmp = x
    else if (x <= 1.65d-113) 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 <= -1.6e-131) {
		tmp = x;
	} else if (x <= 1.65e-113) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e-131:
		tmp = x
	elif x <= 1.65e-113:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e-131)
		tmp = x;
	elseif (x <= 1.65e-113)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e-131)
		tmp = x;
	elseif (x <= 1.65e-113)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e-131], x, If[LessEqual[x, 1.65e-113], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e-131 or 1.6500000000000001e-113 < x

   1. Initial program 86.1%

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

   3. Taylor expanded in y around 0 37.1%

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

   if -1.6e-131 < x < 1.6500000000000001e-113

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0 75.8%

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

   4. Taylor expanded in y around 0 43.4%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.1% 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 86.6%

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

3. Taylor expanded in y around 0 30.2%

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

4. Final simplification 30.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.4% 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 2024039 
(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))))