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

Percentage Accurate: 87.8% → 98.6%

Time: 5.6s

Alternatives: 6

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: 87.8% 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: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -1.15 \cdot 10^{-205} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -1.15e-205) (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 <= -1.15e-205) || !(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 <= (-1.15d-205)) .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 <= -1.15e-205) || !(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 <= -1.15e-205) 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 <= -1.15e-205) || !(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 <= -1.15e-205) || ~((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, -1.15e-205], 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))) < -1.15e-205 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 -1.15e-205 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 16.4%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. fp-cancel-sign-sub-inv N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -1.15 \cdot 10^{-205} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-50} \lor \neg \left(y \leq 8 \cdot 10^{+37}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.6e-50) (not (<= y 8e+37))) (* z (- -1.0 (/ x y))) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e-50) || !(y <= 8e+37)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = y + 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 <= (-6.6d-50)) .or. (.not. (y <= 8d+37))) then
        tmp = z * ((-1.0d0) - (x / y))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e-50) || !(y <= 8e+37)) {
		tmp = z * (-1.0 - (x / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.6e-50) or not (y <= 8e+37):
		tmp = z * (-1.0 - (x / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.6e-50) || !(y <= 8e+37))
		tmp = Float64(z * Float64(-1.0 - Float64(x / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.6e-50) || ~((y <= 8e+37)))
		tmp = z * (-1.0 - (x / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.6e-50], N[Not[LessEqual[y, 8e+37]], $MachinePrecision]], N[(z * N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999997e-50 or 7.99999999999999963e37 < y

   1. Initial program 72.7%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. fp-cancel-sign-sub-inv N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. *-commutative N/A

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

      22. associate-/l* N/A

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

   5. Applied rewrites 74.3%

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

   if -6.5999999999999997e-50 < y < 7.99999999999999963e37

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 83.7%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-out N/A

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

      17. +-commutative N/A

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

      18. lower-neg.f64 N/A

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

      19. +-commutative N/A

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

      20. associate-/l* N/A

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

      21. *-commutative N/A

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

      22. lower-fma.f64 N/A

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

      23. lower-/.f64 18.2

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

   8. Applied rewrites 18.2%

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

   9. Taylor expanded in z around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 83.7

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

   11. Applied rewrites 83.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-50} \lor \neg \left(y \leq 8 \cdot 10^{+37}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-50} \lor \neg \left(y \leq 8 \cdot 10^{+37}\right):\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.6e-50) (not (<= y 8e+37))) (- (fma (/ z y) x z)) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e-50) || !(y <= 8e+37)) {
		tmp = -fma((z / y), x, z);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.6e-50) || !(y <= 8e+37))
		tmp = Float64(-fma(Float64(z / y), x, z));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.6e-50], N[Not[LessEqual[y, 8e+37]], $MachinePrecision]], (-N[(N[(z / y), $MachinePrecision] * x + z), $MachinePrecision]), N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999997e-50 or 7.99999999999999963e37 < y

   1. Initial program 72.7%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 26.9%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-out N/A

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

      17. +-commutative N/A

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

      18. lower-neg.f64 N/A

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

      19. +-commutative N/A

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

      20. associate-/l* N/A

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

      21. *-commutative N/A

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

      22. lower-fma.f64 N/A

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

      23. lower-/.f64 72.2

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

   8. Applied rewrites 72.2%

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

   if -6.5999999999999997e-50 < y < 7.99999999999999963e37

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 83.7%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-out N/A

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

      17. +-commutative N/A

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

      18. lower-neg.f64 N/A

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

      19. +-commutative N/A

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

      20. associate-/l* N/A

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

      21. *-commutative N/A

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

      22. lower-fma.f64 N/A

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

      23. lower-/.f64 18.2

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

   8. Applied rewrites 18.2%

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

   9. Taylor expanded in z around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 83.7

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

   11. Applied rewrites 83.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-50} \lor \neg \left(y \leq 8 \cdot 10^{+37}\right):\\ \;\;\;\;-\mathsf{fma}\left(\frac{z}{y}, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+116} \lor \neg \left(y \leq 8.1 \cdot 10^{+37}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2e+116) (not (<= y 8.1e+37))) (- z) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e+116) || !(y <= 8.1e+37)) {
		tmp = -z;
	} else {
		tmp = y + 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 <= (-2d+116)) .or. (.not. (y <= 8.1d+37))) then
        tmp = -z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e+116) || !(y <= 8.1e+37)) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2e+116) or not (y <= 8.1e+37):
		tmp = -z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2e+116) || !(y <= 8.1e+37))
		tmp = Float64(-z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2e+116) || ~((y <= 8.1e+37)))
		tmp = -z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2e+116], N[Not[LessEqual[y, 8.1e+37]], $MachinePrecision]], (-z), N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000003e116 or 8.10000000000000006e37 < y

   1. Initial program 65.0%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 73.3

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

   5. Applied rewrites 73.3%

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

   if -2.00000000000000003e116 < y < 8.10000000000000006e37

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. div-add N/A

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

      5. distribute-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. associate-/l* N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-neg-out N/A

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

      17. +-commutative N/A

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

      18. lower-neg.f64 N/A

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

      19. +-commutative N/A

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

      20. associate-/l* N/A

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

      21. *-commutative N/A

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

      22. lower-fma.f64 N/A

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

      23. lower-/.f64 27.6

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

   8. Applied rewrites 27.6%

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

   9. Taylor expanded in z around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 74.1

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

   11. Applied rewrites 74.1%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+116} \lor \neg \left(y \leq 8.1 \cdot 10^{+37}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.3% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ -z \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return -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 = -z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 85.3%

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

3. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 37.8

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

5. Applied rewrites 37.8%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Alternative 6: 3.4% accurate, 29.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 85.3%

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

   1. unpow1 N/A

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

   2. metadata-eval N/A

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

   3. sqrt-pow1 N/A

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

   4. pow2 N/A

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

   5. lift-/.f64 N/A

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

   6. lift-/.f64 N/A

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

   7. frac-times N/A

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

   8. sqr-neg-rev N/A

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

   9. associate-/l* N/A

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

   10. sqrt-prod N/A

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

   11. lower-*.f64 N/A

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

   12. lower-sqrt.f64 N/A

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

   13. lower-neg.f64 N/A

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

   14. lower-sqrt.f64 N/A

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

   15. lower-/.f64 N/A

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

   16. lower-neg.f64 N/A

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

   17. lower-*.f64 28.5

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

4. Applied rewrites 28.5%

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

5. Taylor expanded in y around inf

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

   1. associate-*r/ N/A

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

   2. *-commutative N/A

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

   3. unpow2 N/A

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

   4. rem-square-sqrt N/A

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

   5. associate-/l* N/A

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

   6. metadata-eval N/A

      \[\leadsto z \cdot \color{blue}{1} \]

   7. *-rgt-identity 3.3

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

7. Applied rewrites 3.3%

   \[\leadsto \color{blue}{z} \]
8. Add Preprocessing

Developer Target 1: 93.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024320 
(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))))