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

Percentage Accurate: 88.5% → 99.6%

Time: 7.3s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.015:\\ \;\;\;\;\frac{z}{\frac{z - y}{x + y}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{x + y}{\mathsf{fma}\left(\frac{-1}{z}, y, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{z - y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.015)
   (/ z (/ (- z y) (+ x y)))
   (if (<= y 1.6e-59)
     (/ (+ x y) (fma (/ -1.0 z) y 1.0))
     (* (/ (+ x y) (- z y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.015) {
		tmp = z / ((z - y) / (x + y));
	} else if (y <= 1.6e-59) {
		tmp = (x + y) / fma((-1.0 / z), y, 1.0);
	} else {
		tmp = ((x + y) / (z - y)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.015)
		tmp = Float64(z / Float64(Float64(z - y) / Float64(x + y)));
	elseif (y <= 1.6e-59)
		tmp = Float64(Float64(x + y) / fma(Float64(-1.0 / z), y, 1.0));
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(z - y)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.015], N[(z / N[(N[(z - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-59], N[(N[(x + y), $MachinePrecision] / N[(N[(-1.0 / z), $MachinePrecision] * y + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.014999999999999999

   1. Initial program 81.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 81.1

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

   4. Applied rewrites 81.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 81.3

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 81.3

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

   6. Applied rewrites 81.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.8

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

   8. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 99.8

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.8

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

   10. Applied rewrites 99.8%

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

   if -0.014999999999999999 < y < 1.6e-59

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   if 1.6e-59 < y

   1. Initial program 88.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 88.3

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

   4. Applied rewrites 88.3%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 89.5

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 89.5

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

   6. Applied rewrites 89.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.9

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

   8. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.015:\\ \;\;\;\;\frac{z}{\frac{z - y}{x + y}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{x + y}{\mathsf{fma}\left(\frac{-1}{z}, y, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{z - y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ t_1 := \frac{z}{z - y} \cdot \left(x + y\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))) (t_1 (* (/ z (- z y)) (+ x y))))
   (if (<= t_0 -1e-243) t_1 (if (<= t_0 0.0) (* (- -1.0 (/ x y)) z) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double t_1 = (z / (z - y)) * (x + y);
	double tmp;
	if (t_0 <= -1e-243) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    t_1 = (z / (z - y)) * (x + y)
    if (t_0 <= (-1d-243)) then
        tmp = t_1
    else if (t_0 <= 0.0d0) then
        tmp = ((-1.0d0) - (x / y)) * z
    else
        tmp = t_1
    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 t_1 = (z / (z - y)) * (x + y);
	double tmp;
	if (t_0 <= -1e-243) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = (-1.0 - (x / y)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	t_1 = (z / (z - y)) * (x + y)
	tmp = 0
	if t_0 <= -1e-243:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = (-1.0 - (x / y)) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	t_1 = Float64(Float64(z / Float64(z - y)) * Float64(x + y))
	tmp = 0.0
	if (t_0 <= -1e-243)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(-1.0 - Float64(x / y)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	t_1 = (z / (z - y)) * (x + y);
	tmp = 0.0;
	if (t_0 <= -1e-243)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = (-1.0 - (x / y)) * z;
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-243], t$95$1, If[LessEqual[t$95$0, 0.0], N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -9.99999999999999995e-244 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
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 99.9

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 99.9

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

   6. Applied rewrites 99.9%

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

   if -9.99999999999999995e-244 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 19.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. distribute-lft-neg-out N/A

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.9%

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

Alternative 3: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{-x}{y}, z, -z\right)\\ \mathbf{if}\;y \leq -5500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{z - y} \cdot x\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z} + 1, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (/ (- x) y) z (- z))))
   (if (<= y -5500000000.0)
     t_0
     (if (<= y -1.8e-58)
       (* (/ z (- z y)) x)
       (if (<= y 1.46e-8) (fma (+ (/ y z) 1.0) x y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fma((-x / y), z, -z);
	double tmp;
	if (y <= -5500000000.0) {
		tmp = t_0;
	} else if (y <= -1.8e-58) {
		tmp = (z / (z - y)) * x;
	} else if (y <= 1.46e-8) {
		tmp = fma(((y / z) + 1.0), x, y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(Float64(-x) / y), z, Float64(-z))
	tmp = 0.0
	if (y <= -5500000000.0)
		tmp = t_0;
	elseif (y <= -1.8e-58)
		tmp = Float64(Float64(z / Float64(z - y)) * x);
	elseif (y <= 1.46e-8)
		tmp = fma(Float64(Float64(y / z) + 1.0), x, y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[((-x) / y), $MachinePrecision] * z + (-z)), $MachinePrecision]}, If[LessEqual[y, -5500000000.0], t$95$0, If[LessEqual[y, -1.8e-58], N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.46e-8], N[(N[(N[(y / z), $MachinePrecision] + 1.0), $MachinePrecision] * x + y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e9 or 1.46e-8 < y

   1. Initial program 82.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. distribute-lft-neg-out N/A

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 75.8

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

   5. Applied rewrites 75.8%

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

   7. Applied rewrites 75.8%

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

   9. Applied rewrites 75.8%

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

   if -5.5e9 < y < -1.80000000000000005e-58

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-inverses N/A

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

      3. div-sub N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.4

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

   5. Applied rewrites 77.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{z - y}{z}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 77.5%

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

   if -1.80000000000000005e-58 < y < 1.46e-8

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 8.1

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

   5. Applied rewrites 8.1%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. associate-*l/ N/A

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

      7. *-lft-identity N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

      10. associate-/l* N/A

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

      11. *-rgt-identity N/A

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

      12. distribute-lft-in N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

      18. lower-/.f64 84.5

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

   8. Applied rewrites 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z} + 1, x, y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{if}\;y \leq -5500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{z - y} \cdot x\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z} + 1, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- -1.0 (/ x y)) z)))
   (if (<= y -5500000000.0)
     t_0
     (if (<= y -1.8e-58)
       (* (/ z (- z y)) x)
       (if (<= y 1.46e-8) (fma (+ (/ y z) 1.0) x y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (-1.0 - (x / y)) * z;
	double tmp;
	if (y <= -5500000000.0) {
		tmp = t_0;
	} else if (y <= -1.8e-58) {
		tmp = (z / (z - y)) * x;
	} else if (y <= 1.46e-8) {
		tmp = fma(((y / z) + 1.0), x, y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-1.0 - Float64(x / y)) * z)
	tmp = 0.0
	if (y <= -5500000000.0)
		tmp = t_0;
	elseif (y <= -1.8e-58)
		tmp = Float64(Float64(z / Float64(z - y)) * x);
	elseif (y <= 1.46e-8)
		tmp = fma(Float64(Float64(y / z) + 1.0), x, y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -5500000000.0], t$95$0, If[LessEqual[y, -1.8e-58], N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.46e-8], N[(N[(N[(y / z), $MachinePrecision] + 1.0), $MachinePrecision] * x + y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e9 or 1.46e-8 < y

   1. Initial program 82.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. distribute-lft-neg-out N/A

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 75.8

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

   5. Applied rewrites 75.8%

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

   if -5.5e9 < y < -1.80000000000000005e-58

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. *-inverses N/A

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

      3. div-sub N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.4

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

   5. Applied rewrites 77.4%

      \[\leadsto \color{blue}{\frac{x}{\frac{z - y}{z}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 77.5%

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

   if -1.80000000000000005e-58 < y < 1.46e-8

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 8.1

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

   5. Applied rewrites 8.1%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. associate-*l/ N/A

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

      7. *-lft-identity N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

      10. associate-/l* N/A

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

      11. *-rgt-identity N/A

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

      12. distribute-lft-in N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

      18. lower-/.f64 84.5

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

   8. Applied rewrites 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z} + 1, x, y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{z - y} \cdot y\\ \mathbf{if}\;y \leq -7 \cdot 10^{+175}:\\ \;\;\;\;\left(-1 - \frac{z}{y}\right) \cdot z\\ \mathbf{elif}\;y \leq -5500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z (- z y)) y)))
   (if (<= y -7e+175)
     (* (- -1.0 (/ z y)) z)
     (if (<= y -5500000000.0) t_0 (if (<= y 7.8e+46) (+ x y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (z / (z - y)) * y;
	double tmp;
	if (y <= -7e+175) {
		tmp = (-1.0 - (z / y)) * z;
	} else if (y <= -5500000000.0) {
		tmp = t_0;
	} else if (y <= 7.8e+46) {
		tmp = x + y;
	} 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 / (z - y)) * y
    if (y <= (-7d+175)) then
        tmp = ((-1.0d0) - (z / y)) * z
    else if (y <= (-5500000000.0d0)) then
        tmp = t_0
    else if (y <= 7.8d+46) then
        tmp = x + y
    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 / (z - y)) * y;
	double tmp;
	if (y <= -7e+175) {
		tmp = (-1.0 - (z / y)) * z;
	} else if (y <= -5500000000.0) {
		tmp = t_0;
	} else if (y <= 7.8e+46) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / (z - y)) * y
	tmp = 0
	if y <= -7e+175:
		tmp = (-1.0 - (z / y)) * z
	elif y <= -5500000000.0:
		tmp = t_0
	elif y <= 7.8e+46:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / Float64(z - y)) * y)
	tmp = 0.0
	if (y <= -7e+175)
		tmp = Float64(Float64(-1.0 - Float64(z / y)) * z);
	elseif (y <= -5500000000.0)
		tmp = t_0;
	elseif (y <= 7.8e+46)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / (z - y)) * y;
	tmp = 0.0;
	if (y <= -7e+175)
		tmp = (-1.0 - (z / y)) * z;
	elseif (y <= -5500000000.0)
		tmp = t_0;
	elseif (y <= 7.8e+46)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -7e+175], N[(N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, -5500000000.0], t$95$0, If[LessEqual[y, 7.8e+46], N[(x + y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000006e175

   1. Initial program 68.5%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 68.2

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

   4. Applied rewrites 68.2%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 68.5

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 68.5

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

   6. Applied rewrites 68.5%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 56.0

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

   9. Applied rewrites 56.0%

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

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 76.2%

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

   if -7.0000000000000006e175 < y < -5.5e9 or 7.7999999999999999e46 < y

   1. Initial program 84.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 84.9

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

   4. Applied rewrites 84.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 86.0

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 86.0

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

   6. Applied rewrites 86.0%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 61.0

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

   9. Applied rewrites 61.0%

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

   if -5.5e9 < y < 7.7999999999999999e46

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 76.6

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

   5. Applied rewrites 76.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+175}:\\ \;\;\;\;\left(-1 - \frac{z}{y}\right) \cdot z\\ \mathbf{elif}\;y \leq -5500000000:\\ \;\;\;\;\frac{z}{z - y} \cdot y\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+46}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - y} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+80}:\\ \;\;\;\;\frac{z}{\frac{z - y}{x + y}}\\ \mathbf{elif}\;y \leq 10^{-59}:\\ \;\;\;\;\frac{z}{z - y} \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{z - y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+80)
   (/ z (/ (- z y) (+ x y)))
   (if (<= y 1e-59) (* (/ z (- z y)) (+ x y)) (* (/ (+ x y) (- z y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+80) {
		tmp = z / ((z - y) / (x + y));
	} else if (y <= 1e-59) {
		tmp = (z / (z - y)) * (x + y);
	} else {
		tmp = ((x + y) / (z - y)) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.25d+80)) then
        tmp = z / ((z - y) / (x + y))
    else if (y <= 1d-59) then
        tmp = (z / (z - y)) * (x + y)
    else
        tmp = ((x + y) / (z - y)) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+80) {
		tmp = z / ((z - y) / (x + y));
	} else if (y <= 1e-59) {
		tmp = (z / (z - y)) * (x + y);
	} else {
		tmp = ((x + y) / (z - y)) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+80:
		tmp = z / ((z - y) / (x + y))
	elif y <= 1e-59:
		tmp = (z / (z - y)) * (x + y)
	else:
		tmp = ((x + y) / (z - y)) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+80)
		tmp = Float64(z / Float64(Float64(z - y) / Float64(x + y)));
	elseif (y <= 1e-59)
		tmp = Float64(Float64(z / Float64(z - y)) * Float64(x + y));
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(z - y)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e+80)
		tmp = z / ((z - y) / (x + y));
	elseif (y <= 1e-59)
		tmp = (z / (z - y)) * (x + y);
	else
		tmp = ((x + y) / (z - y)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+80], N[(z / N[(N[(z - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-59], N[(N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2499999999999999e80

   1. Initial program 75.5%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 75.3

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

   4. Applied rewrites 75.3%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 75.5

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 75.5

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

   6. Applied rewrites 75.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.8

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

   8. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 99.9

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.9

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

   10. Applied rewrites 99.9%

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

   if -1.2499999999999999e80 < y < 1e-59

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 99.9

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 99.9

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

   6. Applied rewrites 99.9%

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

   if 1e-59 < y

   1. Initial program 88.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 88.3

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

   4. Applied rewrites 88.3%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 89.5

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 89.5

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

   6. Applied rewrites 89.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.9

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

   8. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+80}:\\ \;\;\;\;\frac{z}{\frac{z - y}{x + y}}\\ \mathbf{elif}\;y \leq 10^{-59}:\\ \;\;\;\;\frac{z}{z - y} \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{z - y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{if}\;y \leq -31000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-8}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- -1.0 (/ x y)) z)))
   (if (<= y -31000000000000.0) t_0 (if (<= y 1.46e-8) (+ x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (-1.0 - (x / y)) * z;
	double tmp;
	if (y <= -31000000000000.0) {
		tmp = t_0;
	} else if (y <= 1.46e-8) {
		tmp = x + y;
	} 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 = ((-1.0d0) - (x / y)) * z
    if (y <= (-31000000000000.0d0)) then
        tmp = t_0
    else if (y <= 1.46d-8) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-1.0 - (x / y)) * z;
	double tmp;
	if (y <= -31000000000000.0) {
		tmp = t_0;
	} else if (y <= 1.46e-8) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-1.0 - (x / y)) * z
	tmp = 0
	if y <= -31000000000000.0:
		tmp = t_0
	elif y <= 1.46e-8:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-1.0 - Float64(x / y)) * z)
	tmp = 0.0
	if (y <= -31000000000000.0)
		tmp = t_0;
	elseif (y <= 1.46e-8)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-1.0 - (x / y)) * z;
	tmp = 0.0;
	if (y <= -31000000000000.0)
		tmp = t_0;
	elseif (y <= 1.46e-8)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -31000000000000.0], t$95$0, If[LessEqual[y, 1.46e-8], N[(x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1e13 or 1.46e-8 < y

   1. Initial program 82.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. div-sub N/A

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

      11. associate-*l/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-neg-frac N/A

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

      14. distribute-lft-neg-out N/A

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

      15. lft-mult-inverse N/A

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

      16. metadata-eval N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if -3.1e13 < y < 1.46e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.9

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

   5. Applied rewrites 79.9%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31000000000000:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-8}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - \frac{x}{y}\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.2 \cdot 10^{+147}:\\ \;\;\;\;\frac{x + y}{z - y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.2e+147) (* (/ (+ x y) (- z y)) z) (+ (fma (/ x z) y x) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.2e+147) {
		tmp = ((x + y) / (z - y)) * z;
	} else {
		tmp = fma((x / z), y, x) + y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.2e+147)
		tmp = Float64(Float64(Float64(x + y) / Float64(z - y)) * z);
	else
		tmp = Float64(fma(Float64(x / z), y, x) + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.2e+147], N[(N[(N[(x + y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(x / z), $MachinePrecision] * y + x), $MachinePrecision] + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.2000000000000002e147

   1. Initial program 90.2%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 90.1

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

   4. Applied rewrites 90.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 90.6

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 90.6

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

   6. Applied rewrites 90.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 94.5

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 94.5

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

   8. Applied rewrites 94.5%

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

   if 2.2000000000000002e147 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. lower-/.f64 99.4

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

   5. Applied rewrites 99.4%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.2 \cdot 10^{+147}:\\ \;\;\;\;\frac{x + y}{z - y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, x\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+117}:\\ \;\;\;\;\left(-1 - \frac{z}{y}\right) \cdot z\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.15e+117) (* (- -1.0 (/ z y)) z) (if (<= y 4e+47) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e+117) {
		tmp = (-1.0 - (z / y)) * z;
	} else if (y <= 4e+47) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.15d+117)) then
        tmp = ((-1.0d0) - (z / y)) * z
    else if (y <= 4d+47) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e+117) {
		tmp = (-1.0 - (z / y)) * z;
	} else if (y <= 4e+47) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.15e+117:
		tmp = (-1.0 - (z / y)) * z
	elif y <= 4e+47:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.15e+117)
		tmp = Float64(Float64(-1.0 - Float64(z / y)) * z);
	elseif (y <= 4e+47)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.15e+117)
		tmp = (-1.0 - (z / y)) * z;
	elseif (y <= 4e+47)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.15e+117], N[(N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 4e+47], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 3 regimes

2. if y < -2.14999999999999999e117

   1. Initial program 72.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-frac-neg2 N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 71.8

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

   4. Applied rewrites 71.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*l/ N/A

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

      9. div-inv N/A

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

      10. neg-mul-1 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. div-inv N/A

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

      13. *-inverses N/A

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

      14. div-sub N/A

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

      15. lift--.f64 N/A

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

      16. clear-num N/A

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

      17. lower-/.f64 72.0

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lift-+.f64 72.0

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

   6. Applied rewrites 72.0%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 59.7

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

   9. Applied rewrites 59.7%

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

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 71.1%

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

   if -2.14999999999999999e117 < y < 4.0000000000000002e47

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 71.8

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

   5. Applied rewrites 71.8%

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

   if 4.0000000000000002e47 < y

   1. Initial program 81.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 59.9

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

   5. Applied rewrites 59.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+117}:\\ \;\;\;\;\left(-1 - \frac{z}{y}\right) \cdot z\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+117}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.15e+117) (- z) (if (<= y 4e+47) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e+117) {
		tmp = -z;
	} else if (y <= 4e+47) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.15d+117)) then
        tmp = -z
    else if (y <= 4d+47) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e+117) {
		tmp = -z;
	} else if (y <= 4e+47) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.15e+117:
		tmp = -z
	elif y <= 4e+47:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.15e+117)
		tmp = Float64(-z);
	elseif (y <= 4e+47)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.15e+117)
		tmp = -z;
	elseif (y <= 4e+47)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.15e+117], (-z), If[LessEqual[y, 4e+47], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -2.14999999999999999e117 or 4.0000000000000002e47 < y

   1. Initial program 76.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   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 64.7

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

   5. Applied rewrites 64.7%

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

   if -2.14999999999999999e117 < y < 4.0000000000000002e47

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 71.8

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

   5. Applied rewrites 71.8%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+117}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.6% 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 91.4%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
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 31.7

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

5. Applied rewrites 31.7%

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

Developer Target 1: 94.4% 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 2024277 
(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))))