Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B

Percentage Accurate: 99.8% → 99.9%

Time: 6.4s

Alternatives: 11

Speedup: 1.2×

• 27.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * ((((y + z) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * ((((y + z) + z) + y) + t)) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * ((((y + z) + z) + y) + t)) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(Float64(Float64(Float64(y + z) + z) + y) + t)) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * ((((y + z) + z) + y) + t)) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(N[(y + z), $MachinePrecision] + z), $MachinePrecision] + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma y 5.0 (* (fma 2.0 (+ z y) t) x)))

C

double code(double x, double y, double z, double t) {
	return fma(y, 5.0, (fma(2.0, (z + y), t) * x));
}

Julia

function code(x, y, z, t)
	return fma(y, 5.0, Float64(fma(2.0, Float64(z + y), t) * x))
end

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

   4. lower-fma.f64 100.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

   7. lower-*.f64 100.0

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

   8. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

   9. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

   10. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

   11. associate-+l+ N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

   13. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

   14. count-2 N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

   15. lower-fma.f64 100.0

       \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

   16. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

   17. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   18. lower-+.f64 100.0

       \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]
5. Add Preprocessing

Alternative 2: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+69} \lor \neg \left(z \leq 3.2 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(z + y\right), 2, 5 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, y, t\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e+69) (not (<= z 3.2e+22)))
   (fma (* x (+ z y)) 2.0 (* 5.0 y))
   (fma y 5.0 (* (fma 2.0 y t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+69) || !(z <= 3.2e+22)) {
		tmp = fma((x * (z + y)), 2.0, (5.0 * y));
	} else {
		tmp = fma(y, 5.0, (fma(2.0, y, t) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e+69) || !(z <= 3.2e+22))
		tmp = fma(Float64(x * Float64(z + y)), 2.0, Float64(5.0 * y));
	else
		tmp = fma(y, 5.0, Float64(fma(2.0, y, t) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e+69], N[Not[LessEqual[z, 3.2e+22]], $MachinePrecision]], N[(N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision] * 2.0 + N[(5.0 * y), $MachinePrecision]), $MachinePrecision], N[(y * 5.0 + N[(N[(2.0 * y + t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999992e69 or 3.2e22 < z

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot y + 2 \cdot z\right) + 5 \cdot y} \]

      2. distribute-lft-out N/A

         \[\leadsto x \cdot \color{blue}{\left(2 \cdot \left(y + z\right)\right)} + 5 \cdot y \]

      3. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y + z\right) \cdot 2\right)} + 5 \cdot y \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot 2} + 5 \cdot y \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(y + z\right), 2, 5 \cdot y\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(y + z\right)}, 2, 5 \cdot y\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{\left(z + y\right)}, 2, 5 \cdot y\right) \]

      8. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \color{blue}{\left(z + y\right)}, 2, 5 \cdot y\right) \]

      9. lower-*.f64 90.6

         \[\leadsto \mathsf{fma}\left(x \cdot \left(z + y\right), 2, \color{blue}{5 \cdot y}\right) \]

   5. Applied rewrites 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(z + y\right), 2, 5 \cdot y\right)} \]

   if -1.59999999999999992e69 < z < 3.2e22

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

      4. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      7. lower-*.f64 100.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

      15. lower-fma.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

      16. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

      18. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(t + 2 \cdot y\right)} \cdot x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot y + t\right)} \cdot x\right) \]

      2. lower-fma.f64 100.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y, t\right)} \cdot x\right) \]

   7. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y, t\right)} \cdot x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+69} \lor \neg \left(z \leq 3.2 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(z + y\right), 2, 5 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, y, t\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140} \lor \neg \left(z \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(z + z\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, y, t\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e+140) (not (<= z 3.3e+22)))
   (fma y 5.0 (* (+ z z) x))
   (fma y 5.0 (* (fma 2.0 y t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+140) || !(z <= 3.3e+22)) {
		tmp = fma(y, 5.0, ((z + z) * x));
	} else {
		tmp = fma(y, 5.0, (fma(2.0, y, t) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e+140) || !(z <= 3.3e+22))
		tmp = fma(y, 5.0, Float64(Float64(z + z) * x));
	else
		tmp = fma(y, 5.0, Float64(fma(2.0, y, t) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e+140], N[Not[LessEqual[z, 3.3e+22]], $MachinePrecision]], N[(y * 5.0 + N[(N[(z + z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(y * 5.0 + N[(N[(2.0 * y + t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999996e140 or 3.2999999999999998e22 < z

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

      4. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      7. lower-*.f64 100.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

      15. lower-fma.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

      16. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

      18. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(t + 2 \cdot y\right)} \cdot x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot y + t\right)} \cdot x\right) \]

      2. lower-fma.f64 47.1

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y, t\right)} \cdot x\right) \]

   7. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y, t\right)} \cdot x\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot z\right)} \cdot x\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(z \cdot 2\right)} \cdot x\right) \]

      2. lower-*.f64 88.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(z \cdot 2\right)} \cdot x\right) \]

   10. Applied rewrites 88.0%

       \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(z \cdot 2\right)} \cdot x\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 88.0%

       \[\leadsto \mathsf{fma}\left(y, 5, \left(z + \color{blue}{z}\right) \cdot x\right) \]

   if -8.4999999999999996e140 < z < 3.2999999999999998e22

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

      4. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      7. lower-*.f64 100.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

      15. lower-fma.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

      16. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

      18. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(t + 2 \cdot y\right)} \cdot x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot y + t\right)} \cdot x\right) \]

      2. lower-fma.f64 95.2

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y, t\right)} \cdot x\right) \]

   7. Applied rewrites 95.2%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y, t\right)} \cdot x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140} \lor \neg \left(z \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(z + z\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, y, t\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140} \lor \neg \left(z \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(z + z\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, y, t\right), x, 5 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e+140) (not (<= z 3.3e+22)))
   (fma y 5.0 (* (+ z z) x))
   (fma (fma 2.0 y t) x (* 5.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+140) || !(z <= 3.3e+22)) {
		tmp = fma(y, 5.0, ((z + z) * x));
	} else {
		tmp = fma(fma(2.0, y, t), x, (5.0 * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e+140) || !(z <= 3.3e+22))
		tmp = fma(y, 5.0, Float64(Float64(z + z) * x));
	else
		tmp = fma(fma(2.0, y, t), x, Float64(5.0 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e+140], N[Not[LessEqual[z, 3.3e+22]], $MachinePrecision]], N[(y * 5.0 + N[(N[(z + z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * y + t), $MachinePrecision] * x + N[(5.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999996e140 or 3.2999999999999998e22 < z

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

      4. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      7. lower-*.f64 100.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

      15. lower-fma.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

      16. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

      18. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(t + 2 \cdot y\right)} \cdot x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot y + t\right)} \cdot x\right) \]

      2. lower-fma.f64 47.1

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y, t\right)} \cdot x\right) \]

   7. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y, t\right)} \cdot x\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot z\right)} \cdot x\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(z \cdot 2\right)} \cdot x\right) \]

      2. lower-*.f64 88.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(z \cdot 2\right)} \cdot x\right) \]

   10. Applied rewrites 88.0%

       \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(z \cdot 2\right)} \cdot x\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 88.0%

       \[\leadsto \mathsf{fma}\left(y, 5, \left(z + \color{blue}{z}\right) \cdot x\right) \]

   if -8.4999999999999996e140 < z < 3.2999999999999998e22

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x \cdot \left(t + 2 \cdot y\right) + 5 \cdot y} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(t + 2 \cdot y\right) \cdot x} + 5 \cdot y \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t + 2 \cdot y, x, 5 \cdot y\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot y + t}, x, 5 \cdot y\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, y, t\right)}, x, 5 \cdot y\right) \]

      6. lower-*.f64 95.2

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(2, y, t\right), x, \color{blue}{5 \cdot y}\right) \]

   5. Applied rewrites 95.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, y, t\right), x, 5 \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140} \lor \neg \left(z \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(z + z\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, y, t\right), x, 5 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-161}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq 0.005:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+226}:\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x + x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.4e-161)
   (* t x)
   (if (<= x 0.005) (* 5.0 y) (if (<= x 2.8e+226) (* t x) (* (+ x x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.4e-161) {
		tmp = t * x;
	} else if (x <= 0.005) {
		tmp = 5.0 * y;
	} else if (x <= 2.8e+226) {
		tmp = t * x;
	} else {
		tmp = (x + x) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.4d-161)) then
        tmp = t * x
    else if (x <= 0.005d0) then
        tmp = 5.0d0 * y
    else if (x <= 2.8d+226) then
        tmp = t * x
    else
        tmp = (x + x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.4e-161) {
		tmp = t * x;
	} else if (x <= 0.005) {
		tmp = 5.0 * y;
	} else if (x <= 2.8e+226) {
		tmp = t * x;
	} else {
		tmp = (x + x) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.4e-161:
		tmp = t * x
	elif x <= 0.005:
		tmp = 5.0 * y
	elif x <= 2.8e+226:
		tmp = t * x
	else:
		tmp = (x + x) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.4e-161)
		tmp = Float64(t * x);
	elseif (x <= 0.005)
		tmp = Float64(5.0 * y);
	elseif (x <= 2.8e+226)
		tmp = Float64(t * x);
	else
		tmp = Float64(Float64(x + x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.4e-161)
		tmp = t * x;
	elseif (x <= 0.005)
		tmp = 5.0 * y;
	elseif (x <= 2.8e+226)
		tmp = t * x;
	else
		tmp = (x + x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.4e-161], N[(t * x), $MachinePrecision], If[LessEqual[x, 0.005], N[(5.0 * y), $MachinePrecision], If[LessEqual[x, 2.8e+226], N[(t * x), $MachinePrecision], N[(N[(x + x), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.39999999999999971e-161 or 0.0050000000000000001 < x < 2.8000000000000003e226

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 48.3

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

   5. Applied rewrites 48.3%

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

   if -6.39999999999999971e-161 < x < 0.0050000000000000001

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 66.2

         \[\leadsto \color{blue}{5 \cdot y} \]

   5. Applied rewrites 66.2%

      \[\leadsto \color{blue}{5 \cdot y} \]

   if 2.8000000000000003e226 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

      4. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      7. lower-*.f64 100.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

      15. lower-fma.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

      16. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

      18. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + 2 \cdot x\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + 2 \cdot x\right) \cdot y} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot x + 5\right)} \cdot y \]

      4. lower-fma.f64 58.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 5\right)} \cdot y \]

   7. Applied rewrites 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 5\right) \cdot y} \]

   8. Taylor expanded in x around inf

      \[\leadsto \left(2 \cdot x\right) \cdot y \]
   9. Step-by-step derivation

   10. Applied rewrites 58.5%

       \[\leadsto \left(x \cdot 2\right) \cdot y \]
   11. Step-by-step derivation

   12. Applied rewrites 58.5%

       \[\leadsto \left(x + x\right) \cdot y \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-161}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;x \leq 0.005:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+226}:\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x + x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+110} \lor \neg \left(y \leq 2.4 \cdot 10^{+44}\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t + z\right) + z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.9e+110) (not (<= y 2.4e+44)))
   (* (fma 2.0 x 5.0) y)
   (* (+ (+ t z) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e+110) || !(y <= 2.4e+44)) {
		tmp = fma(2.0, x, 5.0) * y;
	} else {
		tmp = ((t + z) + z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.9e+110) || !(y <= 2.4e+44))
		tmp = Float64(fma(2.0, x, 5.0) * y);
	else
		tmp = Float64(Float64(Float64(t + z) + z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.9e+110], N[Not[LessEqual[y, 2.4e+44]], $MachinePrecision]], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(t + z), $MachinePrecision] + z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9000000000000003e110 or 2.40000000000000013e44 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + 2 \cdot x\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + 2 \cdot x\right) \cdot y} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot x + 5\right)} \cdot y \]

      4. lower-fma.f64 81.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 5\right)} \cdot y \]

   5. Applied rewrites 81.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 5\right) \cdot y} \]

   if -3.9000000000000003e110 < y < 2.40000000000000013e44

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(t + 2 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(t + 2 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot z + t\right)} \cdot x \]

      4. lower-fma.f64 79.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, z, t\right)} \cdot x \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, z, t\right) \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 79.8%

      \[\leadsto \left(\left(t + z\right) + z\right) \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+110} \lor \neg \left(y \leq 2.4 \cdot 10^{+44}\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t + z\right) + z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-161} \lor \neg \left(x \leq 0.0029\right):\\ \;\;\;\;\left(\left(t + z\right) + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4e-161) (not (<= x 0.0029))) (* (+ (+ t z) z) x) (* 5.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e-161) || !(x <= 0.0029)) {
		tmp = ((t + z) + z) * x;
	} else {
		tmp = 5.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4d-161)) .or. (.not. (x <= 0.0029d0))) then
        tmp = ((t + z) + z) * x
    else
        tmp = 5.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e-161) || !(x <= 0.0029)) {
		tmp = ((t + z) + z) * x;
	} else {
		tmp = 5.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4e-161) or not (x <= 0.0029):
		tmp = ((t + z) + z) * x
	else:
		tmp = 5.0 * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4e-161) || !(x <= 0.0029))
		tmp = Float64(Float64(Float64(t + z) + z) * x);
	else
		tmp = Float64(5.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4e-161) || ~((x <= 0.0029)))
		tmp = ((t + z) + z) * x;
	else
		tmp = 5.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4e-161], N[Not[LessEqual[x, 0.0029]], $MachinePrecision]], N[(N[(N[(t + z), $MachinePrecision] + z), $MachinePrecision] * x), $MachinePrecision], N[(5.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000011e-161 or 0.0029 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(t + 2 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(t + 2 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot z + t\right)} \cdot x \]

      4. lower-fma.f64 72.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, z, t\right)} \cdot x \]

   5. Applied rewrites 72.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, z, t\right) \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 72.8%

      \[\leadsto \left(\left(t + z\right) + z\right) \cdot x \]

   if -4.00000000000000011e-161 < x < 0.0029

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 66.2

         \[\leadsto \color{blue}{5 \cdot y} \]

   5. Applied rewrites 66.2%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-161} \lor \neg \left(x \leq 0.0029\right):\\ \;\;\;\;\left(\left(t + z\right) + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(y + y\right) \cdot x\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;\left(\left(t + z\right) + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.9e+110)
   (fma y 5.0 (* (+ y y) x))
   (if (<= y 2.4e+44) (* (+ (+ t z) z) x) (* (fma 2.0 x 5.0) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e+110) {
		tmp = fma(y, 5.0, ((y + y) * x));
	} else if (y <= 2.4e+44) {
		tmp = ((t + z) + z) * x;
	} else {
		tmp = fma(2.0, x, 5.0) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.9e+110)
		tmp = fma(y, 5.0, Float64(Float64(y + y) * x));
	elseif (y <= 2.4e+44)
		tmp = Float64(Float64(Float64(t + z) + z) * x);
	else
		tmp = Float64(fma(2.0, x, 5.0) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.9e+110], N[(y * 5.0 + N[(N[(y + y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+44], N[(N[(N[(t + z), $MachinePrecision] + z), $MachinePrecision] * x), $MachinePrecision], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000003e110

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot 5} + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \]

      4. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      7. lower-*.f64 100.0

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)} \cdot x\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(\left(y + z\right) + z\right) + y\right)} + t\right) \cdot x\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\color{blue}{\left(\left(y + z\right) + z\right)} + y\right) + t\right) \cdot x\right) \]

      11. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) \cdot x\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) \cdot x\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\color{blue}{2 \cdot \left(y + z\right)} + t\right) \cdot x\right) \]

      15. lower-fma.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\mathsf{fma}\left(2, y + z, t\right)} \cdot x\right) \]

      16. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{y + z}, t\right) \cdot x\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

      18. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, \color{blue}{z + y}, t\right) \cdot x\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z + y, t\right) \cdot x\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot y\right)} \cdot x\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 89.9

         \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot y\right)} \cdot x\right) \]

   7. Applied rewrites 89.9%

      \[\leadsto \mathsf{fma}\left(y, 5, \color{blue}{\left(2 \cdot y\right)} \cdot x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 89.9%

      \[\leadsto \mathsf{fma}\left(y, 5, \left(y + \color{blue}{y}\right) \cdot x\right) \]

   if -3.9000000000000003e110 < y < 2.40000000000000013e44

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(t + 2 \cdot z\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(t + 2 \cdot z\right) \cdot x} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot z + t\right)} \cdot x \]

      4. lower-fma.f64 79.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, z, t\right)} \cdot x \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, z, t\right) \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 79.8%

      \[\leadsto \left(\left(t + z\right) + z\right) \cdot x \]

   if 2.40000000000000013e44 < y

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + 2 \cdot x\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + 2 \cdot x\right) \cdot y} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot x + 5\right)} \cdot y \]

      4. lower-fma.f64 77.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 5\right)} \cdot y \]

   5. Applied rewrites 77.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 5\right) \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \left(y + y\right) \cdot x\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;\left(\left(t + z\right) + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+69} \lor \neg \left(z \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e+69) (not (<= z 3.3e+22))) (* (* z x) 2.0) (* t x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+69) || !(z <= 3.3e+22)) {
		tmp = (z * x) * 2.0;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d+69)) .or. (.not. (z <= 3.3d+22))) then
        tmp = (z * x) * 2.0d0
    else
        tmp = t * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+69) || !(z <= 3.3e+22)) {
		tmp = (z * x) * 2.0;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e+69) or not (z <= 3.3e+22):
		tmp = (z * x) * 2.0
	else:
		tmp = t * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e+69) || !(z <= 3.3e+22))
		tmp = Float64(Float64(z * x) * 2.0);
	else
		tmp = Float64(t * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e+69) || ~((z <= 3.3e+22)))
		tmp = (z * x) * 2.0;
	else
		tmp = t * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e+69], N[Not[LessEqual[z, 3.3e+22]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision], N[(t * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999992e69 or 3.2999999999999998e22 < z

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot 2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot 2} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot 2 \]

      4. lower-*.f64 57.9

         \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot 2 \]

   5. Applied rewrites 57.9%

      \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot 2} \]

   if -1.59999999999999992e69 < z < 3.2999999999999998e22

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 50.7

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

   5. Applied rewrites 50.7%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+69} \lor \neg \left(z \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-161} \lor \neg \left(x \leq 0.005\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.4e-161) (not (<= x 0.005))) (* t x) (* 5.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.4e-161) || !(x <= 0.005)) {
		tmp = t * x;
	} else {
		tmp = 5.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-6.4d-161)) .or. (.not. (x <= 0.005d0))) then
        tmp = t * x
    else
        tmp = 5.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.4e-161) || !(x <= 0.005)) {
		tmp = t * x;
	} else {
		tmp = 5.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.4e-161) or not (x <= 0.005):
		tmp = t * x
	else:
		tmp = 5.0 * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.4e-161) || !(x <= 0.005))
		tmp = Float64(t * x);
	else
		tmp = Float64(5.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6.4e-161) || ~((x <= 0.005)))
		tmp = t * x;
	else
		tmp = 5.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.4e-161], N[Not[LessEqual[x, 0.005]], $MachinePrecision]], N[(t * x), $MachinePrecision], N[(5.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.39999999999999971e-161 or 0.0050000000000000001 < x

   1. Initial program 100.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 46.1

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

   5. Applied rewrites 46.1%

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

   if -6.39999999999999971e-161 < x < 0.0050000000000000001

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 66.2

         \[\leadsto \color{blue}{5 \cdot y} \]

   5. Applied rewrites 66.2%

      \[\leadsto \color{blue}{5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-161} \lor \neg \left(x \leq 0.005\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ 5 \cdot y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 5.0 y))

C

double code(double x, double y, double z, double t) {
	return 5.0 * y;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 5.0d0 * y
end function

Java

public static double code(double x, double y, double z, double t) {
	return 5.0 * y;
}

Python

def code(x, y, z, t):
	return 5.0 * y

Julia

function code(x, y, z, t)
	return Float64(5.0 * y)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 5.0 * y;
end

Wolfram

code[x_, y_, z_, t_] := N[(5.0 * y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{5 \cdot y} \]
4. Step-by-step derivation

   1. lower-*.f64 29.1

      \[\leadsto \color{blue}{5 \cdot y} \]

5. Applied rewrites 29.1%

   \[\leadsto \color{blue}{5 \cdot y} \]

6. Final simplification 29.1%

   \[\leadsto 5 \cdot y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))