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

Percentage Accurate: 99.9% → 99.9%

Time: 6.7s

Alternatives: 12

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: 99.9% 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, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. associate-+l+ N/A

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

   4. lower-+.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. associate-+l+ N/A

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

   8. +-commutative N/A

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

   9. count-2 N/A

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

   10. lower-fma.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-+.f64 99.5

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

4. Applied rewrites 99.5%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.6

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. associate-+r+ N/A

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

   9. lift-fma.f64 N/A

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

   10. +-commutative N/A

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

   11. count-2 N/A

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

   12. associate-+l+ N/A

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

   13. associate-+l+ N/A

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

   14. +-commutative N/A

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

   15. count-2 N/A

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

   16. lower-fma.f64 N/A

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

   17. lower-+.f64 99.6

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

6. Applied rewrites 99.6%

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

   1. lift-fma.f64 N/A

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

   2. count-2 N/A

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

   3. lift-+.f64 N/A

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

   4. +-commutative N/A

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

   5. associate-+l+ N/A

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

   6. lift-+.f64 N/A

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

   7. associate-+l+ N/A

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

   8. lower-+.f64 N/A

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

   9. associate-+r+ N/A

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

   10. count-2 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 99.6

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

8. Applied rewrites 99.6%

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

Alternative 2: 56.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{if}\;t \leq -1 \cdot 10^{+81}:\\ \;\;\;\;t \cdot x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+131}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (fma 2.0 x 5.0) y)))
   (if (<= t -1e+81)
     (* t x)
     (if (<= t 2.25e+48)
       t_1
       (if (<= t 6e+131) (* (* z x) 2.0) (if (<= t 1.36e+202) t_1 (* t x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, x, 5.0) * y;
	double tmp;
	if (t <= -1e+81) {
		tmp = t * x;
	} else if (t <= 2.25e+48) {
		tmp = t_1;
	} else if (t <= 6e+131) {
		tmp = (z * x) * 2.0;
	} else if (t <= 1.36e+202) {
		tmp = t_1;
	} else {
		tmp = t * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, x, 5.0) * y)
	tmp = 0.0
	if (t <= -1e+81)
		tmp = Float64(t * x);
	elseif (t <= 2.25e+48)
		tmp = t_1;
	elseif (t <= 6e+131)
		tmp = Float64(Float64(z * x) * 2.0);
	elseif (t <= 1.36e+202)
		tmp = t_1;
	else
		tmp = Float64(t * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t, -1e+81], N[(t * x), $MachinePrecision], If[LessEqual[t, 2.25e+48], t$95$1, If[LessEqual[t, 6e+131], N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t, 1.36e+202], t$95$1, N[(t * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999921e80 or 1.36e202 < t

   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 79.0

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

   5. Applied rewrites 79.0%

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

   if -9.99999999999999921e80 < t < 2.24999999999999998e48 or 6.0000000000000003e131 < t < 1.36e202

   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

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

      2. metadata-eval N/A

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

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

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

      4. neg-sub0 N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(0 - -2 \cdot x\right)} + 5\right) \]

      5. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      6. neg-sub0 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \cdot y \]

      10. associate--r- N/A

          \[\leadsto \color{blue}{\left(\left(0 - -2 \cdot x\right) + 5\right)} \cdot y \]

      11. neg-sub0 N/A

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

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

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

      13. metadata-eval N/A

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

      14. lower-fma.f64 60.6

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

   5. Applied rewrites 60.6%

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

   if 2.24999999999999998e48 < t < 6.0000000000000003e131

   1. Initial program 95.4%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   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 57.5

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

   5. Applied rewrites 57.5%

      \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot 2} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 48.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-19}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-60}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+14} \lor \neg \left(x \leq 4.7 \cdot 10^{+178}\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9e-19)
   (* (* z x) 2.0)
   (if (<= x 1.55e-60)
     (* 5.0 y)
     (if (or (<= x 1.5e+14) (not (<= x 4.7e+178))) (* t x) (* (* 2.0 x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9e-19) {
		tmp = (z * x) * 2.0;
	} else if (x <= 1.55e-60) {
		tmp = 5.0 * y;
	} else if ((x <= 1.5e+14) || !(x <= 4.7e+178)) {
		tmp = t * x;
	} else {
		tmp = (2.0 * 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 <= (-9d-19)) then
        tmp = (z * x) * 2.0d0
    else if (x <= 1.55d-60) then
        tmp = 5.0d0 * y
    else if ((x <= 1.5d+14) .or. (.not. (x <= 4.7d+178))) then
        tmp = t * x
    else
        tmp = (2.0d0 * 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 <= -9e-19) {
		tmp = (z * x) * 2.0;
	} else if (x <= 1.55e-60) {
		tmp = 5.0 * y;
	} else if ((x <= 1.5e+14) || !(x <= 4.7e+178)) {
		tmp = t * x;
	} else {
		tmp = (2.0 * x) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9e-19:
		tmp = (z * x) * 2.0
	elif x <= 1.55e-60:
		tmp = 5.0 * y
	elif (x <= 1.5e+14) or not (x <= 4.7e+178):
		tmp = t * x
	else:
		tmp = (2.0 * x) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9e-19)
		tmp = Float64(Float64(z * x) * 2.0);
	elseif (x <= 1.55e-60)
		tmp = Float64(5.0 * y);
	elseif ((x <= 1.5e+14) || !(x <= 4.7e+178))
		tmp = Float64(t * x);
	else
		tmp = Float64(Float64(2.0 * x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9e-19)
		tmp = (z * x) * 2.0;
	elseif (x <= 1.55e-60)
		tmp = 5.0 * y;
	elseif ((x <= 1.5e+14) || ~((x <= 4.7e+178)))
		tmp = t * x;
	else
		tmp = (2.0 * x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9e-19], N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[x, 1.55e-60], N[(5.0 * y), $MachinePrecision], If[Or[LessEqual[x, 1.5e+14], N[Not[LessEqual[x, 4.7e+178]], $MachinePrecision]], N[(t * x), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.00000000000000026e-19

   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 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 49.0

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

   5. Applied rewrites 49.0%

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

   if -9.00000000000000026e-19 < x < 1.54999999999999994e-60

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 60.6

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

   5. Applied rewrites 60.6%

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

   if 1.54999999999999994e-60 < x < 1.5e14 or 4.69999999999999992e178 < x

   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 inf

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

      1. lower-*.f64 56.2

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

   5. Applied rewrites 56.2%

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

   if 1.5e14 < x < 4.69999999999999992e178

   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

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lower-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. +-commutative N/A

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

      9. count-2 N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. lift-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. count-2 N/A

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

      12. associate-+l+ N/A

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

      13. associate-+l+ N/A

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

      14. +-commutative N/A

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

      15. count-2 N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-+.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]
   8. 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 46.2

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

   9. Applied rewrites 46.2%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 46.0%

       \[\leadsto \left(2 \cdot x\right) \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-19}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-60}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+14} \lor \neg \left(x \leq 4.7 \cdot 10^{+178}\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot x\right) \cdot 2\\ \mathbf{if}\;x \leq -9 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-60}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+48} \lor \neg \left(x \leq 10^{+134}\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* z x) 2.0)))
   (if (<= x -9e-19)
     t_1
     (if (<= x 1.55e-60)
       (* 5.0 y)
       (if (or (<= x 1.25e+48) (not (<= x 1e+134))) (* t x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * x) * 2.0;
	double tmp;
	if (x <= -9e-19) {
		tmp = t_1;
	} else if (x <= 1.55e-60) {
		tmp = 5.0 * y;
	} else if ((x <= 1.25e+48) || !(x <= 1e+134)) {
		tmp = t * x;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (z * x) * 2.0d0
    if (x <= (-9d-19)) then
        tmp = t_1
    else if (x <= 1.55d-60) then
        tmp = 5.0d0 * y
    else if ((x <= 1.25d+48) .or. (.not. (x <= 1d+134))) then
        tmp = t * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * x) * 2.0;
	double tmp;
	if (x <= -9e-19) {
		tmp = t_1;
	} else if (x <= 1.55e-60) {
		tmp = 5.0 * y;
	} else if ((x <= 1.25e+48) || !(x <= 1e+134)) {
		tmp = t * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * x) * 2.0
	tmp = 0
	if x <= -9e-19:
		tmp = t_1
	elif x <= 1.55e-60:
		tmp = 5.0 * y
	elif (x <= 1.25e+48) or not (x <= 1e+134):
		tmp = t * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * x) * 2.0)
	tmp = 0.0
	if (x <= -9e-19)
		tmp = t_1;
	elseif (x <= 1.55e-60)
		tmp = Float64(5.0 * y);
	elseif ((x <= 1.25e+48) || !(x <= 1e+134))
		tmp = Float64(t * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * x) * 2.0;
	tmp = 0.0;
	if (x <= -9e-19)
		tmp = t_1;
	elseif (x <= 1.55e-60)
		tmp = 5.0 * y;
	elseif ((x <= 1.25e+48) || ~((x <= 1e+134)))
		tmp = t * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * x), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[x, -9e-19], t$95$1, If[LessEqual[x, 1.55e-60], N[(5.0 * y), $MachinePrecision], If[Or[LessEqual[x, 1.25e+48], N[Not[LessEqual[x, 1e+134]], $MachinePrecision]], N[(t * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.00000000000000026e-19 or 1.24999999999999993e48 < x < 9.99999999999999921e133

   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 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 51.8

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

   5. Applied rewrites 51.8%

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

   if -9.00000000000000026e-19 < x < 1.54999999999999994e-60

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 60.6

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

   5. Applied rewrites 60.6%

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

   if 1.54999999999999994e-60 < x < 1.24999999999999993e48 or 9.99999999999999921e133 < x

   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 inf

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

      1. lower-*.f64 43.3

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

   5. Applied rewrites 43.3%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-19}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-60}:\\ \;\;\;\;5 \cdot y\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+48} \lor \neg \left(x \leq 10^{+134}\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+18} \lor \neg \left(x \leq 8.8 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z, t\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.06e+18) (not (<= x 8.8e-5)))
   (* (fma 2.0 (+ z y) t) x)
   (fma y 5.0 (* (fma 2.0 z t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.06e+18) || !(x <= 8.8e-5)) {
		tmp = fma(2.0, (z + y), t) * x;
	} else {
		tmp = fma(y, 5.0, (fma(2.0, z, t) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.06e+18) || !(x <= 8.8e-5))
		tmp = Float64(fma(2.0, Float64(z + y), t) * x);
	else
		tmp = fma(y, 5.0, Float64(fma(2.0, z, t) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.06e+18], N[Not[LessEqual[x, 8.8e-5]], $MachinePrecision]], N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision], N[(y * 5.0 + N[(N[(2.0 * z + t), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06e18 or 8.7999999999999998e-5 < 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 32.6

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

   5. Applied rewrites 32.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 99.9

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

   8. Applied rewrites 99.9%

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

   if -1.06e18 < x < 8.7999999999999998e-5

   1. Initial program 99.1%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   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 99.2

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

      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 99.2

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

      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. flip-+ N/A

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

      15. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right) \cdot x\right) \]

      16. +-inverses N/A

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

      17. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right) \cdot x\right) \]

      18. +-inverses N/A

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

      19. flip-+ N/A

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

      20. count-2 N/A

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

      21. lower-fma.f64 98.6

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

   4. Applied rewrites 98.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+18} \lor \neg \left(x \leq 8.8 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, \mathsf{fma}\left(2, z, t\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+18} \lor \neg \left(x \leq 8.8 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, z, t\right), x, 5 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.06e+18) (not (<= x 8.8e-5)))
   (* (fma 2.0 (+ z y) t) x)
   (fma (fma 2.0 z t) x (* 5.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.06e+18) || !(x <= 8.8e-5)) {
		tmp = fma(2.0, (z + y), t) * x;
	} else {
		tmp = fma(fma(2.0, z, t), x, (5.0 * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.06e+18) || !(x <= 8.8e-5))
		tmp = Float64(fma(2.0, Float64(z + y), t) * x);
	else
		tmp = fma(fma(2.0, z, t), x, Float64(5.0 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.06e+18], N[Not[LessEqual[x, 8.8e-5]], $MachinePrecision]], N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision], N[(N[(2.0 * z + t), $MachinePrecision] * x + N[(5.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06e18 or 8.7999999999999998e-5 < 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 32.6

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

   5. Applied rewrites 32.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 99.9

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

   8. Applied rewrites 99.9%

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

   if -1.06e18 < x < 8.7999999999999998e-5

   1. Initial program 99.1%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   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 99.2

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

      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 99.2

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

      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. flip-+ N/A

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

      15. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right) \cdot x\right) \]

      16. +-inverses N/A

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

      17. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right) \cdot x\right) \]

      18. +-inverses N/A

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

      19. flip-+ N/A

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

      20. count-2 N/A

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

      21. lower-fma.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.3

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

   7. Applied rewrites 76.3%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 98.5

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

   10. Applied rewrites 98.5%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+18} \lor \neg \left(x \leq 8.8 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, z, t\right), x, 5 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-11} \lor \neg \left(x \leq 6 \cdot 10^{-201}\right):\\ \;\;\;\;\mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot x, z, 5 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.7e-11) (not (<= x 6e-201)))
   (* (fma 2.0 (+ z y) t) x)
   (fma (* 2.0 x) z (* 5.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.7e-11) || !(x <= 6e-201)) {
		tmp = fma(2.0, (z + y), t) * x;
	} else {
		tmp = fma((2.0 * x), z, (5.0 * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.7e-11) || !(x <= 6e-201))
		tmp = Float64(fma(2.0, Float64(z + y), t) * x);
	else
		tmp = fma(Float64(2.0 * x), z, Float64(5.0 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.7e-11], N[Not[LessEqual[x, 6e-201]], $MachinePrecision]], N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] * z + N[(5.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6999999999999997e-11 or 6.00000000000000004e-201 < x

   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 inf

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

      1. lower-*.f64 35.3

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 93.2

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

   8. Applied rewrites 93.2%

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

   if -5.6999999999999997e-11 < x < 6.00000000000000004e-201

   1. Initial program 98.7%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   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 98.8

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

      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 98.8

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

      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. flip-+ N/A

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

      15. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right) \cdot x\right) \]

      16. +-inverses N/A

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

      17. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right) \cdot x\right) \]

      18. +-inverses N/A

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

      19. flip-+ N/A

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

      20. count-2 N/A

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

      21. lower-fma.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 86.9

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

   7. Applied rewrites 86.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-11} \lor \neg \left(x \leq 6 \cdot 10^{-201}\right):\\ \;\;\;\;\mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot x, z, 5 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-16} \lor \neg \left(x \leq 3.9 \cdot 10^{-17}\right):\\ \;\;\;\;\mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e-16) (not (<= x 3.9e-17)))
   (* (fma 2.0 (+ z y) t) x)
   (fma y 5.0 (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-16) || !(x <= 3.9e-17)) {
		tmp = fma(2.0, (z + y), t) * x;
	} else {
		tmp = fma(y, 5.0, (x * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e-16) || !(x <= 3.9e-17))
		tmp = Float64(fma(2.0, Float64(z + y), t) * x);
	else
		tmp = fma(y, 5.0, Float64(x * t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e-16], N[Not[LessEqual[x, 3.9e-17]], $MachinePrecision]], N[(N[(2.0 * N[(z + y), $MachinePrecision] + t), $MachinePrecision] * x), $MachinePrecision], N[(y * 5.0 + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000011e-16 or 3.89999999999999989e-17 < 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 33.5

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

   5. Applied rewrites 33.5%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 98.6

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

   8. Applied rewrites 98.6%

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

   if -1.60000000000000011e-16 < x < 3.89999999999999989e-17

   1. Initial program 99.0%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   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 99.1

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

      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 99.1

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

      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. flip-+ N/A

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

      15. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\frac{\color{blue}{0}}{\left(y + z\right) - \left(y + z\right)} + t\right) \cdot x\right) \]

      16. +-inverses N/A

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

      17. +-inverses N/A

          \[\leadsto \mathsf{fma}\left(y, 5, \left(\frac{z \cdot z - z \cdot z}{\color{blue}{0}} + t\right) \cdot x\right) \]

      18. +-inverses N/A

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

      19. flip-+ N/A

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

      20. count-2 N/A

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

      21. lower-fma.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.7

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

   7. Applied rewrites 78.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-16} \lor \neg \left(x \leq 3.9 \cdot 10^{-17}\right):\\ \;\;\;\;\mathsf{fma}\left(2, z + y, t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 5, x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{+106} \lor \neg \left(y \leq 8700000000000\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, z, t\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.1e+106) (not (<= y 8700000000000.0)))
   (* (fma 2.0 x 5.0) y)
   (* (fma 2.0 z t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.1e+106) || !(y <= 8700000000000.0)) {
		tmp = fma(2.0, x, 5.0) * y;
	} else {
		tmp = fma(2.0, z, t) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.1e+106) || !(y <= 8700000000000.0))
		tmp = Float64(fma(2.0, x, 5.0) * y);
	else
		tmp = Float64(fma(2.0, z, t) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.1e+106], N[Not[LessEqual[y, 8700000000000.0]], $MachinePrecision]], N[(N[(2.0 * x + 5.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(2.0 * z + t), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.1000000000000003e106 or 8.7e12 < 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

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

      2. metadata-eval N/A

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

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

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

      4. neg-sub0 N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(0 - -2 \cdot x\right)} + 5\right) \]

      5. associate--r- N/A

         \[\leadsto y \cdot \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \]

      6. neg-sub0 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. neg-sub0 N/A

         \[\leadsto \color{blue}{\left(0 - \left(-2 \cdot x - 5\right)\right)} \cdot y \]

      10. associate--r- N/A

          \[\leadsto \color{blue}{\left(\left(0 - -2 \cdot x\right) + 5\right)} \cdot y \]

      11. neg-sub0 N/A

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

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

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

      13. metadata-eval N/A

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

      14. lower-fma.f64 79.8

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

   5. Applied rewrites 79.8%

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

   if -7.1000000000000003e106 < y < 8.7e12

   1. Initial program 99.3%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   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 75.4

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

   5. Applied rewrites 75.4%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.1 \cdot 10^{+106} \lor \neg \left(y \leq 8700000000000\right):\\ \;\;\;\;\mathsf{fma}\left(2, x, 5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, z, t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. associate-+l+ N/A

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

   4. lower-+.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. associate-+l+ N/A

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

   8. +-commutative N/A

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

   9. count-2 N/A

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

   10. lower-fma.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-+.f64 99.5

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

4. Applied rewrites 99.5%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.6

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. associate-+r+ N/A

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

   9. lift-fma.f64 N/A

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

   10. +-commutative N/A

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

   11. count-2 N/A

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

   12. associate-+l+ N/A

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

   13. associate-+l+ N/A

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

   14. +-commutative N/A

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

   15. count-2 N/A

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

   16. lower-fma.f64 N/A

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

   17. lower-+.f64 99.6

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

6. Applied rewrites 99.6%

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

Alternative 11: 47.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-12} \lor \neg \left(x \leq 1.55 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.7e-12) (not (<= x 1.55e-60))) (* t x) (* 5.0 y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.7e-12) || !(x <= 1.55e-60)) {
		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 <= (-3.7d-12)) .or. (.not. (x <= 1.55d-60))) 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 <= -3.7e-12) || !(x <= 1.55e-60)) {
		tmp = t * x;
	} else {
		tmp = 5.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.7e-12) or not (x <= 1.55e-60):
		tmp = t * x
	else:
		tmp = 5.0 * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.7e-12) || !(x <= 1.55e-60))
		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 <= -3.7e-12) || ~((x <= 1.55e-60)))
		tmp = t * x;
	else
		tmp = 5.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.7e-12], N[Not[LessEqual[x, 1.55e-60]], $MachinePrecision]], N[(t * x), $MachinePrecision], N[(5.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.69999999999999999e-12 or 1.54999999999999994e-60 < 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 35.6

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

   5. Applied rewrites 35.6%

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

   if -3.69999999999999999e-12 < x < 1.54999999999999994e-60

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 60.0

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

   5. Applied rewrites 60.0%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-12} \lor \neg \left(x \leq 1.55 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.1% 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 99.5%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 27.8

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

5. Applied rewrites 27.8%

   \[\leadsto \color{blue}{5 \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024299 
(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)))