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

Percentage Accurate: 99.9% → 100.0%

Time: 5.9s

Alternatives: 9

Speedup: 1.1×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 100.0

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 100.0

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 100.0

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

4. Applied rewrites 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+202}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+24}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+160}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+202)
   (* x y)
   (if (<= x -1.55e+24)
     (* x z)
     (if (<= x -7.5e-60)
       (* x y)
       (if (<= x 5.0) (* 5.0 z) (if (<= x 2.2e+160) (* x z) (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+202) {
		tmp = x * y;
	} else if (x <= -1.55e+24) {
		tmp = x * z;
	} else if (x <= -7.5e-60) {
		tmp = x * y;
	} else if (x <= 5.0) {
		tmp = 5.0 * z;
	} else if (x <= 2.2e+160) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.6d+202)) then
        tmp = x * y
    else if (x <= (-1.55d+24)) then
        tmp = x * z
    else if (x <= (-7.5d-60)) then
        tmp = x * y
    else if (x <= 5.0d0) then
        tmp = 5.0d0 * z
    else if (x <= 2.2d+160) then
        tmp = x * z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+202) {
		tmp = x * y;
	} else if (x <= -1.55e+24) {
		tmp = x * z;
	} else if (x <= -7.5e-60) {
		tmp = x * y;
	} else if (x <= 5.0) {
		tmp = 5.0 * z;
	} else if (x <= 2.2e+160) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e+202:
		tmp = x * y
	elif x <= -1.55e+24:
		tmp = x * z
	elif x <= -7.5e-60:
		tmp = x * y
	elif x <= 5.0:
		tmp = 5.0 * z
	elif x <= 2.2e+160:
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+202)
		tmp = Float64(x * y);
	elseif (x <= -1.55e+24)
		tmp = Float64(x * z);
	elseif (x <= -7.5e-60)
		tmp = Float64(x * y);
	elseif (x <= 5.0)
		tmp = Float64(5.0 * z);
	elseif (x <= 2.2e+160)
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e+202)
		tmp = x * y;
	elseif (x <= -1.55e+24)
		tmp = x * z;
	elseif (x <= -7.5e-60)
		tmp = x * y;
	elseif (x <= 5.0)
		tmp = 5.0 * z;
	elseif (x <= 2.2e+160)
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+202], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.55e+24], N[(x * z), $MachinePrecision], If[LessEqual[x, -7.5e-60], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.0], N[(5.0 * z), $MachinePrecision], If[LessEqual[x, 2.2e+160], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.59999999999999998e202 or -1.55000000000000005e24 < x < -7.5000000000000002e-60 or 2.19999999999999992e160 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 69.7

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

   5. Applied rewrites 69.7%

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

   if -4.59999999999999998e202 < x < -1.55000000000000005e24 or 5 < x < 2.19999999999999992e160

   1. Initial program 98.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 100.0

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 100.0

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 99.8

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

   9. Applied rewrites 99.8%

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

   10. Taylor expanded in y around 0

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

   12. Applied rewrites 63.2%

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

   if -7.5000000000000002e-60 < x < 5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 75.6

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

   5. Applied rewrites 75.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+202}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+24}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+160}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;\mathsf{fma}\left(5, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+19)
   (fma z x (* x y))
   (if (<= x 5.0) (fma 5.0 z (* x y)) (* (+ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+19) {
		tmp = fma(z, x, (x * y));
	} else if (x <= 5.0) {
		tmp = fma(5.0, z, (x * y));
	} else {
		tmp = (y + z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+19)
		tmp = fma(z, x, Float64(x * y));
	elseif (x <= 5.0)
		tmp = fma(5.0, z, Float64(x * y));
	else
		tmp = Float64(Float64(y + z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+19], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.0], N[(5.0 * z + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e19

   1. Initial program 98.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 100.0

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 100.0

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 100.0

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

   9. Applied rewrites 100.0%

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

   11. Applied rewrites 100.0%

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

   if -1.3e19 < x < 5

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 99.9

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 99.5%

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

   if 5 < x

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 98.4

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 98.4

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

   6. Applied rewrites 98.4%

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

   7. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 99.8

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

   9. Applied rewrites 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;\mathsf{fma}\left(5, z, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e-60)
   (fma z x (* x y))
   (if (<= x 7.5e-29) (fma z 5.0 (* x z)) (* (+ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-60) {
		tmp = fma(z, x, (x * y));
	} else if (x <= 7.5e-29) {
		tmp = fma(z, 5.0, (x * z));
	} else {
		tmp = (y + z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e-60)
		tmp = fma(z, x, Float64(x * y));
	elseif (x <= 7.5e-29)
		tmp = fma(z, 5.0, Float64(x * z));
	else
		tmp = Float64(Float64(y + z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e-60], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-29], N[(z * 5.0 + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5000000000000002e-60

   1. Initial program 98.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 100.0

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 100.0

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 97.3

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

   9. Applied rewrites 97.3%

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

   11. Applied rewrites 97.3%

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

   if -7.5000000000000002e-60 < x < 7.50000000000000006e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot x} + z \cdot 5 \]

      2. lower-*.f64 78.6

         \[\leadsto \color{blue}{z \cdot x} + z \cdot 5 \]

   5. Applied rewrites 78.6%

      \[\leadsto \color{blue}{z \cdot x} + z \cdot 5 \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{z \cdot x + z \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot 5 + z \cdot x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot 5} + z \cdot x \]

      4. lower-fma.f64 78.7

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

   7. Applied rewrites 78.7%

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

   if 7.50000000000000006e-29 < x

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 98.5

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 98.5

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

   6. Applied rewrites 98.5%

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

   7. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 96.0

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

   9. Applied rewrites 96.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e-60)
   (fma z x (* x y))
   (if (<= x 7.5e-29) (* 5.0 z) (* (+ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-60) {
		tmp = fma(z, x, (x * y));
	} else if (x <= 7.5e-29) {
		tmp = 5.0 * z;
	} else {
		tmp = (y + z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e-60)
		tmp = fma(z, x, Float64(x * y));
	elseif (x <= 7.5e-29)
		tmp = Float64(5.0 * z);
	else
		tmp = Float64(Float64(y + z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e-60], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-29], N[(5.0 * z), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5000000000000002e-60

   1. Initial program 98.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 100.0

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 100.0

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 97.3

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

   9. Applied rewrites 97.3%

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

   11. Applied rewrites 97.3%

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

   if -7.5000000000000002e-60 < x < 7.50000000000000006e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

   if 7.50000000000000006e-29 < x

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 98.5

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 98.5

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

   6. Applied rewrites 98.5%

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

   7. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 96.0

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

   9. Applied rewrites 96.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y + z\right) \cdot x\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ y z) x)))
   (if (<= x -7.5e-60) t_0 (if (<= x 7.5e-29) (* 5.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y + z) * x;
	double tmp;
	if (x <= -7.5e-60) {
		tmp = t_0;
	} else if (x <= 7.5e-29) {
		tmp = 5.0 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y + z) * x
    if (x <= (-7.5d-60)) then
        tmp = t_0
    else if (x <= 7.5d-29) then
        tmp = 5.0d0 * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y + z) * x;
	double tmp;
	if (x <= -7.5e-60) {
		tmp = t_0;
	} else if (x <= 7.5e-29) {
		tmp = 5.0 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y + z) * x
	tmp = 0
	if x <= -7.5e-60:
		tmp = t_0
	elif x <= 7.5e-29:
		tmp = 5.0 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y + z) * x)
	tmp = 0.0
	if (x <= -7.5e-60)
		tmp = t_0;
	elseif (x <= 7.5e-29)
		tmp = Float64(5.0 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y + z) * x;
	tmp = 0.0;
	if (x <= -7.5e-60)
		tmp = t_0;
	elseif (x <= 7.5e-29)
		tmp = 5.0 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -7.5e-60], t$95$0, If[LessEqual[x, 7.5e-29], N[(5.0 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000002e-60 or 7.50000000000000006e-29 < x

   1. Initial program 99.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-+r+ N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. lift--.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-fma.f64 99.3

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 99.3

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

   6. Applied rewrites 99.3%

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

   7. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 96.7

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

   9. Applied rewrites 96.7%

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

   if -7.5000000000000002e-60 < x < 7.50000000000000006e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - -5\right) \cdot z\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-112}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1200000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x -5.0) z)))
   (if (<= z -1.05e-112) t_0 (if (<= z 1200000000.0) (* x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - -5.0) * z;
	double tmp;
	if (z <= -1.05e-112) {
		tmp = t_0;
	} else if (z <= 1200000000.0) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - (-5.0d0)) * z
    if (z <= (-1.05d-112)) then
        tmp = t_0
    else if (z <= 1200000000.0d0) then
        tmp = x * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - -5.0) * z;
	double tmp;
	if (z <= -1.05e-112) {
		tmp = t_0;
	} else if (z <= 1200000000.0) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - -5.0) * z
	tmp = 0
	if z <= -1.05e-112:
		tmp = t_0
	elif z <= 1200000000.0:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - -5.0) * z)
	tmp = 0.0
	if (z <= -1.05e-112)
		tmp = t_0;
	elseif (z <= 1200000000.0)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - -5.0) * z;
	tmp = 0.0;
	if (z <= -1.05e-112)
		tmp = t_0;
	elseif (z <= 1200000000.0)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - -5.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.05e-112], t$95$0, If[LessEqual[z, 1200000000.0], N[(x * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-112 or 1.2e9 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. metadata-eval N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -1.05e-112 < z < 1.2e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-112}:\\ \;\;\;\;\left(x - -5\right) \cdot z\\ \mathbf{elif}\;z \leq 1200000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x - -5\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e-60) (* x y) (if (<= x 7.5e-29) (* 5.0 z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-60) {
		tmp = x * y;
	} else if (x <= 7.5e-29) {
		tmp = 5.0 * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7.5d-60)) then
        tmp = x * y
    else if (x <= 7.5d-29) then
        tmp = 5.0d0 * z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-60) {
		tmp = x * y;
	} else if (x <= 7.5e-29) {
		tmp = 5.0 * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e-60:
		tmp = x * y
	elif x <= 7.5e-29:
		tmp = 5.0 * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e-60)
		tmp = Float64(x * y);
	elseif (x <= 7.5e-29)
		tmp = Float64(5.0 * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e-60)
		tmp = x * y;
	elseif (x <= 7.5e-29)
		tmp = 5.0 * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e-60], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.5e-29], N[(5.0 * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000002e-60 or 7.50000000000000006e-29 < x

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 52.8

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

   5. Applied rewrites 52.8%

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

   if -7.5000000000000002e-60 < x < 7.50000000000000006e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-60}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.2% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 37.7

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

5. Applied rewrites 37.7%

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

Developer Target 1: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024296 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* (+ x 5) z) (* x y)))

  (+ (* x (+ y z)) (* z 5.0)))