Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C

Percentage Accurate: 99.9% → 99.9%

Time: 6.4s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(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 + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(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 + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (fma (cos y) z (+ (sin y) x)))

C

double code(double x, double y, double z) {
	return fma(cos(y), z, (sin(y) + x));
}

Julia

function code(x, y, z)
	return fma(cos(y), z, Float64(sin(y) + x))
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 99.9

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. lower-+.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 89.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+70}:\\ \;\;\;\;\left(x + \sin y\right) + z \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+29)
   (* (cos y) z)
   (if (<= z 1.05e+70) (+ (+ x (sin y)) (* z 1.0)) (fma (cos y) z (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+29) {
		tmp = cos(y) * z;
	} else if (z <= 1.05e+70) {
		tmp = (x + sin(y)) + (z * 1.0);
	} else {
		tmp = fma(cos(y), z, (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+29)
		tmp = Float64(cos(y) * z);
	elseif (z <= 1.05e+70)
		tmp = Float64(Float64(x + sin(y)) + Float64(z * 1.0));
	else
		tmp = fma(cos(y), z, Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+29], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.05e+70], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * 1.0), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000001e29

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      3. lower-cos.f64 89.0

         \[\leadsto \color{blue}{\cos y} \cdot z \]

   7. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\cos y \cdot z} \]

   if -5.0000000000000001e29 < z < 1.05000000000000004e70

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 96.4%

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

   if 1.05000000000000004e70 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 90.5

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

   7. Applied rewrites 90.5%

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

Alternative 3: 83.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+18}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e+18)
   (* (cos y) z)
   (if (<= z 1.45e-14) (+ (sin y) x) (fma (cos y) z (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+18) {
		tmp = cos(y) * z;
	} else if (z <= 1.45e-14) {
		tmp = sin(y) + x;
	} else {
		tmp = fma(cos(y), z, (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e+18)
		tmp = Float64(cos(y) * z);
	elseif (z <= 1.45e-14)
		tmp = Float64(sin(y) + x);
	else
		tmp = fma(cos(y), z, Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e+18], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.45e-14], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e18

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      3. lower-cos.f64 87.9

         \[\leadsto \color{blue}{\cos y} \cdot z \]

   7. Applied rewrites 87.9%

      \[\leadsto \color{blue}{\cos y \cdot z} \]

   if -1.9e18 < z < 1.4500000000000001e-14

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 100.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-sin.f64 99.9

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-inverses N/A

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

      7. rgt-mult-inverse N/A

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

      8. associate-*r/ N/A

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

      9. *-rgt-identity N/A

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

      10. associate-/l* N/A

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

      11. associate-*l/ N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-cos.f64 N/A

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

      19. associate-*l/ N/A

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

      20. associate-/l* N/A

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

      21. *-rgt-identity N/A

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

   10. Applied rewrites 99.9%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 92.8%

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

   if 1.4500000000000001e-14 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 82.3

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

   7. Applied rewrites 82.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+18}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+18} \lor \neg \left(z \leq 1.75 \cdot 10^{+18}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\sin y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e+18) (not (<= z 1.75e+18))) (* (cos y) z) (+ (sin y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+18) || !(z <= 1.75e+18)) {
		tmp = cos(y) * z;
	} else {
		tmp = sin(y) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.9d+18)) .or. (.not. (z <= 1.75d+18))) then
        tmp = cos(y) * z
    else
        tmp = sin(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+18) || !(z <= 1.75e+18)) {
		tmp = Math.cos(y) * z;
	} else {
		tmp = Math.sin(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.9e+18) or not (z <= 1.75e+18):
		tmp = math.cos(y) * z
	else:
		tmp = math.sin(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e+18) || !(z <= 1.75e+18))
		tmp = Float64(cos(y) * z);
	else
		tmp = Float64(sin(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.9e+18) || ~((z <= 1.75e+18)))
		tmp = cos(y) * z;
	else
		tmp = sin(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e+18], N[Not[LessEqual[z, 1.75e+18]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e18 or 1.75e18 < z

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      3. lower-cos.f64 83.0

         \[\leadsto \color{blue}{\cos y} \cdot z \]

   7. Applied rewrites 83.0%

      \[\leadsto \color{blue}{\cos y \cdot z} \]

   if -1.9e18 < z < 1.75e18

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 100.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-sin.f64 99.9

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-inverses N/A

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

      7. rgt-mult-inverse N/A

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

      8. associate-*r/ N/A

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

      9. *-rgt-identity N/A

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

      10. associate-/l* N/A

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

      11. associate-*l/ N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-cos.f64 N/A

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

      19. associate-*l/ N/A

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

      20. associate-/l* N/A

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

      21. *-rgt-identity N/A

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

   10. Applied rewrites 99.9%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 91.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+18} \lor \neg \left(z \leq 1.75 \cdot 10^{+18}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\sin y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -14500000 \lor \neg \left(y \leq 0.026\right):\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -14500000.0) (not (<= y 0.026))) (+ (sin y) x) (+ (+ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -14500000.0) || !(y <= 0.026)) {
		tmp = sin(y) + x;
	} else {
		tmp = (y + x) + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-14500000.0d0)) .or. (.not. (y <= 0.026d0))) then
        tmp = sin(y) + x
    else
        tmp = (y + x) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -14500000.0) || !(y <= 0.026)) {
		tmp = Math.sin(y) + x;
	} else {
		tmp = (y + x) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -14500000.0) or not (y <= 0.026):
		tmp = math.sin(y) + x
	else:
		tmp = (y + x) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -14500000.0) || !(y <= 0.026))
		tmp = Float64(sin(y) + x);
	else
		tmp = Float64(Float64(y + x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -14500000.0) || ~((y <= 0.026)))
		tmp = sin(y) + x;
	else
		tmp = (y + x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -14500000.0], N[Not[LessEqual[y, 0.026]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], N[(N[(y + x), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e7 or 0.0259999999999999988 < y

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 99.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-sin.f64 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-inverses N/A

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

      7. rgt-mult-inverse N/A

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

      8. associate-*r/ N/A

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

      9. *-rgt-identity N/A

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

      10. associate-/l* N/A

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

      11. associate-*l/ N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. associate-/l* N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-cos.f64 N/A

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

      19. associate-*l/ N/A

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

      20. associate-/l* N/A

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

      21. *-rgt-identity N/A

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

   10. Applied rewrites 92.4%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 61.3%

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

   if -1.45e7 < y < 0.0259999999999999988

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 99.3

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

   5. Applied rewrites 99.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14500000 \lor \neg \left(y \leq 0.026\right):\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+31} \lor \neg \left(y \leq 9.2 \cdot 10^{+18}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e+31) (not (<= y 9.2e+18))) (+ z x) (+ (+ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+31) || !(y <= 9.2e+18)) {
		tmp = z + x;
	} else {
		tmp = (y + x) + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.7d+31)) .or. (.not. (y <= 9.2d+18))) then
        tmp = z + x
    else
        tmp = (y + x) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+31) || !(y <= 9.2e+18)) {
		tmp = z + x;
	} else {
		tmp = (y + x) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e+31) or not (y <= 9.2e+18):
		tmp = z + x
	else:
		tmp = (y + x) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e+31) || !(y <= 9.2e+18))
		tmp = Float64(z + x);
	else
		tmp = Float64(Float64(y + x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.7e+31) || ~((y <= 9.2e+18)))
		tmp = z + x;
	else
		tmp = (y + x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e+31], N[Not[LessEqual[y, 9.2e+18]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(N[(y + x), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999986e31 or 9.2e18 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 37.8

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

   5. Applied rewrites 37.8%

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

   if -2.69999999999999986e31 < y < 9.2e18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 93.3

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

   5. Applied rewrites 93.3%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+31} \lor \neg \left(y \leq 9.2 \cdot 10^{+18}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{-93} \lor \neg \left(x \leq 1.25 \cdot 10^{-246}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.15e-93) (not (<= x 1.25e-246))) (+ z x) (+ z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.15e-93) || !(x <= 1.25e-246)) {
		tmp = z + x;
	} else {
		tmp = z + 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 <= (-3.15d-93)) .or. (.not. (x <= 1.25d-246))) then
        tmp = z + x
    else
        tmp = z + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.15e-93) || !(x <= 1.25e-246)) {
		tmp = z + x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.15e-93) or not (x <= 1.25e-246):
		tmp = z + x
	else:
		tmp = z + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.15e-93) || !(x <= 1.25e-246))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.15e-93) || ~((x <= 1.25e-246)))
		tmp = z + x;
	else
		tmp = z + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.15e-93], N[Not[LessEqual[x, 1.25e-246]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.15000000000000014e-93 or 1.2499999999999999e-246 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 72.2

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

   5. Applied rewrites 72.2%

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

   if -3.15000000000000014e-93 < x < 1.2499999999999999e-246

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \sin y} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \sin y \]

      3. lower-fma.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-sin.f64 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.9%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{-93} \lor \neg \left(x \leq 1.25 \cdot 10^{-246}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.6% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{z \cdot \cos y + \sin y} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\cos y \cdot z} + \sin y \]

   3. lower-fma.f64 N/A

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

   4. lower-cos.f64 N/A

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

   5. lower-sin.f64 62.4

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

5. Applied rewrites 62.4%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 32.6%

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

9. Final simplification 32.6%

   \[\leadsto z + y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024324 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))