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

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 13

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\sin y + x\right) + \cos y \cdot z\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-29}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq 10^{-130}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (+ (sin y) x) (* (cos y) z))))
   (if (<= t_0 -5e-29) (+ z x) (if (<= t_0 1e-130) (+ y x) (+ z x)))))

C

double code(double x, double y, double z) {
	double t_0 = (sin(y) + x) + (cos(y) * z);
	double tmp;
	if (t_0 <= -5e-29) {
		tmp = z + x;
	} else if (t_0 <= 1e-130) {
		tmp = y + x;
	} else {
		tmp = z + 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) :: t_0
    real(8) :: tmp
    t_0 = (sin(y) + x) + (cos(y) * z)
    if (t_0 <= (-5d-29)) then
        tmp = z + x
    else if (t_0 <= 1d-130) then
        tmp = y + x
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.sin(y) + x) + (Math.cos(y) * z);
	double tmp;
	if (t_0 <= -5e-29) {
		tmp = z + x;
	} else if (t_0 <= 1e-130) {
		tmp = y + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.sin(y) + x) + (math.cos(y) * z)
	tmp = 0
	if t_0 <= -5e-29:
		tmp = z + x
	elif t_0 <= 1e-130:
		tmp = y + x
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(sin(y) + x) + Float64(cos(y) * z))
	tmp = 0.0
	if (t_0 <= -5e-29)
		tmp = Float64(z + x);
	elseif (t_0 <= 1e-130)
		tmp = Float64(y + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (sin(y) + x) + (cos(y) * z);
	tmp = 0.0;
	if (t_0 <= -5e-29)
		tmp = z + x;
	elseif (t_0 <= 1e-130)
		tmp = y + x;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-29], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, 1e-130], N[(y + x), $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -4.99999999999999986e-29 or 1.0000000000000001e-130 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   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 68.6

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

   5. Applied rewrites 68.6%

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

   if -4.99999999999999986e-29 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 1.0000000000000001e-130

   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. flip3-+ N/A

         \[\leadsto \color{blue}{\frac{{\left(x + \sin y\right)}^{3} + {\left(z \cdot \cos y\right)}^{3}}{\left(x + \sin y\right) \cdot \left(x + \sin y\right) + \left(\left(z \cdot \cos y\right) \cdot \left(z \cdot \cos y\right) - \left(x + \sin y\right) \cdot \left(z \cdot \cos y\right)\right)}} \]

      3. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + \sin y\right) \cdot \left(x + \sin y\right) + \left(\left(z \cdot \cos y\right) \cdot \left(z \cdot \cos y\right) - \left(x + \sin y\right) \cdot \left(z \cdot \cos y\right)\right)}{{\left(x + \sin y\right)}^{3} + {\left(z \cdot \cos y\right)}^{3}}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + \sin y\right) \cdot \left(x + \sin y\right) + \left(\left(z \cdot \cos y\right) \cdot \left(z \cdot \cos y\right) - \left(x + \sin y\right) \cdot \left(z \cdot \cos y\right)\right)}{{\left(x + \sin y\right)}^{3} + {\left(z \cdot \cos y\right)}^{3}}}} \]

      5. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{\left(x + \sin y\right)}^{3} + {\left(z \cdot \cos y\right)}^{3}}{\left(x + \sin y\right) \cdot \left(x + \sin y\right) + \left(\left(z \cdot \cos y\right) \cdot \left(z \cdot \cos y\right) - \left(x + \sin y\right) \cdot \left(z \cdot \cos y\right)\right)}}}} \]

      6. flip3-+ N/A

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

      7. lift-+.f64 N/A

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

      8. inv-pow N/A

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

      9. lower-pow.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 100.0

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

   7. Applied rewrites 100.0%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 100.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\sin y + x\right) + \cos y \cdot z \leq -5 \cdot 10^{-29}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;\left(\sin y + x\right) + \cos y \cdot z \leq 10^{-130}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 4: 89.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\cos y, z, y + x\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+177}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+87}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \mathsf{fma}\left(\frac{\sin y}{x}, x, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (cos y) z (+ y x))))
   (if (<= z -3.6e+177)
     t_0
     (if (<= z -8.8e+87)
       (* (cos y) z)
       (if (<= z 1.65e+108) (fma 1.0 z (fma (/ (sin y) x) x x)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fma(cos(y), z, (y + x));
	double tmp;
	if (z <= -3.6e+177) {
		tmp = t_0;
	} else if (z <= -8.8e+87) {
		tmp = cos(y) * z;
	} else if (z <= 1.65e+108) {
		tmp = fma(1.0, z, fma((sin(y) / x), x, x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(cos(y), z, Float64(y + x))
	tmp = 0.0
	if (z <= -3.6e+177)
		tmp = t_0;
	elseif (z <= -8.8e+87)
		tmp = Float64(cos(y) * z);
	elseif (z <= 1.65e+108)
		tmp = fma(1.0, z, fma(Float64(sin(y) / x), x, x));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+177], t$95$0, If[LessEqual[z, -8.8e+87], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.65e+108], N[(1.0 * z + N[(N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision] * x + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000003e177 or 1.6500000000000001e108 < 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 y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 91.4

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

   7. Applied rewrites 91.4%

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

   if -3.60000000000000003e177 < z < -8.8000000000000003e87

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \cos y} \]
   4. 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 84.2

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

   5. Applied rewrites 84.2%

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

   if -8.8000000000000003e87 < z < 1.6500000000000001e108

   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 y around 0

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

   10. Applied rewrites 94.0%

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

Alternative 5: 85.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\cos y, z, y + x\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+177}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+87}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-50}:\\ \;\;\;\;\sin y + x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+108}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (cos y) z (+ y x))))
   (if (<= z -3.6e+177)
     t_0
     (if (<= z -8.8e+87)
       (* (cos y) z)
       (if (<= z -3.7e-31)
         (+ z x)
         (if (<= z 3.5e-50)
           (+ (sin y) x)
           (if (<= z 1.65e+108) (+ z x) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(cos(y), z, (y + x));
	double tmp;
	if (z <= -3.6e+177) {
		tmp = t_0;
	} else if (z <= -8.8e+87) {
		tmp = cos(y) * z;
	} else if (z <= -3.7e-31) {
		tmp = z + x;
	} else if (z <= 3.5e-50) {
		tmp = sin(y) + x;
	} else if (z <= 1.65e+108) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(cos(y), z, Float64(y + x))
	tmp = 0.0
	if (z <= -3.6e+177)
		tmp = t_0;
	elseif (z <= -8.8e+87)
		tmp = Float64(cos(y) * z);
	elseif (z <= -3.7e-31)
		tmp = Float64(z + x);
	elseif (z <= 3.5e-50)
		tmp = Float64(sin(y) + x);
	elseif (z <= 1.65e+108)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z + N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+177], t$95$0, If[LessEqual[z, -8.8e+87], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, -3.7e-31], N[(z + x), $MachinePrecision], If[LessEqual[z, 3.5e-50], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.65e+108], N[(z + x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.60000000000000003e177 or 1.6500000000000001e108 < 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 y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 91.4

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

   7. Applied rewrites 91.4%

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

   if -3.60000000000000003e177 < z < -8.8000000000000003e87

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \cos y} \]
   4. 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 84.2

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

   5. Applied rewrites 84.2%

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

   if -8.8000000000000003e87 < z < -3.6999999999999998e-31 or 3.49999999999999997e-50 < z < 1.6500000000000001e108

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if -3.6999999999999998e-31 < z < 3.49999999999999997e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 98.1

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

   5. Applied rewrites 98.1%

      \[\leadsto \color{blue}{\sin y + x} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 83.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-50}:\\ \;\;\;\;\sin y + x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+266}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -8.8e+87)
     t_0
     (if (<= z -3.7e-31)
       (+ z x)
       (if (<= z 3.5e-50) (+ (sin y) x) (if (<= z 5.2e+266) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -8.8e+87) {
		tmp = t_0;
	} else if (z <= -3.7e-31) {
		tmp = z + x;
	} else if (z <= 3.5e-50) {
		tmp = sin(y) + x;
	} else if (z <= 5.2e+266) {
		tmp = z + x;
	} 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 = cos(y) * z
    if (z <= (-8.8d+87)) then
        tmp = t_0
    else if (z <= (-3.7d-31)) then
        tmp = z + x
    else if (z <= 3.5d-50) then
        tmp = sin(y) + x
    else if (z <= 5.2d+266) then
        tmp = z + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double tmp;
	if (z <= -8.8e+87) {
		tmp = t_0;
	} else if (z <= -3.7e-31) {
		tmp = z + x;
	} else if (z <= 3.5e-50) {
		tmp = Math.sin(y) + x;
	} else if (z <= 5.2e+266) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -8.8e+87:
		tmp = t_0
	elif z <= -3.7e-31:
		tmp = z + x
	elif z <= 3.5e-50:
		tmp = math.sin(y) + x
	elif z <= 5.2e+266:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -8.8e+87)
		tmp = t_0;
	elseif (z <= -3.7e-31)
		tmp = Float64(z + x);
	elseif (z <= 3.5e-50)
		tmp = Float64(sin(y) + x);
	elseif (z <= 5.2e+266)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	tmp = 0.0;
	if (z <= -8.8e+87)
		tmp = t_0;
	elseif (z <= -3.7e-31)
		tmp = z + x;
	elseif (z <= 3.5e-50)
		tmp = sin(y) + x;
	elseif (z <= 5.2e+266)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -8.8e+87], t$95$0, If[LessEqual[z, -3.7e-31], N[(z + x), $MachinePrecision], If[LessEqual[z, 3.5e-50], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 5.2e+266], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.8000000000000003e87 or 5.20000000000000027e266 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \cos y} \]
   4. 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 85.2

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

   5. Applied rewrites 85.2%

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

   if -8.8000000000000003e87 < z < -3.6999999999999998e-31 or 3.49999999999999997e-50 < z < 5.20000000000000027e266

   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 79.9

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

   5. Applied rewrites 79.9%

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

   if -3.6999999999999998e-31 < z < 3.49999999999999997e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 98.1

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

   5. Applied rewrites 98.1%

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

Alternative 7: 78.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-50}:\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.7e-31) (+ z x) (if (<= z 3.5e-50) (+ (sin y) x) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e-31) {
		tmp = z + x;
	} else if (z <= 3.5e-50) {
		tmp = sin(y) + x;
	} else {
		tmp = z + 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 <= (-3.7d-31)) then
        tmp = z + x
    else if (z <= 3.5d-50) then
        tmp = sin(y) + x
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e-31) {
		tmp = z + x;
	} else if (z <= 3.5e-50) {
		tmp = Math.sin(y) + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.7e-31:
		tmp = z + x
	elif z <= 3.5e-50:
		tmp = math.sin(y) + x
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.7e-31)
		tmp = Float64(z + x);
	elseif (z <= 3.5e-50)
		tmp = Float64(sin(y) + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.7e-31)
		tmp = z + x;
	elseif (z <= 3.5e-50)
		tmp = sin(y) + x;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.7e-31], N[(z + x), $MachinePrecision], If[LessEqual[z, 3.5e-50], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999998e-31 or 3.49999999999999997e-50 < z

   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 67.0

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

   5. Applied rewrites 67.0%

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

   if -3.6999999999999998e-31 < z < 3.49999999999999997e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 98.1

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

   5. Applied rewrites 98.1%

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

Alternative 8: 69.4% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 3.15:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.041666666666666664, y \cdot y, -0.5\right) \cdot z, y \cdot y, z\right) + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1)
   (+ z x)
   (if (<= y 3.15)
     (+ (fma (* (fma 0.041666666666666664 (* y y) -0.5) z) (* y y) z) (+ y x))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1) {
		tmp = z + x;
	} else if (y <= 3.15) {
		tmp = fma((fma(0.041666666666666664, (y * y), -0.5) * z), (y * y), z) + (y + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1)
		tmp = Float64(z + x);
	elseif (y <= 3.15)
		tmp = Float64(fma(Float64(fma(0.041666666666666664, Float64(y * y), -0.5) * z), Float64(y * y), z) + Float64(y + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1], N[(z + x), $MachinePrecision], If[LessEqual[y, 3.15], N[(N[(N[(N[(0.041666666666666664 * N[(y * y), $MachinePrecision] + -0.5), $MachinePrecision] * z), $MachinePrecision] * N[(y * y), $MachinePrecision] + z), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000009 or 3.14999999999999991 < y

   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 45.8

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

   5. Applied rewrites 45.8%

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

   if -3.10000000000000009 < y < 3.14999999999999991

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(y + x\right) + \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{2} \cdot z + \frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(y + x\right) + \color{blue}{\left({y}^{2} \cdot \left(\frac{-1}{2} \cdot z + \frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right) + z\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(y + x\right) + \left(\color{blue}{\left(\frac{-1}{2} \cdot z + \frac{1}{24} \cdot \left({y}^{2} \cdot z\right)\right) \cdot {y}^{2}} + z\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(y + x\right) + \color{blue}{\mathsf{fma}\left(\frac{-1}{2} \cdot z + \frac{1}{24} \cdot \left({y}^{2} \cdot z\right), {y}^{2}, z\right)} \]

      4. associate-*r* N/A

         \[\leadsto \left(y + x\right) + \mathsf{fma}\left(\frac{-1}{2} \cdot z + \color{blue}{\left(\frac{1}{24} \cdot {y}^{2}\right) \cdot z}, {y}^{2}, z\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \left(y + x\right) + \mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{-1}{2} + \frac{1}{24} \cdot {y}^{2}\right)}, {y}^{2}, z\right) \]

      6. +-commutative N/A

         \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \color{blue}{\left(\frac{1}{24} \cdot {y}^{2} + \frac{-1}{2}\right)}, {y}^{2}, z\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \left(\frac{1}{24} \cdot {y}^{2} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right), {y}^{2}, z\right) \]

      8. sub-neg N/A

         \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \color{blue}{\left(\frac{1}{24} \cdot {y}^{2} - \frac{1}{2}\right)}, {y}^{2}, z\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \left(y + x\right) + \mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{1}{24} \cdot {y}^{2} - \frac{1}{2}\right)}, {y}^{2}, z\right) \]

      10. sub-neg N/A

          \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \color{blue}{\left(\frac{1}{24} \cdot {y}^{2} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)}, {y}^{2}, z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \left(\frac{1}{24} \cdot {y}^{2} + \color{blue}{\frac{-1}{2}}\right), {y}^{2}, z\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \color{blue}{\mathsf{fma}\left(\frac{1}{24}, {y}^{2}, \frac{-1}{2}\right)}, {y}^{2}, z\right) \]

      13. unpow2 N/A

          \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \mathsf{fma}\left(\frac{1}{24}, \color{blue}{y \cdot y}, \frac{-1}{2}\right), {y}^{2}, z\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \mathsf{fma}\left(\frac{1}{24}, \color{blue}{y \cdot y}, \frac{-1}{2}\right), {y}^{2}, z\right) \]

      15. unpow2 N/A

          \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \mathsf{fma}\left(\frac{1}{24}, y \cdot y, \frac{-1}{2}\right), \color{blue}{y \cdot y}, z\right) \]

      16. lower-*.f64 99.4

          \[\leadsto \left(y + x\right) + \mathsf{fma}\left(z \cdot \mathsf{fma}\left(0.041666666666666664, y \cdot y, -0.5\right), \color{blue}{y \cdot y}, z\right) \]

   8. Applied rewrites 99.4%

      \[\leadsto \left(y + x\right) + \color{blue}{\mathsf{fma}\left(z \cdot \mathsf{fma}\left(0.041666666666666664, y \cdot y, -0.5\right), y \cdot y, z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 3.15:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.041666666666666664, y \cdot y, -0.5\right) \cdot z, y \cdot y, z\right) + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+21}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 4.7:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666, y, -0.5 \cdot z\right), y, 1\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+21)
   (+ z x)
   (if (<= y 4.7)
     (fma (fma (fma -0.16666666666666666 y (* -0.5 z)) y 1.0) y (+ z x))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+21) {
		tmp = z + x;
	} else if (y <= 4.7) {
		tmp = fma(fma(fma(-0.16666666666666666, y, (-0.5 * z)), y, 1.0), y, (z + x));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+21)
		tmp = Float64(z + x);
	elseif (y <= 4.7)
		tmp = fma(fma(fma(-0.16666666666666666, y, Float64(-0.5 * z)), y, 1.0), y, Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+21], N[(z + x), $MachinePrecision], If[LessEqual[y, 4.7], N[(N[(N[(-0.16666666666666666 * y + N[(-0.5 * z), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e21 or 4.70000000000000018 < y

   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 45.7

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

   5. Applied rewrites 45.7%

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

   if -2.8e21 < y < 4.70000000000000018

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + z\right) + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right) + \left(x + z\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right) \cdot y} + \left(x + z\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right), y, x + z\right)} \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right) + 1}, y, x + z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right) \cdot y} + 1, y, x + z\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y, y, 1\right)}, y, x + z\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{-1}{6} \cdot y + \frac{-1}{2} \cdot z}, y, 1\right), y, x + z\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{-1}{6}, y, \frac{-1}{2} \cdot z\right)}, y, 1\right), y, x + z\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{6}, y, \color{blue}{\frac{-1}{2} \cdot z}\right), y, 1\right), y, x + z\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{6}, y, \frac{-1}{2} \cdot z\right), y, 1\right), y, \color{blue}{z + x}\right) \]

      12. lower-+.f64 98.6

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666, y, -0.5 \cdot z\right), y, 1\right), y, \color{blue}{z + x}\right) \]

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666, y, -0.5 \cdot z\right), y, 1\right), y, z + x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.3% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+21}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 4.7:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z, 1\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e+21)
   (+ z x)
   (if (<= y 4.7) (fma (fma (* -0.5 y) z 1.0) y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e+21) {
		tmp = z + x;
	} else if (y <= 4.7) {
		tmp = fma(fma((-0.5 * y), z, 1.0), y, (z + x));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e+21)
		tmp = Float64(z + x);
	elseif (y <= 4.7)
		tmp = fma(fma(Float64(-0.5 * y), z, 1.0), y, Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.3e+21], N[(z + x), $MachinePrecision], If[LessEqual[y, 4.7], N[(N[(N[(-0.5 * y), $MachinePrecision] * z + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e21 or 4.70000000000000018 < y

   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 45.7

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

   5. Applied rewrites 45.7%

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

   if -3.3e21 < y < 4.70000000000000018

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + z\right) + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right) + \left(x + z\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right) \cdot y} + \left(x + z\right) \]

      4. *-commutative N/A

         \[\leadsto \left(1 + \frac{-1}{2} \cdot \color{blue}{\left(z \cdot y\right)}\right) \cdot y + \left(x + z\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(1 + \color{blue}{\left(\frac{-1}{2} \cdot z\right) \cdot y}\right) \cdot y + \left(x + z\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(1 + \left(\frac{-1}{2} \cdot z\right) \cdot y, y, x + z\right)} \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{-1}{2} \cdot z\right) \cdot y + 1}, y, x + z\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} \cdot \left(z \cdot y\right)} + 1, y, x + z\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{2} \cdot \color{blue}{\left(y \cdot z\right)} + 1, y, x + z\right) \]

      10. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{-1}{2} \cdot y\right) \cdot z} + 1, y, x + z\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{-1}{2} \cdot y, z, 1\right)}, y, x + z\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{-1}{2} \cdot y}, z, 1\right), y, x + z\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z, 1\right), y, \color{blue}{z + x}\right) \]

      14. lower-+.f64 98.5

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z, 1\right), y, \color{blue}{z + x}\right) \]

   5. Applied rewrites 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z, 1\right), y, z + x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 69.2% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3300000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666 \cdot y, y, 1\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3300000000.0)
   (+ z x)
   (if (<= y 2.3e-8)
     (fma (fma (* -0.16666666666666666 y) y 1.0) y (+ z x))
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3300000000.0) {
		tmp = z + x;
	} else if (y <= 2.3e-8) {
		tmp = fma(fma((-0.16666666666666666 * y), y, 1.0), y, (z + x));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3300000000.0)
		tmp = Float64(z + x);
	elseif (y <= 2.3e-8)
		tmp = fma(fma(Float64(-0.16666666666666666 * y), y, 1.0), y, Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3300000000.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 2.3e-8], N[(N[(N[(-0.16666666666666666 * y), $MachinePrecision] * y + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e9 or 2.3000000000000001e-8 < 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 46.3

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

   5. Applied rewrites 46.3%

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

   if -3.3e9 < y < 2.3000000000000001e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + z\right) + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right) + \left(x + z\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right) \cdot y} + \left(x + z\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right), y, x + z\right)} \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right) + 1}, y, x + z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right) \cdot y} + 1, y, x + z\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y, y, 1\right)}, y, x + z\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{-1}{6} \cdot y + \frac{-1}{2} \cdot z}, y, 1\right), y, x + z\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{-1}{6}, y, \frac{-1}{2} \cdot z\right)}, y, 1\right), y, x + z\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{6}, y, \color{blue}{\frac{-1}{2} \cdot z}\right), y, 1\right), y, x + z\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{6}, y, \frac{-1}{2} \cdot z\right), y, 1\right), y, \color{blue}{z + x}\right) \]

      12. lower-+.f64 99.3

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666, y, -0.5 \cdot z\right), y, 1\right), y, \color{blue}{z + x}\right) \]

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666, y, -0.5 \cdot z\right), y, 1\right), y, z + x\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 99.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666 \cdot y, y, 1\right), y, z + x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 69.2% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-8}:\\ \;\;\;\;\left(y + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1) (+ z x) (if (<= y 2.3e-8) (+ (+ y x) z) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1) {
		tmp = z + x;
	} else if (y <= 2.3e-8) {
		tmp = (y + x) + z;
	} else {
		tmp = z + 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 (y <= (-3.1d0)) then
        tmp = z + x
    else if (y <= 2.3d-8) then
        tmp = (y + x) + z
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1) {
		tmp = z + x;
	} else if (y <= 2.3e-8) {
		tmp = (y + x) + z;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1:
		tmp = z + x
	elif y <= 2.3e-8:
		tmp = (y + x) + z
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1)
		tmp = Float64(z + x);
	elseif (y <= 2.3e-8)
		tmp = Float64(Float64(y + x) + z);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1)
		tmp = z + x;
	elseif (y <= 2.3e-8)
		tmp = (y + x) + z;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1], N[(z + x), $MachinePrecision], If[LessEqual[y, 2.3e-8], N[(N[(y + x), $MachinePrecision] + z), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000009 or 2.3000000000000001e-8 < 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 46.3

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

   5. Applied rewrites 46.3%

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

   if -3.10000000000000009 < y < 2.3000000000000001e-8

   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 99.0

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

   5. Applied rewrites 99.0%

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

Alternative 13: 65.3% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

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 + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 66.7

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

5. Applied rewrites 66.7%

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

Reproduce

herbie shell --seed 2024277 
(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))))