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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

4. Applied rewrites 99.9%

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

Alternative 2: 81.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \sin y\right) + \cos y \cdot z\\ \mathbf{if}\;t\_0 \leq -20:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq -0.05:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;t\_0 \leq 10^{-18}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (+ x (sin y)) (* (cos y) z))))
   (if (<= t_0 -20.0)
     (+ z x)
     (if (<= t_0 -0.05)
       (sin y)
       (if (<= t_0 1e-18) (+ y (+ z x)) (if (<= t_0 1.0) (sin y) (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + sin(y)) + (cos(y) * z);
	double tmp;
	if (t_0 <= -20.0) {
		tmp = z + x;
	} else if (t_0 <= -0.05) {
		tmp = sin(y);
	} else if (t_0 <= 1e-18) {
		tmp = y + (z + x);
	} else if (t_0 <= 1.0) {
		tmp = sin(y);
	} 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 = (x + sin(y)) + (cos(y) * z)
    if (t_0 <= (-20.0d0)) then
        tmp = z + x
    else if (t_0 <= (-0.05d0)) then
        tmp = sin(y)
    else if (t_0 <= 1d-18) then
        tmp = y + (z + x)
    else if (t_0 <= 1.0d0) then
        tmp = sin(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.sin(y)) + (Math.cos(y) * z);
	double tmp;
	if (t_0 <= -20.0) {
		tmp = z + x;
	} else if (t_0 <= -0.05) {
		tmp = Math.sin(y);
	} else if (t_0 <= 1e-18) {
		tmp = y + (z + x);
	} else if (t_0 <= 1.0) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.sin(y)) + (math.cos(y) * z)
	tmp = 0
	if t_0 <= -20.0:
		tmp = z + x
	elif t_0 <= -0.05:
		tmp = math.sin(y)
	elif t_0 <= 1e-18:
		tmp = y + (z + x)
	elif t_0 <= 1.0:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + sin(y)) + Float64(cos(y) * z))
	tmp = 0.0
	if (t_0 <= -20.0)
		tmp = Float64(z + x);
	elseif (t_0 <= -0.05)
		tmp = sin(y);
	elseif (t_0 <= 1e-18)
		tmp = Float64(y + Float64(z + x));
	elseif (t_0 <= 1.0)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + sin(y)) + (cos(y) * z);
	tmp = 0.0;
	if (t_0 <= -20.0)
		tmp = z + x;
	elseif (t_0 <= -0.05)
		tmp = sin(y);
	elseif (t_0 <= 1e-18)
		tmp = y + (z + x);
	elseif (t_0 <= 1.0)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -20.0], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, -0.05], N[Sin[y], $MachinePrecision], If[LessEqual[t$95$0, 1e-18], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -20 or 1 < (+.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 77.8

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

   5. Applied rewrites 77.8%

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

   if -20 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -0.050000000000000003 or 1.0000000000000001e-18 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 1

   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. lower-fma.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-sin.f64 98.5

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \sin y \]
   7. Step-by-step derivation

   8. Applied rewrites 95.5%

      \[\leadsto \sin y \]

   if -0.050000000000000003 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 1.0000000000000001e-18

   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. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \sin y\right) + \cos y \cdot z \leq -20:\\ \;\;\;\;z + x\\ \mathbf{elif}\;\left(x + \sin y\right) + \cos y \cdot z \leq -0.05:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;\left(x + \sin y\right) + \cos y \cdot z \leq 10^{-18}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;\left(x + \sin y\right) + \cos y \cdot z \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{-46}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma x (/ (* (cos y) z) x) x)))
   (if (<= x -6.5e-46) t_0 (if (<= x 1.25e-22) (fma z (cos y) (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(x, ((cos(y) * z) / x), x);
	double tmp;
	if (x <= -6.5e-46) {
		tmp = t_0;
	} else if (x <= 1.25e-22) {
		tmp = fma(z, cos(y), sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(x, Float64(Float64(cos(y) * z) / x), x)
	tmp = 0.0
	if (x <= -6.5e-46)
		tmp = t_0;
	elseif (x <= 1.25e-22)
		tmp = fma(z, cos(y), sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision] / x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -6.5e-46], t$95$0, If[LessEqual[x, 1.25e-22], N[(z * N[Cos[y], $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999966e-46 or 1.24999999999999988e-22 < x

   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. 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. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-cos.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-sin.f64 99.9

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 97.0%

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

   if -6.49999999999999966e-46 < x < 1.24999999999999988e-22

   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. lower-fma.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-sin.f64 91.3

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

   5. Applied rewrites 91.3%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ t_1 := \mathsf{fma}\left(x, \frac{t\_0}{x}, x\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-47}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)) (t_1 (fma x (/ t_0 x) x)))
   (if (<= z -1.65e+118)
     t_0
     (if (<= z -8.2e-82)
       t_1
       (if (<= z 8.4e-47) (+ x (sin y)) (if (<= z 1.32e+97) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double t_1 = fma(x, (t_0 / x), x);
	double tmp;
	if (z <= -1.65e+118) {
		tmp = t_0;
	} else if (z <= -8.2e-82) {
		tmp = t_1;
	} else if (z <= 8.4e-47) {
		tmp = x + sin(y);
	} else if (z <= 1.32e+97) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	t_1 = fma(x, Float64(t_0 / x), x)
	tmp = 0.0
	if (z <= -1.65e+118)
		tmp = t_0;
	elseif (z <= -8.2e-82)
		tmp = t_1;
	elseif (z <= 8.4e-47)
		tmp = Float64(x + sin(y));
	elseif (z <= 1.32e+97)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(t$95$0 / x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.65e+118], t$95$0, If[LessEqual[z, -8.2e-82], t$95$1, If[LessEqual[z, 8.4e-47], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e+97], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e118 or 1.31999999999999994e97 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-cos.f64 88.3

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

   5. Applied rewrites 88.3%

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

   if -1.65e118 < z < -8.19999999999999992e-82 or 8.4000000000000003e-47 < z < 1.31999999999999994e97

   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. 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. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-cos.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-sin.f64 96.0

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

   7. Applied rewrites 96.0%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 91.2%

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

   if -8.19999999999999992e-82 < z < 8.4000000000000003e-47

   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 96.7

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

   5. Applied rewrites 96.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+118}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-47}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-82}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-47}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+121}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -3.3e+118)
     t_0
     (if (<= z -8.2e-82)
       (+ z x)
       (if (<= z 8.4e-47) (+ x (sin y)) (if (<= z 2.95e+121) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -3.3e+118) {
		tmp = t_0;
	} else if (z <= -8.2e-82) {
		tmp = z + x;
	} else if (z <= 8.4e-47) {
		tmp = x + sin(y);
	} else if (z <= 2.95e+121) {
		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 <= (-3.3d+118)) then
        tmp = t_0
    else if (z <= (-8.2d-82)) then
        tmp = z + x
    else if (z <= 8.4d-47) then
        tmp = x + sin(y)
    else if (z <= 2.95d+121) 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 <= -3.3e+118) {
		tmp = t_0;
	} else if (z <= -8.2e-82) {
		tmp = z + x;
	} else if (z <= 8.4e-47) {
		tmp = x + Math.sin(y);
	} else if (z <= 2.95e+121) {
		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 <= -3.3e+118:
		tmp = t_0
	elif z <= -8.2e-82:
		tmp = z + x
	elif z <= 8.4e-47:
		tmp = x + math.sin(y)
	elif z <= 2.95e+121:
		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 <= -3.3e+118)
		tmp = t_0;
	elseif (z <= -8.2e-82)
		tmp = Float64(z + x);
	elseif (z <= 8.4e-47)
		tmp = Float64(x + sin(y));
	elseif (z <= 2.95e+121)
		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 <= -3.3e+118)
		tmp = t_0;
	elseif (z <= -8.2e-82)
		tmp = z + x;
	elseif (z <= 8.4e-47)
		tmp = x + sin(y);
	elseif (z <= 2.95e+121)
		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, -3.3e+118], t$95$0, If[LessEqual[z, -8.2e-82], N[(z + x), $MachinePrecision], If[LessEqual[z, 8.4e-47], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.95e+121], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e118 or 2.95000000000000007e121 < 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. lower-*.f64 N/A

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

      2. lower-cos.f64 89.5

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

   5. Applied rewrites 89.5%

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

   if -3.3e118 < z < -8.19999999999999992e-82 or 8.4000000000000003e-47 < z < 2.95000000000000007e121

   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 82.6

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

   5. Applied rewrites 82.6%

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

   if -8.19999999999999992e-82 < z < 8.4000000000000003e-47

   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 96.7

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

   5. Applied rewrites 96.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-82}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-47}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+121}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -23000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-15}:\\ \;\;\;\;z + \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot -0.5, 1\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -23000.0)
     t_0
     (if (<= y 3.9e-15) (+ z (fma y (fma y (* z -0.5) 1.0) x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -23000.0) {
		tmp = t_0;
	} else if (y <= 3.9e-15) {
		tmp = z + fma(y, fma(y, (z * -0.5), 1.0), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -23000.0)
		tmp = t_0;
	elseif (y <= 3.9e-15)
		tmp = Float64(z + fma(y, fma(y, Float64(z * -0.5), 1.0), x));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -23000.0], t$95$0, If[LessEqual[y, 3.9e-15], N[(z + N[(y * N[(y * N[(z * -0.5), $MachinePrecision] + 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -23000 or 3.90000000000000026e-15 < y

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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 61.1

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

   5. Applied rewrites 61.1%

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

   if -23000 < y < 3.90000000000000026e-15

   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

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

      3. associate-+l+ N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23000:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-15}:\\ \;\;\;\;z + \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot -0.5, 1\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% 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 69.4

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

5. Applied rewrites 69.4%

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

Alternative 8: 29.9% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y + z), $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. lower-fma.f64 N/A

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

   3. lower-cos.f64 N/A

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

   4. lower-sin.f64 55.8

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

5. Applied rewrites 55.8%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 28.0%

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

9. Final simplification 28.0%

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

Reproduce

herbie shell --seed 2024222 
(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))))