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

Percentage Accurate: 99.9% → 99.9%

Time: 11.6s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ \mathbf{if}\;t\_0 \leq -50:\\ \;\;\;\;1 + \mathsf{fma}\left(y, -z, x\right)\\ \mathbf{elif}\;t\_0 \leq 0.995:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))))
   (if (<= t_0 -50.0)
     (+ 1.0 (fma y (- z) x))
     (if (<= t_0 0.995) (cos y) (- x (fma y z -1.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double tmp;
	if (t_0 <= -50.0) {
		tmp = 1.0 + fma(y, -z, x);
	} else if (t_0 <= 0.995) {
		tmp = cos(y);
	} else {
		tmp = x - fma(y, z, -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	tmp = 0.0
	if (t_0 <= -50.0)
		tmp = Float64(1.0 + fma(y, Float64(-z), x));
	elseif (t_0 <= 0.995)
		tmp = cos(y);
	else
		tmp = Float64(x - fma(y, z, -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -50.0], N[(1.0 + N[(y * (-z) + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.995], N[Cos[y], $MachinePrecision], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 55.3

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

   5. Applied rewrites 55.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.2%

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

   if -50 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.994999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 11.3%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. lower-/.f64 N/A

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

   7. Applied rewrites 11.3%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 95.5

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

   10. Applied rewrites 95.5%

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

   11. Taylor expanded in x around 0

       \[\leadsto \cos y \]
   12. Step-by-step derivation

   13. Applied rewrites 90.3%

       \[\leadsto \cos y \]

   if 0.994999999999999996 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 74.7

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

   5. Applied rewrites 74.7%

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

Alternative 3: 99.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + 1\right) - z \cdot \sin y\\ \mathbf{if}\;z \leq -50000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.9:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x 1.0) (* z (sin y)))))
   (if (<= z -50000000.0) t_0 (if (<= z 0.9) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * sin(y));
	double tmp;
	if (z <= -50000000.0) {
		tmp = t_0;
	} else if (z <= 0.9) {
		tmp = x + cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + 1.0d0) - (z * sin(y))
    if (z <= (-50000000.0d0)) then
        tmp = t_0
    else if (z <= 0.9d0) then
        tmp = x + cos(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * Math.sin(y));
	double tmp;
	if (z <= -50000000.0) {
		tmp = t_0;
	} else if (z <= 0.9) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + 1.0) - (z * math.sin(y))
	tmp = 0
	if z <= -50000000.0:
		tmp = t_0
	elif z <= 0.9:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + 1.0) - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -50000000.0)
		tmp = t_0;
	elseif (z <= 0.9)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + 1.0) - (z * sin(y));
	tmp = 0.0;
	if (z <= -50000000.0)
		tmp = t_0;
	elseif (z <= 0.9)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -50000000.0], t$95$0, If[LessEqual[z, 0.9], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5e7 or 0.900000000000000022 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 99.6%

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

   if -5e7 < z < 0.900000000000000022

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 98.8

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

   5. Applied rewrites 98.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -50000000:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{elif}\;z \leq 0.9:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -z \cdot \sin y\\ \mathbf{if}\;z \leq -9 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* z (sin y)))))
   (if (<= z -9e+106) t_0 (if (<= z 2.3e+119) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -(z * sin(y));
	double tmp;
	if (z <= -9e+106) {
		tmp = t_0;
	} else if (z <= 2.3e+119) {
		tmp = x + cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -(z * sin(y))
    if (z <= (-9d+106)) then
        tmp = t_0
    else if (z <= 2.3d+119) then
        tmp = x + cos(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -(z * Math.sin(y));
	double tmp;
	if (z <= -9e+106) {
		tmp = t_0;
	} else if (z <= 2.3e+119) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(z * math.sin(y))
	tmp = 0
	if z <= -9e+106:
		tmp = t_0
	elif z <= 2.3e+119:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -9e+106)
		tmp = t_0;
	elseif (z <= 2.3e+119)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(z * sin(y));
	tmp = 0.0;
	if (z <= -9e+106)
		tmp = t_0;
	elseif (z <= 2.3e+119)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -9e+106], t$95$0, If[LessEqual[z, 2.3e+119], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999994e106 or 2.3000000000000001e119 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-sin.f64 69.2

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

   5. Applied rewrites 69.2%

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

   if -8.9999999999999994e106 < z < 2.3000000000000001e119

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 92.1

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

   5. Applied rewrites 92.1%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+106}:\\ \;\;\;\;-z \cdot \sin y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -0.0135:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2100000:\\ \;\;\;\;\left(x + 1\right) - y \cdot \mathsf{fma}\left(y, y \cdot \left(z \cdot \mathsf{fma}\left(y, y \cdot 0.008333333333333333, -0.16666666666666666\right)\right), z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -0.0135)
     t_0
     (if (<= y 2100000.0)
       (-
        (+ x 1.0)
        (*
         y
         (fma
          y
          (* y (* z (fma y (* y 0.008333333333333333) -0.16666666666666666)))
          z)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -0.0135) {
		tmp = t_0;
	} else if (y <= 2100000.0) {
		tmp = (x + 1.0) - (y * fma(y, (y * (z * fma(y, (y * 0.008333333333333333), -0.16666666666666666))), z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -0.0135)
		tmp = t_0;
	elseif (y <= 2100000.0)
		tmp = Float64(Float64(x + 1.0) - Float64(y * fma(y, Float64(y * Float64(z * fma(y, Float64(y * 0.008333333333333333), -0.16666666666666666))), z)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0135], t$95$0, If[LessEqual[y, 2100000.0], N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(y * N[(y * N[(z * N[(y * N[(y * 0.008333333333333333), $MachinePrecision] + -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0134999999999999998 or 2.1e6 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 63.3

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

   5. Applied rewrites 63.3%

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

   if -0.0134999999999999998 < y < 2.1e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x + 1\right) - y \cdot \color{blue}{\left({y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right) + z\right)} \]

      3. unpow2 N/A

         \[\leadsto \left(x + 1\right) - y \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right) + z\right) \]

      4. associate-*l* N/A

         \[\leadsto \left(x + 1\right) - y \cdot \left(\color{blue}{y \cdot \left(y \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right)} + z\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(x + 1\right) - y \cdot \color{blue}{\mathsf{fma}\left(y, y \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right), z\right)} \]

   8. Applied rewrites 98.2%

      \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \mathsf{fma}\left(y, y \cdot \left(z \cdot \mathsf{fma}\left(y, y \cdot 0.008333333333333333, -0.16666666666666666\right)\right), z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0135:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 2100000:\\ \;\;\;\;\left(x + 1\right) - y \cdot \mathsf{fma}\left(y, y \cdot \left(z \cdot \mathsf{fma}\left(y, y \cdot 0.008333333333333333, -0.16666666666666666\right)\right), z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.3% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.014:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \mathbf{elif}\;y \leq 18500000000000:\\ \;\;\;\;\left(x + 1\right) - y \cdot \mathsf{fma}\left(y, y \cdot \left(z \cdot \mathsf{fma}\left(y, y \cdot 0.008333333333333333, -0.16666666666666666\right)\right), z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.014)
   (* x (+ 1.0 (/ 1.0 x)))
   (if (<= y 18500000000000.0)
     (-
      (+ x 1.0)
      (*
       y
       (fma
        y
        (* y (* z (fma y (* y 0.008333333333333333) -0.16666666666666666)))
        z)))
     (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.014) {
		tmp = x * (1.0 + (1.0 / x));
	} else if (y <= 18500000000000.0) {
		tmp = (x + 1.0) - (y * fma(y, (y * (z * fma(y, (y * 0.008333333333333333), -0.16666666666666666))), z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.014)
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	elseif (y <= 18500000000000.0)
		tmp = Float64(Float64(x + 1.0) - Float64(y * fma(y, Float64(y * Float64(z * fma(y, Float64(y * 0.008333333333333333), -0.16666666666666666))), z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.014], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 18500000000000.0], N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(y * N[(y * N[(z * N[(y * N[(y * 0.008333333333333333), $MachinePrecision] + -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0140000000000000003

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-- N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 99.7

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate--l+ N/A

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

      12. lower-+.f64 N/A

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

      13. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. div-sub N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-cos.f64 92.8

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

   7. Applied rewrites 92.8%

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

   8. Taylor expanded in y around 0

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 49.5%

       \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]

   if -0.0140000000000000003 < y < 1.85e13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x + 1\right) - y \cdot \color{blue}{\left({y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right) + z\right)} \]

      3. unpow2 N/A

         \[\leadsto \left(x + 1\right) - y \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right) + z\right) \]

      4. associate-*l* N/A

         \[\leadsto \left(x + 1\right) - y \cdot \left(\color{blue}{y \cdot \left(y \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right)} + z\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(x + 1\right) - y \cdot \color{blue}{\mathsf{fma}\left(y, y \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right), z\right)} \]

   8. Applied rewrites 97.6%

      \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \mathsf{fma}\left(y, y \cdot \left(z \cdot \mathsf{fma}\left(y, y \cdot 0.008333333333333333, -0.16666666666666666\right)\right), z\right)} \]

   if 1.85e13 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 30.1

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 30.1%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 69.4% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -64:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 25:\\ \;\;\;\;1 + \mathsf{fma}\left(\mathsf{fma}\left(y, z \cdot 0.16666666666666666, -0.5\right), y \cdot y, \mathsf{fma}\left(y, -z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -64.0)
   (+ x 1.0)
   (if (<= y 25.0)
     (+
      1.0
      (fma (fma y (* z 0.16666666666666666) -0.5) (* y y) (fma y (- z) x)))
     (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -64.0) {
		tmp = x + 1.0;
	} else if (y <= 25.0) {
		tmp = 1.0 + fma(fma(y, (z * 0.16666666666666666), -0.5), (y * y), fma(y, -z, x));
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -64.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 25.0)
		tmp = Float64(1.0 + fma(fma(y, Float64(z * 0.16666666666666666), -0.5), Float64(y * y), fma(y, Float64(-z), x)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -64.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 25.0], N[(1.0 + N[(N[(y * N[(z * 0.16666666666666666), $MachinePrecision] + -0.5), $MachinePrecision] * N[(y * y), $MachinePrecision] + N[(y * (-z) + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 49.7

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{x + 1} \]

   if -64 < y < 25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 99.0

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

   5. Applied rewrites 99.0%

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

   7. Applied rewrites 99.0%

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

   if 25 < y

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-- N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 99.6

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate--l+ N/A

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

      12. lower-+.f64 N/A

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

      13. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. div-sub N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-cos.f64 87.9

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

   7. Applied rewrites 87.9%

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

   8. Taylor expanded in y around 0

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 29.0%

       \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 69.4% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -64:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 25:\\ \;\;\;\;1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot 0.16666666666666666, -0.5\right), -z\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -64.0)
   (+ x 1.0)
   (if (<= y 25.0)
     (+ 1.0 (fma y (fma y (fma y (* z 0.16666666666666666) -0.5) (- z)) x))
     (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -64.0) {
		tmp = x + 1.0;
	} else if (y <= 25.0) {
		tmp = 1.0 + fma(y, fma(y, fma(y, (z * 0.16666666666666666), -0.5), -z), x);
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -64.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 25.0)
		tmp = Float64(1.0 + fma(y, fma(y, fma(y, Float64(z * 0.16666666666666666), -0.5), Float64(-z)), x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -64.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 25.0], N[(1.0 + N[(y * N[(y * N[(y * N[(z * 0.16666666666666666), $MachinePrecision] + -0.5), $MachinePrecision] + (-z)), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 49.7

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{x + 1} \]

   if -64 < y < 25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 99.0

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

   5. Applied rewrites 99.0%

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

   if 25 < y

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-- N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 99.6

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate--l+ N/A

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

      12. lower-+.f64 N/A

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

      13. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. div-sub N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-cos.f64 87.9

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

   7. Applied rewrites 87.9%

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

   8. Taylor expanded in y around 0

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 29.0%

       \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 69.2% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -62:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 8200000000:\\ \;\;\;\;\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -62.0)
   (+ x 1.0)
   (if (<= y 8200000000.0)
     (fma y (- (* y -0.5) z) (+ x 1.0))
     (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -62.0) {
		tmp = x + 1.0;
	} else if (y <= 8200000000.0) {
		tmp = fma(y, ((y * -0.5) - z), (x + 1.0));
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -62.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 8200000000.0)
		tmp = fma(y, Float64(Float64(y * -0.5) - z), Float64(x + 1.0));
	else
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -62.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 8200000000.0], N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -62

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 49.7

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{x + 1} \]

   if -62 < y < 8.2e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 97.0

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

   5. Applied rewrites 97.0%

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

   if 8.2e9 < y

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-- N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 99.6

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. associate--l+ N/A

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

      12. lower-+.f64 N/A

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

      13. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. div-sub N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-cos.f64 87.5

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

   7. Applied rewrites 87.5%

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

   8. Taylor expanded in y around 0

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 29.9%

       \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.2% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -62:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 8200000000:\\ \;\;\;\;\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -62.0)
   (+ x 1.0)
   (if (<= y 8200000000.0) (fma y (- (* y -0.5) z) (+ x 1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -62.0) {
		tmp = x + 1.0;
	} else if (y <= 8200000000.0) {
		tmp = fma(y, ((y * -0.5) - z), (x + 1.0));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -62.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 8200000000.0)
		tmp = fma(y, Float64(Float64(y * -0.5) - z), Float64(x + 1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -62.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 8200000000.0], N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -62 or 8.2e9 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 40.2

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 40.2%

      \[\leadsto \color{blue}{x + 1} \]

   if -62 < y < 8.2e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 97.0

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

   5. Applied rewrites 97.0%

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

Alternative 11: 69.2% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 34000000000000:\\ \;\;\;\;1 + \mathsf{fma}\left(y, -z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2)
   (+ x 1.0)
   (if (<= y 34000000000000.0) (+ 1.0 (fma y (- z) x)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2) {
		tmp = x + 1.0;
	} else if (y <= 34000000000000.0) {
		tmp = 1.0 + fma(y, -z, x);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2)
		tmp = Float64(x + 1.0);
	elseif (y <= 34000000000000.0)
		tmp = Float64(1.0 + fma(y, Float64(-z), x));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 34000000000000.0], N[(1.0 + N[(y * (-z) + x), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000002 or 3.4e13 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 40.3

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 40.3%

      \[\leadsto \color{blue}{x + 1} \]

   if -3.2000000000000002 < y < 3.4e13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 96.7

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 96.2%

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

Alternative 12: 69.2% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 34000000000000:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2)
   (+ x 1.0)
   (if (<= y 34000000000000.0) (- x (fma y z -1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2) {
		tmp = x + 1.0;
	} else if (y <= 34000000000000.0) {
		tmp = x - fma(y, z, -1.0);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2)
		tmp = Float64(x + 1.0);
	elseif (y <= 34000000000000.0)
		tmp = Float64(x - fma(y, z, -1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 34000000000000.0], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000002 or 3.4e13 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 40.3

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 40.3%

      \[\leadsto \color{blue}{x + 1} \]

   if -3.2000000000000002 < y < 3.4e13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 96.2

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

   5. Applied rewrites 96.2%

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

Alternative 13: 61.2% accurate, 53.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{x + 1} \]

   2. lower-+.f64 57.8

      \[\leadsto \color{blue}{x + 1} \]

5. Applied rewrites 57.8%

   \[\leadsto \color{blue}{x + 1} \]
6. Add Preprocessing

Alternative 14: 21.2% accurate, 212.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{x + 1} \]

   2. lower-+.f64 57.8

      \[\leadsto \color{blue}{x + 1} \]

5. Applied rewrites 57.8%

   \[\leadsto \color{blue}{x + 1} \]

6. Taylor expanded in x around 0

   \[\leadsto 1 \]
7. Step-by-step derivation

8. Applied rewrites 18.9%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024220 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))