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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 10

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. lift-+.f64 N/A

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

   3. associate--l+ N/A

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

   4. +-commutative N/A

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

   5. lower-+.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. fp-cancel-sub-sign-inv N/A

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

   8. +-commutative N/A

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

   9. lower-fma.f64 N/A

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

   10. lower-neg.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 96.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+79} \lor \neg \left(z \leq 1.65 \cdot 10^{-68}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.36e+79) (not (<= z 1.65e-68)))
   (- (+ x 1.0) (* z (sin y)))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.36e+79) || !(z <= 1.65e-68)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = cos(y) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.36d+79)) .or. (.not. (z <= 1.65d-68))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.36e+79) || !(z <= 1.65e-68)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.36e+79) or not (z <= 1.65e-68):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.36e+79) || !(z <= 1.65e-68))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.36e+79) || ~((z <= 1.65e-68)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.36e+79], N[Not[LessEqual[z, 1.65e-68]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.36000000000000003e79 or 1.6499999999999999e-68 < 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 99.8%

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

   if -1.36000000000000003e79 < z < 1.6499999999999999e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. *-lft-identity N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

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

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

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

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-sin.f64 N/A

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

      17. lower-cos.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+79} \lor \neg \left(z \leq 1.65 \cdot 10^{-68}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+168} \lor \neg \left(z \leq 3.3 \cdot 10^{+128}\right):\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+168) (not (<= z 3.3e+128)))
   (* (- z) (sin y))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+168) || !(z <= 3.3e+128)) {
		tmp = -z * sin(y);
	} else {
		tmp = cos(y) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.5d+168)) .or. (.not. (z <= 3.3d+128))) then
        tmp = -z * sin(y)
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+168) || !(z <= 3.3e+128)) {
		tmp = -z * Math.sin(y);
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e+168) or not (z <= 3.3e+128):
		tmp = -z * math.sin(y)
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e+168) || !(z <= 3.3e+128))
		tmp = Float64(Float64(-z) * sin(y));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e+168) || ~((z <= 3.3e+128)))
		tmp = -z * sin(y);
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e+168], N[Not[LessEqual[z, 3.3e+128]], $MachinePrecision]], N[((-z) * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999983e168 or 3.3000000000000001e128 < 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. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-sin.f64 75.9

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

   5. Applied rewrites 75.9%

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

   if -2.49999999999999983e168 < z < 3.3000000000000001e128

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. *-lft-identity N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

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

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

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

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-sin.f64 N/A

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

      17. lower-cos.f64 99.4

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

   5. Applied rewrites 99.4%

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

   7. Applied rewrites 96.3%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 90.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+168} \lor \neg \left(z \leq 3.3 \cdot 10^{+128}\right):\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 2.5 \cdot 10^{-12}\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(0.16666666666666666 \cdot z\right) \cdot y - 0.5, y, -z\right), y, 1 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.5) (not (<= y 2.5e-12)))
   (+ (cos y) x)
   (fma (fma (- (* (* 0.16666666666666666 z) y) 0.5) y (- z)) y (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.5) || !(y <= 2.5e-12)) {
		tmp = cos(y) + x;
	} else {
		tmp = fma(fma((((0.16666666666666666 * z) * y) - 0.5), y, -z), y, (1.0 + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.5) || !(y <= 2.5e-12))
		tmp = Float64(cos(y) + x);
	else
		tmp = fma(fma(Float64(Float64(Float64(0.16666666666666666 * z) * y) - 0.5), y, Float64(-z)), y, Float64(1.0 + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.5], N[Not[LessEqual[y, 2.5e-12]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(N[(N[(0.16666666666666666 * z), $MachinePrecision] * y), $MachinePrecision] - 0.5), $MachinePrecision] * y + (-z)), $MachinePrecision] * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.5 or 2.49999999999999985e-12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. *-lft-identity N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

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

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

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

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

      14. lower-fma.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-sin.f64 N/A

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

      17. lower-cos.f64 90.9

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

   5. Applied rewrites 90.9%

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

   7. Applied rewrites 90.9%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 65.0%

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

   if -0.5 < y < 2.49999999999999985e-12

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

   5. Applied rewrites 100.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 2.5 \cdot 10^{-12}\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(0.16666666666666666 \cdot z\right) \cdot y - 0.5, y, -z\right), y, 1 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.4% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.45 \cdot 10^{-13}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.45e-13)
   (+ 1.0 x)
   (if (<= x 2.2e-19) (fma (- z) y 1.0) (- x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.45e-13) {
		tmp = 1.0 + x;
	} else if (x <= 2.2e-19) {
		tmp = fma(-z, y, 1.0);
	} else {
		tmp = x - (z * y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.45e-13)
		tmp = Float64(1.0 + x);
	elseif (x <= 2.2e-19)
		tmp = fma(Float64(-z), y, 1.0);
	else
		tmp = Float64(x - Float64(z * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.45e-13], N[(1.0 + x), $MachinePrecision], If[LessEqual[x, 2.2e-19], N[((-z) * y + 1.0), $MachinePrecision], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.44999999999999994e-13

   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. lower-+.f64 84.3

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

   5. Applied rewrites 84.3%

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

   if -3.44999999999999994e-13 < x < 2.1999999999999998e-19

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(\frac{-1}{2} \cdot y - z\right)\right)} \]
   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 55.0

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

   5. Applied rewrites 55.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{-1}{2} \cdot y - z, y, 1\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 55.0%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(-1 \cdot z, y, 1\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 55.7%

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

   if 2.1999999999999998e-19 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(\frac{-1}{2} \cdot y - z\right)\right)} \]
   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 57.5

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

   5. Applied rewrites 57.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 57.6%

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

   9. Taylor expanded in z around inf

      \[\leadsto x - y \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 74.3%

       \[\leadsto x - z \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 65.3% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.2e+48) (+ 1.0 x) (+ (fma (- z) y 1.0) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e+48) {
		tmp = 1.0 + x;
	} else {
		tmp = fma(-z, y, 1.0) + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.2e+48)
		tmp = Float64(1.0 + x);
	else
		tmp = Float64(fma(Float64(-z), y, 1.0) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.2e+48], N[(1.0 + x), $MachinePrecision], N[(N[((-z) * y + 1.0), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.1999999999999999e48

   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. lower-+.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if -5.1999999999999999e48 < x

   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. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 63.7

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

   7. Applied rewrites 63.7%

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

Alternative 7: 65.3% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.2e+48) (+ 1.0 x) (fma (- z) y (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e+48) {
		tmp = 1.0 + x;
	} else {
		tmp = fma(-z, y, (1.0 + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.2e+48)
		tmp = Float64(1.0 + x);
	else
		tmp = fma(Float64(-z), y, Float64(1.0 + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.2e+48], N[(1.0 + x), $MachinePrecision], N[((-z) * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.1999999999999999e48

   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. lower-+.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if -5.1999999999999999e48 < x

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-+.f64 63.7

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

   5. Applied rewrites 63.7%

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

Alternative 8: 63.5% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+168}:\\ \;\;\;\;x - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.6e+168) (- x (* z y)) (+ 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.6e+168) {
		tmp = x - (z * y);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.6d+168)) then
        tmp = x - (z * y)
    else
        tmp = 1.0d0 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.6e+168) {
		tmp = x - (z * y);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.6e+168:
		tmp = x - (z * y)
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.6e+168)
		tmp = Float64(x - Float64(z * y));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.6e+168)
		tmp = x - (z * y);
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.6e+168], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e168

   1. Initial program 99.7%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   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. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-+.f64 55.1

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

   5. Applied rewrites 55.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 55.1%

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

   9. Taylor expanded in z around inf

      \[\leadsto x - y \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 52.1%

       \[\leadsto x - z \cdot y \]

   if -2.6e168 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-+.f64 67.8

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

   5. Applied rewrites 67.8%

      \[\leadsto \color{blue}{1 + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 61.6% accurate, 53.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 1.0 + 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 = 1.0d0 + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(1.0 + x), $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. lower-+.f64 62.4

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

5. Applied rewrites 62.4%

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

Alternative 10: 21.3% 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. lower-+.f64 62.4

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

5. Applied rewrites 62.4%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 22.6%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024326 
(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))))