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

Percentage Accurate: 99.9% → 99.9%

Time: 8.8s

Alternatives: 16

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ t_1 := \left(\cos y + x\right) - t\_0\\ t_2 := \left(1 + x\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -5000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.999:\\ \;\;\;\;\mathsf{fma}\left(\frac{\cos y}{x}, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z))
        (t_1 (- (+ (cos y) x) t_0))
        (t_2 (- (+ 1.0 x) t_0)))
   (if (<= t_1 -5000.0) t_2 (if (<= t_1 0.999) (fma (/ (cos y) x) x x) t_2))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double t_1 = (cos(y) + x) - t_0;
	double t_2 = (1.0 + x) - t_0;
	double tmp;
	if (t_1 <= -5000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.999) {
		tmp = fma((cos(y) / x), x, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	t_1 = Float64(Float64(cos(y) + x) - t_0)
	t_2 = Float64(Float64(1.0 + x) - t_0)
	tmp = 0.0
	if (t_1 <= -5000.0)
		tmp = t_2;
	elseif (t_1 <= 0.999)
		tmp = fma(Float64(cos(y) / x), x, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 + x), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -5000.0], t$95$2, If[LessEqual[t$95$1, 0.999], N[(N[(N[Cos[y], $MachinePrecision] / x), $MachinePrecision] * x + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -5e3 or 0.998999999999999999 < (-.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

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

   5. Applied rewrites 99.2%

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

   if -5e3 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.998999999999999999

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   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. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. pow2 N/A

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

      6. lower-pow.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. pow2 N/A

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

      11. lower-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. +-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 99.9

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

      19. lift-+.f64 N/A

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

      20. +-commutative N/A

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

      21. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate--r+ N/A

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

      5. associate-*r/ N/A

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

      6. div-sub N/A

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

      7. div-sub N/A

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

      8. associate--r+ N/A

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

      9. lower-*.f64 N/A

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 95.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\cos y + x\right) - \sin y \cdot z \leq -5000:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \mathbf{elif}\;\left(\cos y + x\right) - \sin y \cdot z \leq 0.999:\\ \;\;\;\;\mathsf{fma}\left(\frac{\cos y}{x}, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y + x\\ t_1 := \sin y \cdot z\\ t_2 := t\_0 - t\_1\\ t_3 := \left(1 + x\right) - t\_1\\ \mathbf{if}\;t\_2 \leq -5000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0.999:\\ \;\;\;\;t\_0 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (cos y) x))
        (t_1 (* (sin y) z))
        (t_2 (- t_0 t_1))
        (t_3 (- (+ 1.0 x) t_1)))
   (if (<= t_2 -5000.0) t_3 (if (<= t_2 0.999) (- t_0 (* z y)) t_3))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) + x;
	double t_1 = sin(y) * z;
	double t_2 = t_0 - t_1;
	double t_3 = (1.0 + x) - t_1;
	double tmp;
	if (t_2 <= -5000.0) {
		tmp = t_3;
	} else if (t_2 <= 0.999) {
		tmp = t_0 - (z * y);
	} else {
		tmp = t_3;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = cos(y) + x
    t_1 = sin(y) * z
    t_2 = t_0 - t_1
    t_3 = (1.0d0 + x) - t_1
    if (t_2 <= (-5000.0d0)) then
        tmp = t_3
    else if (t_2 <= 0.999d0) then
        tmp = t_0 - (z * y)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) + x;
	double t_1 = Math.sin(y) * z;
	double t_2 = t_0 - t_1;
	double t_3 = (1.0 + x) - t_1;
	double tmp;
	if (t_2 <= -5000.0) {
		tmp = t_3;
	} else if (t_2 <= 0.999) {
		tmp = t_0 - (z * y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) + x
	t_1 = math.sin(y) * z
	t_2 = t_0 - t_1
	t_3 = (1.0 + x) - t_1
	tmp = 0
	if t_2 <= -5000.0:
		tmp = t_3
	elif t_2 <= 0.999:
		tmp = t_0 - (z * y)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) + x)
	t_1 = Float64(sin(y) * z)
	t_2 = Float64(t_0 - t_1)
	t_3 = Float64(Float64(1.0 + x) - t_1)
	tmp = 0.0
	if (t_2 <= -5000.0)
		tmp = t_3;
	elseif (t_2 <= 0.999)
		tmp = Float64(t_0 - Float64(z * y));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) + x;
	t_1 = sin(y) * z;
	t_2 = t_0 - t_1;
	t_3 = (1.0 + x) - t_1;
	tmp = 0.0;
	if (t_2 <= -5000.0)
		tmp = t_3;
	elseif (t_2 <= 0.999)
		tmp = t_0 - (z * y);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(1.0 + x), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -5000.0], t$95$3, If[LessEqual[t$95$2, 0.999], N[(t$95$0 - N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -5e3 or 0.998999999999999999 < (-.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

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

   5. Applied rewrites 99.2%

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

   if -5e3 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.998999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.1

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

   5. Applied rewrites 53.1%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\cos y + x\right) - \sin y \cdot z \leq -5000:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \mathbf{elif}\;\left(\cos y + x\right) - \sin y \cdot z \leq 0.999:\\ \;\;\;\;\left(\cos y + x\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ t_1 := \left(\cos y + x\right) - t\_0\\ t_2 := \left(1 + x\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -5000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.999:\\ \;\;\;\;\cos y - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z))
        (t_1 (- (+ (cos y) x) t_0))
        (t_2 (- (+ 1.0 x) t_0)))
   (if (<= t_1 -5000.0) t_2 (if (<= t_1 0.999) (- (cos y) (* z y)) t_2))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double t_1 = (cos(y) + x) - t_0;
	double t_2 = (1.0 + x) - t_0;
	double tmp;
	if (t_1 <= -5000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.999) {
		tmp = cos(y) - (z * y);
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = sin(y) * z
    t_1 = (cos(y) + x) - t_0
    t_2 = (1.0d0 + x) - t_0
    if (t_1 <= (-5000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.999d0) then
        tmp = cos(y) - (z * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * z;
	double t_1 = (Math.cos(y) + x) - t_0;
	double t_2 = (1.0 + x) - t_0;
	double tmp;
	if (t_1 <= -5000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.999) {
		tmp = Math.cos(y) - (z * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * z
	t_1 = (math.cos(y) + x) - t_0
	t_2 = (1.0 + x) - t_0
	tmp = 0
	if t_1 <= -5000.0:
		tmp = t_2
	elif t_1 <= 0.999:
		tmp = math.cos(y) - (z * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	t_1 = Float64(Float64(cos(y) + x) - t_0)
	t_2 = Float64(Float64(1.0 + x) - t_0)
	tmp = 0.0
	if (t_1 <= -5000.0)
		tmp = t_2;
	elseif (t_1 <= 0.999)
		tmp = Float64(cos(y) - Float64(z * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * z;
	t_1 = (cos(y) + x) - t_0;
	t_2 = (1.0 + x) - t_0;
	tmp = 0.0;
	if (t_1 <= -5000.0)
		tmp = t_2;
	elseif (t_1 <= 0.999)
		tmp = cos(y) - (z * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 + x), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -5000.0], t$95$2, If[LessEqual[t$95$1, 0.999], N[(N[Cos[y], $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -5e3 or 0.998999999999999999 < (-.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

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

   5. Applied rewrites 99.2%

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

   if -5e3 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.998999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.1

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

   5. Applied rewrites 53.1%

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

   6. Taylor expanded in x around 0

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

      1. lower-cos.f64 53.1

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

   8. Applied rewrites 53.1%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\cos y + x\right) - \sin y \cdot z \leq -5000:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \mathbf{elif}\;\left(\cos y + x\right) - \sin y \cdot z \leq 0.999:\\ \;\;\;\;\cos y - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + x\right) - \sin y \cdot z\\ \mathbf{if}\;x \leq -7 \cdot 10^{-6}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(-z, \sin y, \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ 1.0 x) (* (sin y) z))))
   (if (<= x -7e-6) t_0 (if (<= x 1.2e-14) (fma (- z) (sin y) (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 + x) - (sin(y) * z);
	double tmp;
	if (x <= -7e-6) {
		tmp = t_0;
	} else if (x <= 1.2e-14) {
		tmp = fma(-z, sin(y), cos(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 + x) - Float64(sin(y) * z))
	tmp = 0.0
	if (x <= -7e-6)
		tmp = t_0;
	elseif (x <= 1.2e-14)
		tmp = fma(Float64(-z), sin(y), cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 + x), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-6], t$95$0, If[LessEqual[x, 1.2e-14], N[((-z) * N[Sin[y], $MachinePrecision] + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.99999999999999989e-6 or 1.2e-14 < 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

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

   5. Applied rewrites 99.9%

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

   if -6.99999999999999989e-6 < x < 1.2e-14

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-sin.f64 N/A

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

      7. lower-cos.f64 99.4

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

   5. Applied rewrites 99.4%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-6}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(-z, \sin y, \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-288}:\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{elif}\;x \leq 80000000000000:\\ \;\;\;\;\cos y - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e-25)
   (+ 1.0 x)
   (if (<= x -1.35e-288)
     (* (- z) (sin y))
     (if (<= x 80000000000000.0) (- (cos y) (* z y)) (+ 1.0 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e-25) {
		tmp = 1.0 + x;
	} else if (x <= -1.35e-288) {
		tmp = -z * sin(y);
	} else if (x <= 80000000000000.0) {
		tmp = cos(y) - (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 (x <= (-1.9d-25)) then
        tmp = 1.0d0 + x
    else if (x <= (-1.35d-288)) then
        tmp = -z * sin(y)
    else if (x <= 80000000000000.0d0) then
        tmp = cos(y) - (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 (x <= -1.9e-25) {
		tmp = 1.0 + x;
	} else if (x <= -1.35e-288) {
		tmp = -z * Math.sin(y);
	} else if (x <= 80000000000000.0) {
		tmp = Math.cos(y) - (z * y);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e-25:
		tmp = 1.0 + x
	elif x <= -1.35e-288:
		tmp = -z * math.sin(y)
	elif x <= 80000000000000.0:
		tmp = math.cos(y) - (z * y)
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e-25)
		tmp = Float64(1.0 + x);
	elseif (x <= -1.35e-288)
		tmp = Float64(Float64(-z) * sin(y));
	elseif (x <= 80000000000000.0)
		tmp = Float64(cos(y) - 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 (x <= -1.9e-25)
		tmp = 1.0 + x;
	elseif (x <= -1.35e-288)
		tmp = -z * sin(y);
	elseif (x <= 80000000000000.0)
		tmp = cos(y) - (z * y);
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e-25], N[(1.0 + x), $MachinePrecision], If[LessEqual[x, -1.35e-288], N[((-z) * N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 80000000000000.0], N[(N[Cos[y], $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8999999999999999e-25 or 8e13 < 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

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

      1. lower-+.f64 86.3

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

   5. Applied rewrites 86.3%

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

   if -1.8999999999999999e-25 < x < -1.3500000000000001e-288

   1. Initial program 99.7%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   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 60.7

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

   5. Applied rewrites 60.7%

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

   if -1.3500000000000001e-288 < x < 8e13

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in x around 0

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

      1. lower-cos.f64 70.1

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

   8. Applied rewrites 70.1%

      \[\leadsto \color{blue}{\cos y} - z \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 69.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot \sin y\\ \mathbf{if}\;z \leq -4 \cdot 10^{+179}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+49}:\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) (sin y))))
   (if (<= z -4e+179) t_0 (if (<= z 1.75e+49) (+ 1.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -z * sin(y);
	double tmp;
	if (z <= -4e+179) {
		tmp = t_0;
	} else if (z <= 1.75e+49) {
		tmp = 1.0 + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z * sin(y)
    if (z <= (-4d+179)) then
        tmp = t_0
    else if (z <= 1.75d+49) then
        tmp = 1.0d0 + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z * Math.sin(y);
	double tmp;
	if (z <= -4e+179) {
		tmp = t_0;
	} else if (z <= 1.75e+49) {
		tmp = 1.0 + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * math.sin(y)
	tmp = 0
	if z <= -4e+179:
		tmp = t_0
	elif z <= 1.75e+49:
		tmp = 1.0 + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) * sin(y))
	tmp = 0.0
	if (z <= -4e+179)
		tmp = t_0;
	elseif (z <= 1.75e+49)
		tmp = Float64(1.0 + x);
	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 <= -4e+179)
		tmp = t_0;
	elseif (z <= 1.75e+49)
		tmp = 1.0 + x;
	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, -4e+179], t$95$0, If[LessEqual[z, 1.75e+49], N[(1.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999992e179 or 1.74999999999999987e49 < 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 71.4

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

   5. Applied rewrites 71.4%

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

   if -3.99999999999999992e179 < z < 1.74999999999999987e49

   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 75.1

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

   5. Applied rewrites 75.1%

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

Alternative 8: 69.5% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+52}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z \cdot y, -0.5\right) \cdot y - z, y, 1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+52)
   (+ 1.0 x)
   (if (<= y 3.1e+15)
     (fma (- (* (fma 0.16666666666666666 (* z y) -0.5) y) z) y (+ 1.0 x))
     (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+52) {
		tmp = 1.0 + x;
	} else if (y <= 3.1e+15) {
		tmp = fma(((fma(0.16666666666666666, (z * y), -0.5) * y) - z), y, (1.0 + x));
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+52)
		tmp = Float64(1.0 + x);
	elseif (y <= 3.1e+15)
		tmp = fma(Float64(Float64(fma(0.16666666666666666, Float64(z * y), -0.5) * y) - z), y, Float64(1.0 + x));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+52], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 3.1e+15], N[(N[(N[(N[(0.16666666666666666 * N[(z * y), $MachinePrecision] + -0.5), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e52 or 3.1e15 < 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. lower-+.f64 43.3

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

   5. Applied rewrites 43.3%

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

   if -2.3e52 < y < 3.1e15

   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. 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. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-+.f64 91.7

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

   5. Applied rewrites 91.7%

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

Alternative 9: 69.7% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+28}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot y - z, y, 1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+28)
   (+ 1.0 x)
   (if (<= y 7e+15) (fma (- (* -0.5 y) z) y (+ 1.0 x)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+28) {
		tmp = 1.0 + x;
	} else if (y <= 7e+15) {
		tmp = fma(((-0.5 * y) - z), y, (1.0 + x));
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+28)
		tmp = Float64(1.0 + x);
	elseif (y <= 7e+15)
		tmp = fma(Float64(Float64(-0.5 * y) - z), y, Float64(1.0 + x));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+28], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 7e+15], N[(N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999994e28 or 7e15 < 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. lower-+.f64 42.7

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

   5. Applied rewrites 42.7%

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

   if -8.9999999999999994e28 < y < 7e15

   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. *-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 93.4

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

   5. Applied rewrites 93.4%

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

Alternative 10: 69.5% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+28}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e+28)
   (+ 1.0 x)
   (if (<= y 1.22e+82) (fma (- z) y (+ 1.0 x)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+28) {
		tmp = 1.0 + x;
	} else if (y <= 1.22e+82) {
		tmp = fma(-z, y, (1.0 + x));
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.2e+28)
		tmp = Float64(1.0 + x);
	elseif (y <= 1.22e+82)
		tmp = fma(Float64(-z), y, Float64(1.0 + x));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.2e+28], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 1.22e+82], N[((-z) * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999986e28 or 1.22000000000000008e82 < 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. lower-+.f64 40.2

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

   5. Applied rewrites 40.2%

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

   if -2.19999999999999986e28 < y < 1.22000000000000008e82

   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. 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. lower--.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-+.f64 87.4

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

   5. Applied rewrites 87.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.4%

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

Alternative 11: 69.5% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+28}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+82}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e+28)
   (+ 1.0 x)
   (if (<= y 1.22e+82) (- x (fma z y -1.0)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+28) {
		tmp = 1.0 + x;
	} else if (y <= 1.22e+82) {
		tmp = x - fma(z, y, -1.0);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.2e+28)
		tmp = Float64(1.0 + x);
	elseif (y <= 1.22e+82)
		tmp = Float64(x - fma(z, y, -1.0));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.2e+28], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 1.22e+82], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999986e28 or 1.22000000000000008e82 < 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. lower-+.f64 40.2

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

   5. Applied rewrites 40.2%

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

   if -2.19999999999999986e28 < y < 1.22000000000000008e82

   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. *-commutative N/A

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 89.4

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

   5. Applied rewrites 89.4%

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

Alternative 12: 66.8% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-5}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;x \leq 80000000000000:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.85e-5)
   (+ 1.0 x)
   (if (<= x 80000000000000.0) (fma (- z) y 1.0) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.85e-5) {
		tmp = 1.0 + x;
	} else if (x <= 80000000000000.0) {
		tmp = fma(-z, y, 1.0);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.85e-5)
		tmp = Float64(1.0 + x);
	elseif (x <= 80000000000000.0)
		tmp = fma(Float64(-z), y, 1.0);
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.85e-5], N[(1.0 + x), $MachinePrecision], If[LessEqual[x, 80000000000000.0], N[((-z) * y + 1.0), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.84999999999999991e-5 or 8e13 < x

   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 88.1

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

   5. Applied rewrites 88.1%

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

   if -1.84999999999999991e-5 < x < 8e13

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-sin.f64 N/A

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

      7. lower-cos.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.5%

      \[\leadsto 1 - \color{blue}{z \cdot y} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.5%

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

Alternative 13: 66.8% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-5}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;x \leq 80000000000000:\\ \;\;\;\;1 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.85e-5)
   (+ 1.0 x)
   (if (<= x 80000000000000.0) (- 1.0 (* z y)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.85e-5) {
		tmp = 1.0 + x;
	} else if (x <= 80000000000000.0) {
		tmp = 1.0 - (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 (x <= (-1.85d-5)) then
        tmp = 1.0d0 + x
    else if (x <= 80000000000000.0d0) then
        tmp = 1.0d0 - (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 (x <= -1.85e-5) {
		tmp = 1.0 + x;
	} else if (x <= 80000000000000.0) {
		tmp = 1.0 - (z * y);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.85e-5:
		tmp = 1.0 + x
	elif x <= 80000000000000.0:
		tmp = 1.0 - (z * y)
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.85e-5)
		tmp = Float64(1.0 + x);
	elseif (x <= 80000000000000.0)
		tmp = Float64(1.0 - 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 (x <= -1.85e-5)
		tmp = 1.0 + x;
	elseif (x <= 80000000000000.0)
		tmp = 1.0 - (z * y);
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.85e-5], N[(1.0 + x), $MachinePrecision], If[LessEqual[x, 80000000000000.0], N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.84999999999999991e-5 or 8e13 < x

   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 88.1

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

   5. Applied rewrites 88.1%

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

   if -1.84999999999999991e-5 < x < 8e13

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-sin.f64 N/A

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

      7. lower-cos.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.5%

      \[\leadsto 1 - \color{blue}{z \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 61.5% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.46 \cdot 10^{+162}:\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.46e+162) (+ 1.0 x) (* (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.46e+162) {
		tmp = 1.0 + x;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 1.46d+162) then
        tmp = 1.0d0 + x
    else
        tmp = -z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.46e+162) {
		tmp = 1.0 + x;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.46e+162:
		tmp = 1.0 + x
	else:
		tmp = -z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.46e+162)
		tmp = Float64(1.0 + x);
	else
		tmp = Float64(Float64(-z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.46e+162)
		tmp = 1.0 + x;
	else
		tmp = -z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.46e+162], N[(1.0 + x), $MachinePrecision], N[((-z) * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.4599999999999999e162

   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 66.0

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

   5. Applied rewrites 66.0%

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

   if 1.4599999999999999e162 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-sin.f64 N/A

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

      7. lower-cos.f64 81.8

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 47.3%

      \[\leadsto 1 - \color{blue}{z \cdot y} \]

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 41.8%

       \[\leadsto \left(-z\right) \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 62.0% 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 60.7

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

5. Applied rewrites 60.7%

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

Alternative 16: 21.0% 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 60.7

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

5. Applied rewrites 60.7%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 18.2%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024296 
(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))))