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

Percentage Accurate: 99.9% → 99.9%

Time: 9.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 79.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \sin y\right) + \cos y \cdot z\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq -0.005:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (+ x (sin y)) (* (cos y) z))))
   (if (<= t_0 -2e+28)
     (+ z x)
     (if (<= t_0 -0.005)
       (sin y)
       (if (<= t_0 5e-12)
         (+ y (+ z x))
         (if (<= t_0 2e+18) (sin y) (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + sin(y)) + (cos(y) * z);
	double tmp;
	if (t_0 <= -2e+28) {
		tmp = z + x;
	} else if (t_0 <= -0.005) {
		tmp = sin(y);
	} else if (t_0 <= 5e-12) {
		tmp = y + (z + x);
	} else if (t_0 <= 2e+18) {
		tmp = sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + sin(y)) + (cos(y) * z)
    if (t_0 <= (-2d+28)) then
        tmp = z + x
    else if (t_0 <= (-0.005d0)) then
        tmp = sin(y)
    else if (t_0 <= 5d-12) then
        tmp = y + (z + x)
    else if (t_0 <= 2d+18) then
        tmp = sin(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.sin(y)) + (Math.cos(y) * z);
	double tmp;
	if (t_0 <= -2e+28) {
		tmp = z + x;
	} else if (t_0 <= -0.005) {
		tmp = Math.sin(y);
	} else if (t_0 <= 5e-12) {
		tmp = y + (z + x);
	} else if (t_0 <= 2e+18) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.sin(y)) + (math.cos(y) * z)
	tmp = 0
	if t_0 <= -2e+28:
		tmp = z + x
	elif t_0 <= -0.005:
		tmp = math.sin(y)
	elif t_0 <= 5e-12:
		tmp = y + (z + x)
	elif t_0 <= 2e+18:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + sin(y)) + Float64(cos(y) * z))
	tmp = 0.0
	if (t_0 <= -2e+28)
		tmp = Float64(z + x);
	elseif (t_0 <= -0.005)
		tmp = sin(y);
	elseif (t_0 <= 5e-12)
		tmp = Float64(y + Float64(z + x));
	elseif (t_0 <= 2e+18)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + sin(y)) + (cos(y) * z);
	tmp = 0.0;
	if (t_0 <= -2e+28)
		tmp = z + x;
	elseif (t_0 <= -0.005)
		tmp = sin(y);
	elseif (t_0 <= 5e-12)
		tmp = y + (z + x);
	elseif (t_0 <= 2e+18)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+28], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, -0.005], N[Sin[y], $MachinePrecision], If[LessEqual[t$95$0, 5e-12], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+18], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -1.99999999999999992e28 or 2e18 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 80.9

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

   5. Applied rewrites 80.9%

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

   if -1.99999999999999992e28 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -0.0050000000000000001 or 4.9999999999999997e-12 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 2e18

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-sin.f64 94.1

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 86.2%

      \[\leadsto \sin y \]

   if -0.0050000000000000001 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 4.9999999999999997e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \sin y\right) + \cos y \cdot z \leq -2 \cdot 10^{+28}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;\left(x + \sin y\right) + \cos y \cdot z \leq -0.005:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;\left(x + \sin y\right) + \cos y \cdot z \leq 5 \cdot 10^{-12}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;\left(x + \sin y\right) + \cos y \cdot z \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{if}\;x \leq -14500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma x (/ (* (cos y) z) x) x)))
   (if (<= x -14500000.0)
     t_0
     (if (<= x 2.8e-23) (fma z (cos y) (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(x, ((cos(y) * z) / x), x);
	double tmp;
	if (x <= -14500000.0) {
		tmp = t_0;
	} else if (x <= 2.8e-23) {
		tmp = fma(z, cos(y), sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(x, Float64(Float64(cos(y) * z) / x), x)
	tmp = 0.0
	if (x <= -14500000.0)
		tmp = t_0;
	elseif (x <= 2.8e-23)
		tmp = fma(z, cos(y), sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision] / x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -14500000.0], t$95$0, If[LessEqual[x, 2.8e-23], N[(z * N[Cos[y], $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e7 or 2.7999999999999997e-23 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 89.7

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-cos.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-sin.f64 99.9

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

   8. Applied rewrites 99.9%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 99.1%

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

   if -1.45e7 < x < 2.7999999999999997e-23

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-sin.f64 95.3

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

   5. Applied rewrites 95.3%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -14500000:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(x, \cos y \cdot \frac{z}{x}, x\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t\_0}{x}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -8.5e+67)
     t_0
     (if (<= z -1.45e-25)
       (fma x (* (cos y) (/ z x)) x)
       (if (<= z 3.2e-20)
         (+ x (sin y))
         (if (<= z 6.8e+152) (fma x (/ t_0 x) x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -8.5e+67) {
		tmp = t_0;
	} else if (z <= -1.45e-25) {
		tmp = fma(x, (cos(y) * (z / x)), x);
	} else if (z <= 3.2e-20) {
		tmp = x + sin(y);
	} else if (z <= 6.8e+152) {
		tmp = fma(x, (t_0 / x), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -8.5e+67)
		tmp = t_0;
	elseif (z <= -1.45e-25)
		tmp = fma(x, Float64(cos(y) * Float64(z / x)), x);
	elseif (z <= 3.2e-20)
		tmp = Float64(x + sin(y));
	elseif (z <= 6.8e+152)
		tmp = fma(x, Float64(t_0 / x), x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -8.5e+67], t$95$0, If[LessEqual[z, -1.45e-25], N[(x * N[(N[Cos[y], $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.2e-20], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+152], N[(x * N[(t$95$0 / x), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.50000000000000038e67 or 6.80000000000000041e152 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-cos.f64 83.6

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

   5. Applied rewrites 83.6%

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

   if -8.50000000000000038e67 < z < -1.45e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 82.3

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-cos.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-sin.f64 99.9

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

   8. Applied rewrites 99.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 81.8%

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

   12. Taylor expanded in z around inf

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

   14. Applied rewrites 93.8%

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

   if -1.45e-25 < z < 3.1999999999999997e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 93.6

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

   5. Applied rewrites 93.6%

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

   if 3.1999999999999997e-20 < z < 6.80000000000000041e152

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 72.7

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-cos.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-sin.f64 91.7

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

   8. Applied rewrites 91.7%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 89.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(x, \cos y \cdot \frac{z}{x}, x\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ t_1 := \mathsf{fma}\left(x, \cos y \cdot \frac{z}{x}, x\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)) (t_1 (fma x (* (cos y) (/ z x)) x)))
   (if (<= z -8.5e+67)
     t_0
     (if (<= z -1.45e-25)
       t_1
       (if (<= z 3.2e-20) (+ x (sin y)) (if (<= z 6.8e+152) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double t_1 = fma(x, (cos(y) * (z / x)), x);
	double tmp;
	if (z <= -8.5e+67) {
		tmp = t_0;
	} else if (z <= -1.45e-25) {
		tmp = t_1;
	} else if (z <= 3.2e-20) {
		tmp = x + sin(y);
	} else if (z <= 6.8e+152) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	t_1 = fma(x, Float64(cos(y) * Float64(z / x)), x)
	tmp = 0.0
	if (z <= -8.5e+67)
		tmp = t_0;
	elseif (z <= -1.45e-25)
		tmp = t_1;
	elseif (z <= 3.2e-20)
		tmp = Float64(x + sin(y));
	elseif (z <= 6.8e+152)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(N[Cos[y], $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -8.5e+67], t$95$0, If[LessEqual[z, -1.45e-25], t$95$1, If[LessEqual[z, 3.2e-20], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+152], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000038e67 or 6.80000000000000041e152 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-cos.f64 83.6

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

   5. Applied rewrites 83.6%

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

   if -8.50000000000000038e67 < z < -1.45e-25 or 3.1999999999999997e-20 < z < 6.80000000000000041e152

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 75.6

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-cos.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-sin.f64 94.2

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

   8. Applied rewrites 94.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 71.9%

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

   12. Taylor expanded in z around inf

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

   14. Applied rewrites 90.8%

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

   if -1.45e-25 < z < 3.1999999999999997e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 93.6

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

   5. Applied rewrites 93.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(x, \cos y \cdot \frac{z}{x}, x\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(x, \cos y \cdot \frac{z}{x}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -9 \cdot 10^{+230}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+65}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -9e+230)
     t_0
     (if (<= z -1.6e-25) (+ z x) (if (<= z 3.85e+65) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -9e+230) {
		tmp = t_0;
	} else if (z <= -1.6e-25) {
		tmp = z + x;
	} else if (z <= 3.85e+65) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(y) * z
    if (z <= (-9d+230)) then
        tmp = t_0
    else if (z <= (-1.6d-25)) then
        tmp = z + x
    else if (z <= 3.85d+65) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double tmp;
	if (z <= -9e+230) {
		tmp = t_0;
	} else if (z <= -1.6e-25) {
		tmp = z + x;
	} else if (z <= 3.85e+65) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -9e+230:
		tmp = t_0
	elif z <= -1.6e-25:
		tmp = z + x
	elif z <= 3.85e+65:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -9e+230)
		tmp = t_0;
	elseif (z <= -1.6e-25)
		tmp = Float64(z + x);
	elseif (z <= 3.85e+65)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	tmp = 0.0;
	if (z <= -9e+230)
		tmp = t_0;
	elseif (z <= -1.6e-25)
		tmp = z + x;
	elseif (z <= 3.85e+65)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -9e+230], t$95$0, If[LessEqual[z, -1.6e-25], N[(z + x), $MachinePrecision], If[LessEqual[z, 3.85e+65], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999998e230 or 3.85000000000000019e65 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-cos.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if -8.9999999999999998e230 < z < -1.6000000000000001e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -1.6000000000000001e-25 < z < 3.85000000000000019e65

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 90.5

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

   5. Applied rewrites 90.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+230}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+65}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+50}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0305:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -2.25e+50) t_0 (if (<= y 0.0305) (+ y (+ z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -2.25e+50) {
		tmp = t_0;
	} else if (y <= 0.0305) {
		tmp = y + (z + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + sin(y)
    if (y <= (-2.25d+50)) then
        tmp = t_0
    else if (y <= 0.0305d0) then
        tmp = y + (z + x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.sin(y);
	double tmp;
	if (y <= -2.25e+50) {
		tmp = t_0;
	} else if (y <= 0.0305) {
		tmp = y + (z + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.sin(y)
	tmp = 0
	if y <= -2.25e+50:
		tmp = t_0
	elif y <= 0.0305:
		tmp = y + (z + x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -2.25e+50)
		tmp = t_0;
	elseif (y <= 0.0305)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + sin(y);
	tmp = 0.0;
	if (y <= -2.25e+50)
		tmp = t_0;
	elseif (y <= 0.0305)
		tmp = y + (z + x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+50], t$95$0, If[LessEqual[y, 0.0305], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25000000000000007e50 or 0.030499999999999999 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-sin.f64 64.8

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

   5. Applied rewrites 64.8%

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

   if -2.25000000000000007e50 < y < 0.030499999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 98.1

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

   5. Applied rewrites 98.1%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+50}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq 0.0305:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 70.6

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

5. Applied rewrites 70.6%

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

Alternative 9: 30.1% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lower-cos.f64 N/A

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

   4. lower-sin.f64 57.7

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

5. Applied rewrites 57.7%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 30.9%

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

9. Final simplification 30.9%

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

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))