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

Percentage Accurate: 99.9% → 99.9%

Time: 9.7s

Alternatives: 12

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: 95.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ t_1 := \mathsf{fma}\left(x, \frac{t\_0}{x}, x\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;t\_0 + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)) (t_1 (fma x (/ t_0 x) x)))
   (if (<= x -2.8e-34) t_1 (if (<= x 1.8e-18) (+ t_0 (sin y)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double t_1 = fma(x, (t_0 / x), x);
	double tmp;
	if (x <= -2.8e-34) {
		tmp = t_1;
	} else if (x <= 1.8e-18) {
		tmp = t_0 + sin(y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	t_1 = fma(x, Float64(t_0 / x), x)
	tmp = 0.0
	if (x <= -2.8e-34)
		tmp = t_1;
	elseif (x <= 1.8e-18)
		tmp = Float64(t_0 + sin(y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(t$95$0 / x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -2.8e-34], t$95$1, If[LessEqual[x, 1.8e-18], N[(t$95$0 + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999997e-34 or 1.80000000000000005e-18 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 89.4

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

   5. Applied rewrites 89.4%

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

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. mul-1-neg N/A

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

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

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

      9. remove-double-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower-fma.f64 N/A

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 98.6%

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

   if -2.79999999999999997e-34 < x < 1.80000000000000005e-18

   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. lower-sin.f64 97.3

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

   5. Applied rewrites 97.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;\cos y \cdot z + \sin y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma x (/ (* (cos y) z) x) x)))
   (if (<= x -2.8e-34) t_0 (if (<= x 1.8e-18) (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 <= -2.8e-34) {
		tmp = t_0;
	} else if (x <= 1.8e-18) {
		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 <= -2.8e-34)
		tmp = t_0;
	elseif (x <= 1.8e-18)
		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, -2.8e-34], t$95$0, If[LessEqual[x, 1.8e-18], N[(z * N[Cos[y], $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999997e-34 or 1.80000000000000005e-18 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 89.4

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

   5. Applied rewrites 89.4%

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

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. mul-1-neg N/A

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

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

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

      9. remove-double-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower-fma.f64 N/A

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 98.6%

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

   if -2.79999999999999997e-34 < x < 1.80000000000000005e-18

   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 97.3

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

   5. Applied rewrites 97.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;\left(x + \sin y\right) + z \cdot 1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t\_0}{x}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -2.3e+107)
     t_0
     (if (<= z 3.1e-18)
       (+ (+ x (sin y)) (* z 1.0))
       (if (<= z 3.1e+196) (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 <= -2.3e+107) {
		tmp = t_0;
	} else if (z <= 3.1e-18) {
		tmp = (x + sin(y)) + (z * 1.0);
	} else if (z <= 3.1e+196) {
		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 <= -2.3e+107)
		tmp = t_0;
	elseif (z <= 3.1e-18)
		tmp = Float64(Float64(x + sin(y)) + Float64(z * 1.0));
	elseif (z <= 3.1e+196)
		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, -2.3e+107], t$95$0, If[LessEqual[z, 3.1e-18], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+196], N[(x * N[(t$95$0 / x), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e107 or 3.1000000000000001e196 < z

   1. Initial program 99.7%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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 94.1

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

   5. Applied rewrites 94.1%

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

   if -2.3e107 < z < 3.10000000000000007e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 97.1%

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

   if 3.10000000000000007e-18 < z < 3.1000000000000001e196

   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 71.6

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

   5. Applied rewrites 71.6%

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

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. mul-1-neg N/A

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

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

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

      9. remove-double-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower-fma.f64 N/A

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

   8. Applied rewrites 89.7%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 88.4%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-18}:\\ \;\;\;\;\left(x + \sin y\right) + z \cdot 1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{\cos y \cdot z}{x}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -11500000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-46}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+122}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -2.3e+107)
     t_0
     (if (<= z -11500000000.0)
       (+ z x)
       (if (<= z 2.9e-46) (+ x (sin y)) (if (<= z 2.95e+122) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -2.3e+107) {
		tmp = t_0;
	} else if (z <= -11500000000.0) {
		tmp = z + x;
	} else if (z <= 2.9e-46) {
		tmp = x + sin(y);
	} else if (z <= 2.95e+122) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(y) * z
    if (z <= (-2.3d+107)) then
        tmp = t_0
    else if (z <= (-11500000000.0d0)) then
        tmp = z + x
    else if (z <= 2.9d-46) then
        tmp = x + sin(y)
    else if (z <= 2.95d+122) then
        tmp = z + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double tmp;
	if (z <= -2.3e+107) {
		tmp = t_0;
	} else if (z <= -11500000000.0) {
		tmp = z + x;
	} else if (z <= 2.9e-46) {
		tmp = x + Math.sin(y);
	} else if (z <= 2.95e+122) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -2.3e+107:
		tmp = t_0
	elif z <= -11500000000.0:
		tmp = z + x
	elif z <= 2.9e-46:
		tmp = x + math.sin(y)
	elif z <= 2.95e+122:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -2.3e+107)
		tmp = t_0;
	elseif (z <= -11500000000.0)
		tmp = Float64(z + x);
	elseif (z <= 2.9e-46)
		tmp = Float64(x + sin(y));
	elseif (z <= 2.95e+122)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	tmp = 0.0;
	if (z <= -2.3e+107)
		tmp = t_0;
	elseif (z <= -11500000000.0)
		tmp = z + x;
	elseif (z <= 2.9e-46)
		tmp = x + sin(y);
	elseif (z <= 2.95e+122)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.3e+107], t$95$0, If[LessEqual[z, -11500000000.0], N[(z + x), $MachinePrecision], If[LessEqual[z, 2.9e-46], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.95e+122], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e107 or 2.95000000000000016e122 < z

   1. Initial program 99.7%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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 86.7

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

   5. Applied rewrites 86.7%

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

   if -2.3e107 < z < -1.15e10 or 2.90000000000000005e-46 < z < 2.95000000000000016e122

   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 81.4

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

   5. Applied rewrites 81.4%

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

   if -1.15e10 < z < 2.90000000000000005e-46

   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 94.6

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

   5. Applied rewrites 94.6%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -11500000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-46}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+122}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+122}:\\ \;\;\;\;\left(x + \sin y\right) + z \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -2.3e+107)
     t_0
     (if (<= z 2.95e+122) (+ (+ x (sin y)) (* z 1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -2.3e+107) {
		tmp = t_0;
	} else if (z <= 2.95e+122) {
		tmp = (x + sin(y)) + (z * 1.0);
	} 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 <= (-2.3d+107)) then
        tmp = t_0
    else if (z <= 2.95d+122) then
        tmp = (x + sin(y)) + (z * 1.0d0)
    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 <= -2.3e+107) {
		tmp = t_0;
	} else if (z <= 2.95e+122) {
		tmp = (x + Math.sin(y)) + (z * 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -2.3e+107:
		tmp = t_0
	elif z <= 2.95e+122:
		tmp = (x + math.sin(y)) + (z * 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -2.3e+107)
		tmp = t_0;
	elseif (z <= 2.95e+122)
		tmp = Float64(Float64(x + sin(y)) + Float64(z * 1.0));
	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 <= -2.3e+107)
		tmp = t_0;
	elseif (z <= 2.95e+122)
		tmp = (x + sin(y)) + (z * 1.0);
	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, -2.3e+107], t$95$0, If[LessEqual[z, 2.95e+122], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e107 or 2.95000000000000016e122 < z

   1. Initial program 99.7%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   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 86.7

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

   5. Applied rewrites 86.7%

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

   if -2.3e107 < z < 2.95000000000000016e122

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 94.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+122}:\\ \;\;\;\;\left(x + \sin y\right) + z \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -2.5e+18) t_0 (if (<= y 5.7e-8) (+ y (+ z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -2.5e+18) {
		tmp = t_0;
	} else if (y <= 5.7e-8) {
		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 <= (-2.5d+18)) then
        tmp = t_0
    else if (y <= 5.7d-8) 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 <= -2.5e+18) {
		tmp = t_0;
	} else if (y <= 5.7e-8) {
		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 <= -2.5e+18:
		tmp = t_0
	elif y <= 5.7e-8:
		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 <= -2.5e+18)
		tmp = t_0;
	elseif (y <= 5.7e-8)
		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 <= -2.5e+18)
		tmp = t_0;
	elseif (y <= 5.7e-8)
		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, -2.5e+18], t$95$0, If[LessEqual[y, 5.7e-8], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e18 or 5.70000000000000009e-8 < 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 68.9

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

   5. Applied rewrites 68.9%

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

   if -2.5e18 < y < 5.70000000000000009e-8

   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 98.3

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

   5. Applied rewrites 98.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.9% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+27}:\\ \;\;\;\;z + \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot -0.5, 1\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+50)
   (+ z x)
   (if (<= y 7.5e+27) (+ z (fma y (fma y (* z -0.5) 1.0) x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+50) {
		tmp = z + x;
	} else if (y <= 7.5e+27) {
		tmp = z + fma(y, fma(y, (z * -0.5), 1.0), x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+50)
		tmp = Float64(z + x);
	elseif (y <= 7.5e+27)
		tmp = Float64(z + fma(y, fma(y, Float64(z * -0.5), 1.0), x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+50], N[(z + x), $MachinePrecision], If[LessEqual[y, 7.5e+27], N[(z + N[(y * N[(y * N[(z * -0.5), $MachinePrecision] + 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000003e50 or 7.5000000000000002e27 < 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 48.8

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

   5. Applied rewrites 48.8%

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

   if -6.5000000000000003e50 < y < 7.5000000000000002e27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

Alternative 9: 70.2% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+53}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.95e+57) (+ z x) (if (<= y 1.3e+53) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+57) {
		tmp = z + x;
	} else if (y <= 1.3e+53) {
		tmp = y + (z + x);
	} 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) :: tmp
    if (y <= (-1.95d+57)) then
        tmp = z + x
    else if (y <= 1.3d+53) then
        tmp = y + (z + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+57) {
		tmp = z + x;
	} else if (y <= 1.3e+53) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.95e+57:
		tmp = z + x
	elif y <= 1.3e+53:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.95e+57)
		tmp = Float64(z + x);
	elseif (y <= 1.3e+53)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.95e+57)
		tmp = z + x;
	elseif (y <= 1.3e+53)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.95e+57], N[(z + x), $MachinePrecision], If[LessEqual[y, 1.3e+53], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.94999999999999984e57 or 1.29999999999999999e53 < 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 50.5

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

   5. Applied rewrites 50.5%

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

   if -1.94999999999999984e57 < y < 1.29999999999999999e53

   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 84.2

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

   5. Applied rewrites 84.2%

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

Alternative 10: 51.3% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+14}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-38}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e+14) (+ y x) (if (<= x 5.8e-38) (+ y z) (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e+14) {
		tmp = y + x;
	} else if (x <= 5.8e-38) {
		tmp = y + z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.8d+14)) then
        tmp = y + x
    else if (x <= 5.8d-38) then
        tmp = y + z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e+14) {
		tmp = y + x;
	} else if (x <= 5.8e-38) {
		tmp = y + z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.8e+14:
		tmp = y + x
	elif x <= 5.8e-38:
		tmp = y + z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e+14)
		tmp = Float64(y + x);
	elseif (x <= 5.8e-38)
		tmp = Float64(y + z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.8e+14)
		tmp = y + x;
	elseif (x <= 5.8e-38)
		tmp = y + z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e+14], N[(y + x), $MachinePrecision], If[LessEqual[x, 5.8e-38], N[(y + z), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e14 or 5.79999999999999988e-38 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 90.6

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. lower-+.f64 N/A

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

      4. lower-+.f64 63.3

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

   8. Applied rewrites 63.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 57.2%

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

   if -1.8e14 < x < 5.79999999999999988e-38

   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 34.4

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

   5. Applied rewrites 34.4%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. lower-+.f64 N/A

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

      4. lower-+.f64 39.5

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

   8. Applied rewrites 39.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 34.6%

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

Alternative 11: 66.2% 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 64.2

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

5. Applied rewrites 64.2%

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

Alternative 12: 39.1% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y + 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 64.2

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

5. Applied rewrites 64.2%

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

6. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. associate-+r+ N/A

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

   3. lower-+.f64 N/A

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

   4. lower-+.f64 52.1

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

8. Applied rewrites 52.1%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 36.8%

    \[\leadsto y + \color{blue}{x} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024233 
(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))))