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

Percentage Accurate: 99.9% → 99.9%

Time: 9.5s

Alternatives: 15

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. *-commutative 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. fma-def 99.9%

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-5}:\\ \;\;\;\;\left(x + 1\right) - t_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\cos y - t_0\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(\sin y, z, -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z)))
   (if (<= x -3.4e-5)
     (- (+ x 1.0) t_0)
     (if (<= x 9e-72) (- (cos y) t_0) (- x (fma (sin y) z -1.0))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double tmp;
	if (x <= -3.4e-5) {
		tmp = (x + 1.0) - t_0;
	} else if (x <= 9e-72) {
		tmp = cos(y) - t_0;
	} else {
		tmp = x - fma(sin(y), z, -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	tmp = 0.0
	if (x <= -3.4e-5)
		tmp = Float64(Float64(x + 1.0) - t_0);
	elseif (x <= 9e-72)
		tmp = Float64(cos(y) - t_0);
	else
		tmp = Float64(x - fma(sin(y), z, -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[x, -3.4e-5], N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, 9e-72], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision], N[(x - N[(N[Sin[y], $MachinePrecision] * z + -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -3.4e-5 < x < 9e-72

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   if 9e-72 < x

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. fma-def 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 99.3%

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

   6. Taylor expanded in y around inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. *-commutative 99.3%

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

      3. sub-neg 99.3%

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

      4. +-commutative 99.3%

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

      5. associate-+l- 99.3%

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

      6. fma-neg 99.3%

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

      7. metadata-eval 99.3%

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

   8. Simplified 99.3%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-5}:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(\sin y, z, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x + 1\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(\sin y, z, -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e-5)
   (fma (sin y) (- z) (+ x 1.0))
   (if (<= x 9e-72) (- (cos y) (* (sin y) z)) (- x (fma (sin y) z -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e-5) {
		tmp = fma(sin(y), -z, (x + 1.0));
	} else if (x <= 9e-72) {
		tmp = cos(y) - (sin(y) * z);
	} else {
		tmp = x - fma(sin(y), z, -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e-5)
		tmp = fma(sin(y), Float64(-z), Float64(x + 1.0));
	elseif (x <= 9e-72)
		tmp = Float64(cos(y) - Float64(sin(y) * z));
	else
		tmp = Float64(x - fma(sin(y), z, -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e-5], N[(N[Sin[y], $MachinePrecision] * (-z) + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-72], N[(N[Cos[y], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Sin[y], $MachinePrecision] * z + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4e-5

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. fma-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   if -3.4e-5 < x < 9e-72

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   if 9e-72 < x

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. fma-def 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 99.3%

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

   6. Taylor expanded in y around inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. *-commutative 99.3%

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

      3. sub-neg 99.3%

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

      4. +-commutative 99.3%

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

      5. associate-+l- 99.3%

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

      6. fma-neg 99.3%

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

      7. metadata-eval 99.3%

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

   8. Simplified 99.3%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x + 1\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(\sin y, z, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -47000:\\ \;\;\;\;x - \mathsf{fma}\left(\sin y, z, -1\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -47000.0)
   (- x (fma (sin y) z -1.0))
   (if (<= z 1.0) (+ x (cos y)) (- (+ x 1.0) (* (sin y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -47000.0) {
		tmp = x - fma(sin(y), z, -1.0);
	} else if (z <= 1.0) {
		tmp = x + cos(y);
	} else {
		tmp = (x + 1.0) - (sin(y) * z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -47000.0)
		tmp = Float64(x - fma(sin(y), z, -1.0));
	elseif (z <= 1.0)
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(Float64(x + 1.0) - Float64(sin(y) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -47000.0], N[(x - N[(N[Sin[y], $MachinePrecision] * z + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -47000

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. fma-def 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 98.8%

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

   6. Taylor expanded in y around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. *-commutative 98.8%

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

      3. sub-neg 98.8%

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

      4. +-commutative 98.8%

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

      5. associate-+l- 98.8%

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

      6. fma-neg 98.8%

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

      7. metadata-eval 98.8%

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

   8. Simplified 98.8%

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

   if -47000 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

   if 1 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -47000:\\ \;\;\;\;x - \mathsf{fma}\left(\sin y, z, -1\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 6: 79.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -0.000165:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+197} \lor \neg \left(y \leq 1.22 \cdot 10^{+280}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -0.000165)
     t_0
     (if (<= y 7.5e-7)
       (- (+ x 1.0) (* y z))
       (if (or (<= y 3.1e+197) (not (<= y 1.22e+280)))
         t_0
         (* (sin y) (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -0.000165) {
		tmp = t_0;
	} else if (y <= 7.5e-7) {
		tmp = (x + 1.0) - (y * z);
	} else if ((y <= 3.1e+197) || !(y <= 1.22e+280)) {
		tmp = t_0;
	} else {
		tmp = sin(y) * -z;
	}
	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 + cos(y)
    if (y <= (-0.000165d0)) then
        tmp = t_0
    else if (y <= 7.5d-7) then
        tmp = (x + 1.0d0) - (y * z)
    else if ((y <= 3.1d+197) .or. (.not. (y <= 1.22d+280))) then
        tmp = t_0
    else
        tmp = sin(y) * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.cos(y);
	double tmp;
	if (y <= -0.000165) {
		tmp = t_0;
	} else if (y <= 7.5e-7) {
		tmp = (x + 1.0) - (y * z);
	} else if ((y <= 3.1e+197) || !(y <= 1.22e+280)) {
		tmp = t_0;
	} else {
		tmp = Math.sin(y) * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	tmp = 0
	if y <= -0.000165:
		tmp = t_0
	elif y <= 7.5e-7:
		tmp = (x + 1.0) - (y * z)
	elif (y <= 3.1e+197) or not (y <= 1.22e+280):
		tmp = t_0
	else:
		tmp = math.sin(y) * -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -0.000165)
		tmp = t_0;
	elseif (y <= 7.5e-7)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	elseif ((y <= 3.1e+197) || !(y <= 1.22e+280))
		tmp = t_0;
	else
		tmp = Float64(sin(y) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	tmp = 0.0;
	if (y <= -0.000165)
		tmp = t_0;
	elseif (y <= 7.5e-7)
		tmp = (x + 1.0) - (y * z);
	elseif ((y <= 3.1e+197) || ~((y <= 1.22e+280)))
		tmp = t_0;
	else
		tmp = sin(y) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.000165], t$95$0, If[LessEqual[y, 7.5e-7], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.1e+197], N[Not[LessEqual[y, 1.22e+280]], $MachinePrecision]], t$95$0, N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e-4 or 7.5000000000000002e-7 < y < 3.1e197 or 1.2199999999999999e280 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.9%

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

      1. +-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -1.65e-4 < y < 7.5000000000000002e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   if 3.1e197 < y < 1.2199999999999999e280

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 74.6%

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

      1. associate-*r* 74.6%

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

      2. neg-mul-1 74.6%

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

      3. *-commutative 74.6%

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

   5. Simplified 74.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000165:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+197} \lor \neg \left(y \leq 1.22 \cdot 10^{+280}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -47000 \lor \neg \left(z \leq 2\right):\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -47000.0) (not (<= z 2.0)))
   (- (+ x 1.0) (* (sin y) z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -47000.0) || !(z <= 2.0)) {
		tmp = (x + 1.0) - (sin(y) * z);
	} else {
		tmp = x + cos(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 <= (-47000.0d0)) .or. (.not. (z <= 2.0d0))) then
        tmp = (x + 1.0d0) - (sin(y) * z)
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -47000.0) || !(z <= 2.0)) {
		tmp = (x + 1.0) - (Math.sin(y) * z);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -47000.0) or not (z <= 2.0):
		tmp = (x + 1.0) - (math.sin(y) * z)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -47000.0) || !(z <= 2.0))
		tmp = Float64(Float64(x + 1.0) - Float64(sin(y) * z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -47000.0) || ~((z <= 2.0)))
		tmp = (x + 1.0) - (sin(y) * z);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -47000.0], N[Not[LessEqual[z, 2.0]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -47000 or 2 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.3%

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

   if -47000 < z < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -47000 \lor \neg \left(z \leq 2\right):\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-93}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3e+24)
   x
   (if (<= x -5.2e-93)
     (- (+ x 1.0) (* y z))
     (if (<= x 9e-72) (cos y) (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3e+24) {
		tmp = x;
	} else if (x <= -5.2e-93) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 9e-72) {
		tmp = cos(y);
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-3d+24)) then
        tmp = x
    else if (x <= (-5.2d-93)) then
        tmp = (x + 1.0d0) - (y * z)
    else if (x <= 9d-72) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3e+24) {
		tmp = x;
	} else if (x <= -5.2e-93) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 9e-72) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3e+24:
		tmp = x
	elif x <= -5.2e-93:
		tmp = (x + 1.0) - (y * z)
	elif x <= 9e-72:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3e+24)
		tmp = x;
	elseif (x <= -5.2e-93)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	elseif (x <= 9e-72)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3e+24)
		tmp = x;
	elseif (x <= -5.2e-93)
		tmp = (x + 1.0) - (y * z);
	elseif (x <= 9e-72)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3e+24], x, If[LessEqual[x, -5.2e-93], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-72], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.99999999999999995e24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.5%

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

   if -2.99999999999999995e24 < x < -5.1999999999999997e-93

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.1%

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

   4. Taylor expanded in y around 0 78.5%

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

   if -5.1999999999999997e-93 < x < 9e-72

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 69.5%

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

      1. +-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in x around 0 69.5%

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

   if 9e-72 < 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 79.1%

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

      1. +-commutative 79.1%

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

   5. Simplified 79.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-93}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -72000 \lor \neg \left(z \leq 9 \cdot 10^{+32}\right):\\ \;\;\;\;x - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -72000.0) (not (<= z 9e+32)))
   (- x (* (sin y) z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -72000.0) || !(z <= 9e+32)) {
		tmp = x - (sin(y) * z);
	} else {
		tmp = x + cos(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 <= (-72000.0d0)) .or. (.not. (z <= 9d+32))) then
        tmp = x - (sin(y) * z)
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -72000.0) || !(z <= 9e+32)) {
		tmp = x - (Math.sin(y) * z);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -72000.0) or not (z <= 9e+32):
		tmp = x - (math.sin(y) * z)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -72000.0) || !(z <= 9e+32))
		tmp = Float64(x - Float64(sin(y) * z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -72000.0) || ~((z <= 9e+32)))
		tmp = x - (sin(y) * z);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -72000.0], N[Not[LessEqual[z, 9e+32]], $MachinePrecision]], N[(x - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -72000 or 9.0000000000000007e32 < z

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. fma-def 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 99.3%

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

   6. Taylor expanded in y around inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. *-commutative 99.2%

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

      3. sub-neg 99.2%

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

      4. +-commutative 99.2%

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

      5. associate-+l- 99.2%

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

      6. fma-neg 99.3%

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

      7. metadata-eval 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in z around inf 90.3%

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

   if -72000 < z < 9.0000000000000007e32

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -72000 \lor \neg \left(z \leq 9 \cdot 10^{+32}\right):\\ \;\;\;\;x - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000165 \lor \neg \left(y \leq 7.5 \cdot 10^{-7}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.000165) (not (<= y 7.5e-7)))
   (+ x (cos y))
   (- (+ x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.000165) || !(y <= 7.5e-7)) {
		tmp = x + cos(y);
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	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 <= (-0.000165d0)) .or. (.not. (y <= 7.5d-7))) then
        tmp = x + cos(y)
    else
        tmp = (x + 1.0d0) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.000165) || !(y <= 7.5e-7)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.000165) or not (y <= 7.5e-7):
		tmp = x + math.cos(y)
	else:
		tmp = (x + 1.0) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.000165) || !(y <= 7.5e-7))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.000165) || ~((y <= 7.5e-7)))
		tmp = x + cos(y);
	else
		tmp = (x + 1.0) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.000165], N[Not[LessEqual[y, 7.5e-7]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e-4 or 7.5000000000000002e-7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 67.5%

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

      1. +-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -1.65e-4 < y < 7.5000000000000002e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000165 \lor \neg \left(y \leq 7.5 \cdot 10^{-7}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+79} \lor \neg \left(y \leq 7.5 \cdot 10^{-7}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e+79) (not (<= y 7.5e-7))) (+ x 1.0) (- (+ x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+79) || !(y <= 7.5e-7)) {
		tmp = x + 1.0;
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	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 <= (-3.2d+79)) .or. (.not. (y <= 7.5d-7))) then
        tmp = x + 1.0d0
    else
        tmp = (x + 1.0d0) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+79) || !(y <= 7.5e-7)) {
		tmp = x + 1.0;
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e+79) or not (y <= 7.5e-7):
		tmp = x + 1.0
	else:
		tmp = (x + 1.0) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e+79) || !(y <= 7.5e-7))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.2e+79) || ~((y <= 7.5e-7)))
		tmp = x + 1.0;
	else
		tmp = (x + 1.0) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e+79], N[Not[LessEqual[y, 7.5e-7]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000003e79 or 7.5000000000000002e-7 < 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 45.3%

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

      1. +-commutative 45.3%

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

   5. Simplified 45.3%

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

   if -3.20000000000000003e79 < y < 7.5000000000000002e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

   4. Taylor expanded in y around 0 95.9%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+79} \lor \neg \left(y \leq 7.5 \cdot 10^{-7}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.2% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-5} \lor \neg \left(x \leq 7.5 \cdot 10^{-12}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e-5) (not (<= x 7.5e-12))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e-5) || !(x <= 7.5e-12)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	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 <= (-5.2d-5)) .or. (.not. (x <= 7.5d-12))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e-5) || !(x <= 7.5e-12)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e-5) or not (x <= 7.5e-12):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e-5) || !(x <= 7.5e-12))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.2e-5) || ~((x <= 7.5e-12)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e-5], N[Not[LessEqual[x, 7.5e-12]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.19999999999999968e-5 or 7.5e-12 < 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 86.5%

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

      1. +-commutative 86.5%

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

   5. Simplified 86.5%

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

   if -5.19999999999999968e-5 < x < 7.5e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.9%

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

   4. Taylor expanded in y around 0 52.8%

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

   5. Taylor expanded in x around 0 52.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-5} \lor \neg \left(x \leq 7.5 \cdot 10^{-12}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.0% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.25e-23) x (if (<= x 3.5) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-23) {
		tmp = x;
	} else if (x <= 3.5) {
		tmp = 1.0;
	} else {
		tmp = 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 <= (-2.25d-23)) then
        tmp = x
    else if (x <= 3.5d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-23) {
		tmp = x;
	} else if (x <= 3.5) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.25e-23:
		tmp = x
	elif x <= 3.5:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.25e-23)
		tmp = x;
	elseif (x <= 3.5)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.25e-23)
		tmp = x;
	elseif (x <= 3.5)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.25e-23], x, If[LessEqual[x, 3.5], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.24999999999999987e-23 or 3.5 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.4%

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

   if -2.24999999999999987e-23 < x < 3.5

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y} \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right) \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}} \]

      2. pow3 98.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{3}} \]

      3. associate--l+ 98.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 75.4%

      \[\leadsto {\left(\sqrt[3]{x + \left(\color{blue}{1} - z \cdot \sin y\right)}\right)}^{3} \]

   6. Taylor expanded in x around 0 58.8%

      \[\leadsto {\color{blue}{\left({\left(1 - z \cdot \sin y\right)}^{0.3333333333333333}\right)}}^{3} \]
   7. Step-by-step derivation

      1. unpow1/3 74.6%

         \[\leadsto {\color{blue}{\left(\sqrt[3]{1 - z \cdot \sin y}\right)}}^{3} \]

      2. *-commutative 74.6%

         \[\leadsto {\left(\sqrt[3]{1 - \color{blue}{\sin y \cdot z}}\right)}^{3} \]

   8. Simplified 74.6%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{1 - \sin y \cdot z}\right)}}^{3} \]

   9. Taylor expanded in y around 0 40.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.2% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 65.5%

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

   1. +-commutative 65.5%

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

5. Simplified 65.5%

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

6. Final simplification 65.5%

   \[\leadsto x + 1 \]
7. Add Preprocessing

Alternative 15: 22.0% accurate, 207.0× 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. Step-by-step derivation

   1. add-cube-cbrt 98.1%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y} \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right) \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}} \]

   2. pow3 98.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{3}} \]

   3. associate--l+ 98.2%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{3} \]

4. Applied egg-rr 98.2%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{3}} \]

5. Taylor expanded in y around 0 87.5%

   \[\leadsto {\left(\sqrt[3]{x + \left(\color{blue}{1} - z \cdot \sin y\right)}\right)}^{3} \]

6. Taylor expanded in x around 0 31.0%

   \[\leadsto {\color{blue}{\left({\left(1 - z \cdot \sin y\right)}^{0.3333333333333333}\right)}}^{3} \]
7. Step-by-step derivation

   1. unpow1/3 42.5%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{1 - z \cdot \sin y}\right)}}^{3} \]

   2. *-commutative 42.5%

      \[\leadsto {\left(\sqrt[3]{1 - \color{blue}{\sin y \cdot z}}\right)}^{3} \]

8. Simplified 42.5%

   \[\leadsto {\color{blue}{\left(\sqrt[3]{1 - \sin y \cdot z}\right)}}^{3} \]

9. Taylor expanded in y around 0 20.0%

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

10. Final simplification 20.0%

    \[\leadsto 1 \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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))))