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

Percentage Accurate: 99.9% → 99.9%

Time: 11.0s

Alternatives: 12

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: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x + 1\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1)
   (fma (sin y) (- z) (+ x 1.0))
   (if (<= z 3.5e-16) (+ x (cos y)) (- (+ x 1.0) (* (sin y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1) {
		tmp = fma(sin(y), -z, (x + 1.0));
	} else if (z <= 3.5e-16) {
		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 <= -3.1)
		tmp = fma(sin(y), Float64(-z), Float64(x + 1.0));
	elseif (z <= 3.5e-16)
		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, -3.1], N[(N[Sin[y], $MachinePrecision] * (-z) + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-16], 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 < -3.10000000000000009

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 99.7%

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

   if -3.10000000000000009 < z < 3.50000000000000017e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.2%

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

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   if 3.50000000000000017e-16 < z

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 54.8%

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

      2. pow2 54.8%

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

   4. Applied egg-rr 54.8%

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

   5. Taylor expanded in y around 0 54.0%

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

      1. unpow2 54.0%

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

      2. add-sqr-sqrt 99.1%

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

      3. *-commutative 99.1%

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

   7. Applied egg-rr 99.1%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x + 1\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 4: 84.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \sin y \cdot z\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+227}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{+175}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+141} \lor \neg \left(z \leq 1.12 \cdot 10^{+88}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (sin y) z))))
   (if (<= z -1.1e+227)
     t_0
     (if (<= z -5.9e+175)
       (+ 1.0 (- x (* y z)))
       (if (or (<= z -1.05e+141) (not (<= z 1.12e+88))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (sin(y) * z);
	double tmp;
	if (z <= -1.1e+227) {
		tmp = t_0;
	} else if (z <= -5.9e+175) {
		tmp = 1.0 + (x - (y * z));
	} else if ((z <= -1.05e+141) || !(z <= 1.12e+88)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (sin(y) * z)
    if (z <= (-1.1d+227)) then
        tmp = t_0
    else if (z <= (-5.9d+175)) then
        tmp = 1.0d0 + (x - (y * z))
    else if ((z <= (-1.05d+141)) .or. (.not. (z <= 1.12d+88))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (Math.sin(y) * z);
	double tmp;
	if (z <= -1.1e+227) {
		tmp = t_0;
	} else if (z <= -5.9e+175) {
		tmp = 1.0 + (x - (y * z));
	} else if ((z <= -1.05e+141) || !(z <= 1.12e+88)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (math.sin(y) * z)
	tmp = 0
	if z <= -1.1e+227:
		tmp = t_0
	elif z <= -5.9e+175:
		tmp = 1.0 + (x - (y * z))
	elif (z <= -1.05e+141) or not (z <= 1.12e+88):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(sin(y) * z))
	tmp = 0.0
	if (z <= -1.1e+227)
		tmp = t_0;
	elseif (z <= -5.9e+175)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	elseif ((z <= -1.05e+141) || !(z <= 1.12e+88))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (sin(y) * z);
	tmp = 0.0;
	if (z <= -1.1e+227)
		tmp = t_0;
	elseif (z <= -5.9e+175)
		tmp = 1.0 + (x - (y * z));
	elseif ((z <= -1.05e+141) || ~((z <= 1.12e+88)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+227], t$95$0, If[LessEqual[z, -5.9e+175], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.05e+141], N[Not[LessEqual[z, 1.12e+88]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001e227 or -5.9000000000000003e175 < z < -1.0499999999999999e141 or 1.12000000000000006e88 < z

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. add-sqr-sqrt 56.0%

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

      5. associate-*r* 56.1%

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

      6. fma-def 56.1%

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

   4. Applied egg-rr 56.1%

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

   5. Taylor expanded in y around 0 56.1%

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

   6. Taylor expanded in x around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. *-commutative 82.4%

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

      3. unsub-neg 82.4%

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

      4. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   if -1.1000000000000001e227 < z < -5.9000000000000003e175

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   5. Simplified 89.5%

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

   if -1.0499999999999999e141 < z < 1.12000000000000006e88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.6%

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

      1. +-commutative 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+227}:\\ \;\;\;\;1 - \sin y \cdot z\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{+175}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+141} \lor \neg \left(z \leq 1.12 \cdot 10^{+88}\right):\\ \;\;\;\;1 - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+226}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+185}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+144} \lor \neg \left(z \leq 1.42 \cdot 10^{+88}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -8.2e+226)
     t_0
     (if (<= z -1.05e+185)
       (+ 1.0 (- x (* y z)))
       (if (or (<= z -3e+144) (not (<= z 1.42e+88))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -8.2e+226) {
		tmp = t_0;
	} else if (z <= -1.05e+185) {
		tmp = 1.0 + (x - (y * z));
	} else if ((z <= -3e+144) || !(z <= 1.42e+88)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) * -z
    if (z <= (-8.2d+226)) then
        tmp = t_0
    else if (z <= (-1.05d+185)) then
        tmp = 1.0d0 + (x - (y * z))
    else if ((z <= (-3d+144)) .or. (.not. (z <= 1.42d+88))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -8.2e+226) {
		tmp = t_0;
	} else if (z <= -1.05e+185) {
		tmp = 1.0 + (x - (y * z));
	} else if ((z <= -3e+144) || !(z <= 1.42e+88)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -8.2e+226:
		tmp = t_0
	elif z <= -1.05e+185:
		tmp = 1.0 + (x - (y * z))
	elif (z <= -3e+144) or not (z <= 1.42e+88):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -8.2e+226)
		tmp = t_0;
	elseif (z <= -1.05e+185)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	elseif ((z <= -3e+144) || !(z <= 1.42e+88))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -8.2e+226)
		tmp = t_0;
	elseif (z <= -1.05e+185)
		tmp = 1.0 + (x - (y * z));
	elseif ((z <= -3e+144) || ~((z <= 1.42e+88)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -8.2e+226], t$95$0, If[LessEqual[z, -1.05e+185], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3e+144], N[Not[LessEqual[z, 1.42e+88]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.19999999999999971e226 or -1.05e185 < z < -2.9999999999999999e144 or 1.41999999999999996e88 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 68.8%

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

      1. associate-*r* 68.8%

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

      2. neg-mul-1 68.8%

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

      3. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   if -8.19999999999999971e226 < z < -1.05e185

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   5. Simplified 89.5%

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

   if -2.9999999999999999e144 < z < 1.41999999999999996e88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.6%

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

      1. +-commutative 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+226}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+185}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+144} \lor \neg \left(z \leq 1.42 \cdot 10^{+88}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05) (not (<= z 3.5e-16)))
   (- (+ x 1.0) (* (sin y) z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05) || !(z <= 3.5e-16)) {
		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 <= (-1.05d0)) .or. (.not. (z <= 3.5d-16))) 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 <= -1.05) || !(z <= 3.5e-16)) {
		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 <= -1.05) or not (z <= 3.5e-16):
		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 <= -1.05) || !(z <= 3.5e-16))
		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 <= -1.05) || ~((z <= 3.5e-16)))
		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, -1.05], N[Not[LessEqual[z, 3.5e-16]], $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 < -1.05000000000000004 or 3.50000000000000017e-16 < z

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 49.4%

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

      2. pow2 49.4%

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

   4. Applied egg-rr 49.4%

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

   5. Taylor expanded in y around 0 49.0%

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

      1. unpow2 49.0%

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

      2. add-sqr-sqrt 99.4%

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

      3. *-commutative 99.4%

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

   7. Applied egg-rr 99.4%

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

   if -1.05000000000000004 < z < 3.50000000000000017e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.2%

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

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.041 \lor \neg \left(y \leq 0.0026\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.041) (not (<= y 0.0026)))
   (+ x (cos y))
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.041) || !(y <= 0.0026)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x - (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 <= (-0.041d0)) .or. (.not. (y <= 0.0026d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.041) || !(y <= 0.0026)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.041) or not (y <= 0.0026):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.041) || !(y <= 0.0026))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.041) || ~((y <= 0.0026)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.041], N[Not[LessEqual[y, 0.0026]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0410000000000000017 or 0.0025999999999999999 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 58.2%

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

      1. +-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -0.0410000000000000017 < y < 0.0025999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.041 \lor \neg \left(y \leq 0.0026\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-12} \lor \neg \left(x \leq 1.6 \cdot 10^{-42}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.5e-12) (not (<= x 1.6e-42))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-12) || !(x <= 1.6e-42)) {
		tmp = x + 1.0;
	} else {
		tmp = 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 ((x <= (-3.5d-12)) .or. (.not. (x <= 1.6d-42))) then
        tmp = x + 1.0d0
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-12) || !(x <= 1.6e-42)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.5e-12) or not (x <= 1.6e-42):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.5e-12) || !(x <= 1.6e-42))
		tmp = Float64(x + 1.0);
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.5e-12) || ~((x <= 1.6e-42)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-12], N[Not[LessEqual[x, 1.6e-42]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e-12 or 1.60000000000000012e-42 < 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 75.8%

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

      1. +-commutative 75.8%

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

   5. Simplified 75.8%

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

   if -3.5e-12 < x < 1.60000000000000012e-42

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 62.1%

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

      1. +-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in x around 0 62.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-12} \lor \neg \left(x \leq 1.6 \cdot 10^{-42}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+24} \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e+24) (not (<= y 0.0072))) (+ x 1.0) (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+24) || !(y <= 0.0072)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (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 <= (-5.8d+24)) .or. (.not. (y <= 0.0072d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+24) || !(y <= 0.0072)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e+24) or not (y <= 0.0072):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e+24) || !(y <= 0.0072))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.8e+24) || ~((y <= 0.0072)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e+24], N[Not[LessEqual[y, 0.0072]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999958e24 or 0.0071999999999999998 < 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 37.9%

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

      1. +-commutative 37.9%

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

   5. Simplified 37.9%

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

   if -5.79999999999999958e24 < y < 0.0071999999999999998

   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%

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

      1. mul-1-neg 97.3%

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

      2. unsub-neg 97.3%

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

   5. Simplified 97.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+24} \lor \neg \left(y \leq 0.0072\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.8% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -17200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -17200000000000.0) x (if (<= x 1.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -17200000000000.0) {
		tmp = x;
	} else if (x <= 1.0) {
		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 <= (-17200000000000.0d0)) then
        tmp = x
    else if (x <= 1.0d0) 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 <= -17200000000000.0) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -17200000000000.0:
		tmp = x
	elif x <= 1.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -17200000000000.0)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -17200000000000.0)
		tmp = x;
	elseif (x <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -17200000000000.0], x, If[LessEqual[x, 1.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.72e13 or 1 < 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 78.2%

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

   if -1.72e13 < x < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 40.7%

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

      1. +-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in x around 0 39.6%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -17200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% 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 59.5%

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

   1. +-commutative 59.5%

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

5. Simplified 59.5%

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

6. Final simplification 59.5%

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

Alternative 12: 21.2% 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. Taylor expanded in y around 0 59.5%

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

   1. +-commutative 59.5%

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

5. Simplified 59.5%

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

6. Taylor expanded in x around 0 21.5%

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

7. Final simplification 21.5%

   \[\leadsto 1 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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))))