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

Percentage Accurate: 99.9% → 99.9%

Time: 9.7s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;x - t\_0\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;\cos y - t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (<= x -1.0)
     (- x t_0)
     (if (<= x 2.5e-12) (- (cos y) t_0) (* x (- 1.0 (* z (/ (sin y) x))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if (x <= -1.0) {
		tmp = x - t_0;
	} else if (x <= 2.5e-12) {
		tmp = cos(y) - t_0;
	} else {
		tmp = x * (1.0 - (z * (sin(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) :: t_0
    real(8) :: tmp
    t_0 = z * sin(y)
    if (x <= (-1.0d0)) then
        tmp = x - t_0
    else if (x <= 2.5d-12) then
        tmp = cos(y) - t_0
    else
        tmp = x * (1.0d0 - (z * (sin(y) / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if (x <= -1.0) {
		tmp = x - t_0;
	} else if (x <= 2.5e-12) {
		tmp = Math.cos(y) - t_0;
	} else {
		tmp = x * (1.0 - (z * (Math.sin(y) / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if x <= -1.0:
		tmp = x - t_0
	elif x <= 2.5e-12:
		tmp = math.cos(y) - t_0
	else:
		tmp = x * (1.0 - (z * (math.sin(y) / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x - t_0);
	elseif (x <= 2.5e-12)
		tmp = Float64(cos(y) - t_0);
	else
		tmp = Float64(x * Float64(1.0 - Float64(z * Float64(sin(y) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x - t_0;
	elseif (x <= 2.5e-12)
		tmp = cos(y) - t_0;
	else
		tmp = x * (1.0 - (z * (sin(y) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.0], N[(x - t$95$0), $MachinePrecision], If[LessEqual[x, 2.5e-12], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision], N[(x * N[(1.0 - N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. associate--l+ 99.9%

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

      2. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-/l* 98.8%

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

      4. distribute-rgt-neg-in 98.8%

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

      5. distribute-neg-frac2 98.8%

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

   8. Simplified 98.8%

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

   9. Taylor expanded in x around 0 98.9%

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

       1. associate-*r* 98.9%

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

       2. mul-1-neg 98.9%

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

       3. cancel-sign-sub-inv 98.9%

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

   11. Simplified 98.9%

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

   if -1 < x < 2.49999999999999985e-12

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.6%

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

   if 2.49999999999999985e-12 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 96.7%

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

      1. mul-1-neg 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-/l* 96.7%

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

      4. distribute-rgt-neg-in 96.7%

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

      5. distribute-neg-frac2 96.7%

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

   8. Simplified 96.7%

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

   9. Taylor expanded in x around inf 96.7%

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

       1. mul-1-neg 96.7%

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

       2. *-commutative 96.7%

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

       3. associate-*r/ 96.7%

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

       4. unsub-neg 96.7%

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

       5. associate-*r/ 96.7%

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

       6. *-commutative 96.7%

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

       7. associate-/l* 96.7%

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

   11. Simplified 96.7%

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

Alternative 3: 92.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+59} \lor \neg \left(z \leq 7.7 \cdot 10^{+37}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.5e+59) (not (<= z 7.7e+37)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+59) || !(z <= 7.7e+37)) {
		tmp = x - (z * sin(y));
	} 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 <= (-7.5d+59)) .or. (.not. (z <= 7.7d+37))) then
        tmp = x - (z * sin(y))
    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 <= -7.5e+59) || !(z <= 7.7e+37)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.5e+59) or not (z <= 7.7e+37):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.5e+59) || !(z <= 7.7e+37))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.5e+59) || ~((z <= 7.7e+37)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.5e+59], N[Not[LessEqual[z, 7.7e+37]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4999999999999996e59 or 7.70000000000000022e37 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. associate--l+ 83.2%

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

      2. div-sub 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in z around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-/l* 69.3%

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

      4. distribute-rgt-neg-in 69.3%

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

      5. distribute-neg-frac2 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in x around 0 89.4%

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

       1. associate-*r* 89.4%

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

       2. mul-1-neg 89.4%

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

       3. cancel-sign-sub-inv 89.4%

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

   11. Simplified 89.4%

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

   if -7.4999999999999996e59 < z < 7.70000000000000022e37

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+59} \lor \neg \left(z \leq 7.7 \cdot 10^{+37}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+101} \lor \neg \left(z \leq 1.5 \cdot 10^{+161}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+101) (not (<= z 1.5e+161)))
   (* (sin y) (- z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+101) || !(z <= 1.5e+161)) {
		tmp = 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 <= (-6d+101)) .or. (.not. (z <= 1.5d+161))) then
        tmp = 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 <= -6e+101) || !(z <= 1.5e+161)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e+101) or not (z <= 1.5e+161):
		tmp = math.sin(y) * -z
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e+101) || !(z <= 1.5e+161))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6e+101) || ~((z <= 1.5e+161)))
		tmp = sin(y) * -z;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e+101], N[Not[LessEqual[z, 1.5e+161]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999986e101 or 1.50000000000000006e161 < 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 69.9%

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

      1. associate-*r* 69.9%

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

      2. neg-mul-1 69.9%

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

      3. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -5.99999999999999986e101 < z < 1.50000000000000006e161

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 89.5%

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

      1. +-commutative 89.5%

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

   5. Simplified 89.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+101} \lor \neg \left(z \leq 1.5 \cdot 10^{+161}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.34 \lor \neg \left(y \leq 5.8 \cdot 10^{+45}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.34) (not (<= y 5.8e+45)))
   (+ x (cos y))
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.34) || !(y <= 5.8e+45)) {
		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 <= (-0.34d0)) .or. (.not. (y <= 5.8d+45))) 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 <= -0.34) || !(y <= 5.8e+45)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.34) or not (y <= 5.8e+45):
		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 <= -0.34) || !(y <= 5.8e+45))
		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 <= -0.34) || ~((y <= 5.8e+45)))
		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, -0.34], N[Not[LessEqual[y, 5.8e+45]], $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 < -0.340000000000000024 or 5.7999999999999994e45 < 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 61.2%

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

      1. +-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -0.340000000000000024 < y < 5.7999999999999994e45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.9%

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

      1. mul-1-neg 95.9%

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

      2. unsub-neg 95.9%

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

   5. Simplified 95.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.34 \lor \neg \left(y \leq 5.8 \cdot 10^{+45}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.0% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+51}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -90.0)
   (+ x 1.0)
   (if (<= y 3.1e+51)
     (+ 1.0 (+ x (* y (- (* y -0.5) z))))
     (* x (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -90.0) {
		tmp = x + 1.0;
	} else if (y <= 3.1e+51) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-90.0d0)) then
        tmp = x + 1.0d0
    else if (y <= 3.1d+51) then
        tmp = 1.0d0 + (x + (y * ((y * (-0.5d0)) - z)))
    else
        tmp = x * (1.0d0 + (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -90.0) {
		tmp = x + 1.0;
	} else if (y <= 3.1e+51) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else {
		tmp = x * (1.0 + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -90.0:
		tmp = x + 1.0
	elif y <= 3.1e+51:
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)))
	else:
		tmp = x * (1.0 + (1.0 / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -90.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 3.1e+51)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	else
		tmp = Float64(x * Float64(1.0 + Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -90.0)
		tmp = x + 1.0;
	elseif (y <= 3.1e+51)
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	else
		tmp = x * (1.0 + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -90.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 3.1e+51], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -90

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 50.7%

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

      1. +-commutative 50.7%

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

   5. Simplified 50.7%

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

   if -90 < y < 3.10000000000000011e51

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.3%

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

   if 3.10000000000000011e51 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 88.1%

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

      1. associate--l+ 88.1%

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

      2. div-sub 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in y around 0 33.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+51}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.2% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -23000 \lor \neg \left(y \leq 1.62 \cdot 10^{+47}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -23000.0) (not (<= y 1.62e+47)))
   (+ x 1.0)
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -23000.0) || !(y <= 1.62e+47)) {
		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 <= (-23000.0d0)) .or. (.not. (y <= 1.62d+47))) 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 <= -23000.0) || !(y <= 1.62e+47)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -23000.0) or not (y <= 1.62e+47):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -23000.0) || !(y <= 1.62e+47))
		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 <= -23000.0) || ~((y <= 1.62e+47)))
		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, -23000.0], N[Not[LessEqual[y, 1.62e+47]], $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 < -23000 or 1.6200000000000001e47 < 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 44.0%

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

      1. +-commutative 44.0%

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

   5. Simplified 44.0%

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

   if -23000 < y < 1.6200000000000001e47

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.8%

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

      1. mul-1-neg 94.8%

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

      2. unsub-neg 94.8%

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

   5. Simplified 94.8%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23000 \lor \neg \left(y \leq 1.62 \cdot 10^{+47}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00031 \lor \neg \left(x \leq 1.55\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.00031) (not (<= x 1.55))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.00031) || !(x <= 1.55)) {
		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 <= (-0.00031d0)) .or. (.not. (x <= 1.55d0))) 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 <= -0.00031) || !(x <= 1.55)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.00031) or not (x <= 1.55):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.00031) || !(x <= 1.55))
		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 <= -0.00031) || ~((x <= 1.55)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.00031], N[Not[LessEqual[x, 1.55]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e-4 or 1.55000000000000004 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. +-commutative 84.6%

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

   5. Simplified 84.6%

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

   if -3.1e-4 < x < 1.55000000000000004

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 83.3%

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

      1. associate--l+ 83.3%

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

      2. div-sub 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in y around 0 49.1%

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

      1. +-commutative 49.1%

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

      2. mul-1-neg 49.1%

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

      3. unsub-neg 49.1%

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

      4. associate-/l* 41.4%

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

   8. Simplified 41.4%

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

   9. Taylor expanded in x around 0 53.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00031 \lor \neg \left(x \leq 1.55\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.6% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+235}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.7e+235) (* z (- y)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e+235) {
		tmp = z * -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 (z <= (-3.7d+235)) then
        tmp = z * -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 (z <= -3.7e+235) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.7e+235:
		tmp = z * -y
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.7e+235)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.7e+235)
		tmp = z * -y;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.7e+235], N[(z * (-y)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999998e235

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. div-sub 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in y around 0 37.1%

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

      1. +-commutative 37.1%

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

      2. mul-1-neg 37.1%

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

      3. unsub-neg 37.1%

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

      4. associate-/l* 29.2%

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

   8. Simplified 29.2%

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

   9. Taylor expanded in y around inf 45.1%

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

       1. neg-mul-1 45.1%

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

       2. distribute-rgt-neg-in 45.1%

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

   11. Simplified 45.1%

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

   if -3.6999999999999998e235 < 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 64.6%

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

      1. +-commutative 64.6%

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

   5. Simplified 64.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+235}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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 62.1%

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

   1. +-commutative 62.1%

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

5. Simplified 62.1%

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

Alternative 11: 42.3% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 44.0%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(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))))