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

Percentage Accurate: 99.9% → 99.9%

Time: 11.8s

Alternatives: 8

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. Final simplification 99.9%

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

Alternative 2: 81.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -15.8 \lor \neg \left(y \leq 4.15 \cdot 10^{+58}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (or (<= y -15.8) (not (<= y 4.15e+58))) t_0 (- t_0 (* y z)))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if ((y <= -15.8) || !(y <= 4.15e+58)) {
		tmp = t_0;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x + cos(y)
    if ((y <= (-15.8d0)) .or. (.not. (y <= 4.15d+58))) then
        tmp = t_0
    else
        tmp = t_0 - (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 <= -15.8) || !(y <= 4.15e+58)) {
		tmp = t_0;
	} else {
		tmp = t_0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	tmp = 0
	if (y <= -15.8) or not (y <= 4.15e+58):
		tmp = t_0
	else:
		tmp = t_0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if ((y <= -15.8) || !(y <= 4.15e+58))
		tmp = t_0;
	else
		tmp = Float64(t_0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	tmp = 0.0;
	if ((y <= -15.8) || ~((y <= 4.15e+58)))
		tmp = t_0;
	else
		tmp = t_0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -15.8], N[Not[LessEqual[y, 4.15e+58]], $MachinePrecision]], t$95$0, N[(t$95$0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -15.800000000000001 or 4.1499999999999998e58 < y

   1. Initial program 99.9%

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

      1. add-log-exp 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. add-cube-cbrt 99.1%

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

      2. pow3 99.1%

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

      3. log-pow 99.2%

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

      4. pow1/3 99.2%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 99.6%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.8%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 41.4%

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

      1. *-commutative 41.4%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 41.4%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in z around 0 67.3%

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

       1. +-commutative 67.3%

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

   11. Simplified 67.3%

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

   if -15.800000000000001 < y < 4.1499999999999998e58

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15.8 \lor \neg \left(y \leq 4.15 \cdot 10^{+58}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \]

Alternative 3: 81.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00045 \lor \neg \left(y \leq 0.0004\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(\left(x - y \cdot z\right) + -0.5 \cdot \left(y \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00045) (not (<= y 0.0004)))
   (+ x (cos y))
   (+ 1.0 (+ (- x (* y z)) (* -0.5 (* y y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00045) || !(y <= 0.0004)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + ((x - (y * z)) + (-0.5 * (y * 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 ((y <= (-0.00045d0)) .or. (.not. (y <= 0.0004d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + ((x - (y * z)) + ((-0.5d0) * (y * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00045) || !(y <= 0.0004)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + ((x - (y * z)) + (-0.5 * (y * y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00045) or not (y <= 0.0004):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + ((x - (y * z)) + (-0.5 * (y * y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00045) || !(y <= 0.0004))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(Float64(x - Float64(y * z)) + Float64(-0.5 * Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00045) || ~((y <= 0.0004)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + ((x - (y * z)) + (-0.5 * (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00045], N[Not[LessEqual[y, 0.0004]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e-4 or 4.00000000000000019e-4 < y

   1. Initial program 99.9%

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

      1. add-log-exp 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. add-cube-cbrt 99.0%

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

      2. pow3 99.0%

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

      3. log-pow 99.1%

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

      4. pow1/3 99.2%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 99.6%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.8%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 43.2%

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

      1. *-commutative 43.2%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 43.2%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in z around 0 66.7%

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

       1. +-commutative 66.7%

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

   11. Simplified 66.7%

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

   if -4.4999999999999999e-4 < y < 4.00000000000000019e-4

   1. Initial program 100.0%

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

      1. add-log-exp 83.7%

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

   3. Applied egg-rr 83.7%

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

      1. add-cube-cbrt 83.7%

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

      2. pow3 83.7%

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

      3. log-pow 83.7%

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

      4. pow1/3 83.7%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 83.7%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.9%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.9%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in y around 0 99.9%

      \[\leadsto \color{blue}{1 + \left(x + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 99.9%

          \[\leadsto 1 + \left(x + \left(\color{blue}{\left(-y \cdot z\right)} + -0.5 \cdot {y}^{2}\right)\right) \]

       2. distribute-rgt-neg-out 99.9%

          \[\leadsto 1 + \left(x + \left(\color{blue}{y \cdot \left(-z\right)} + -0.5 \cdot {y}^{2}\right)\right) \]

       3. associate-+r+ 99.9%

          \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot \left(-z\right)\right) + -0.5 \cdot {y}^{2}\right)} \]

       4. distribute-rgt-neg-out 99.9%

          \[\leadsto 1 + \left(\left(x + \color{blue}{\left(-y \cdot z\right)}\right) + -0.5 \cdot {y}^{2}\right) \]

       5. sub-neg 99.9%

          \[\leadsto 1 + \left(\color{blue}{\left(x - y \cdot z\right)} + -0.5 \cdot {y}^{2}\right) \]

       6. unpow2 99.9%

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

   11. Simplified 99.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00045 \lor \neg \left(y \leq 0.0004\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(\left(x - y \cdot z\right) + -0.5 \cdot \left(y \cdot y\right)\right)\\ \end{array} \]

Alternative 4: 70.4% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 58000000000000:\\ \;\;\;\;1 + \left(\left(x - y \cdot z\right) + -0.5 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8)
   (+ x 1.0)
   (if (<= y 58000000000000.0)
     (+ 1.0 (+ (- x (* y z)) (* -0.5 (* y y))))
     (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8) {
		tmp = x + 1.0;
	} else if (y <= 58000000000000.0) {
		tmp = 1.0 + ((x - (y * z)) + (-0.5 * (y * 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 (y <= (-4.8d0)) then
        tmp = x + 1.0d0
    else if (y <= 58000000000000.0d0) then
        tmp = 1.0d0 + ((x - (y * z)) + ((-0.5d0) * (y * 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 (y <= -4.8) {
		tmp = x + 1.0;
	} else if (y <= 58000000000000.0) {
		tmp = 1.0 + ((x - (y * z)) + (-0.5 * (y * y)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8:
		tmp = x + 1.0
	elif y <= 58000000000000.0:
		tmp = 1.0 + ((x - (y * z)) + (-0.5 * (y * y)))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8)
		tmp = Float64(x + 1.0);
	elseif (y <= 58000000000000.0)
		tmp = Float64(1.0 + Float64(Float64(x - Float64(y * z)) + Float64(-0.5 * Float64(y * y))));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.8)
		tmp = x + 1.0;
	elseif (y <= 58000000000000.0)
		tmp = 1.0 + ((x - (y * z)) + (-0.5 * (y * y)));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 58000000000000.0], N[(1.0 + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999982 or 5.8e13 < y

   1. Initial program 99.9%

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

      1. add-log-exp 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. add-cube-cbrt 99.0%

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

      2. pow3 99.0%

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

      3. log-pow 99.0%

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

      4. pow1/3 99.2%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 99.6%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.8%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 42.3%

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

      1. *-commutative 42.3%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 42.3%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in y around 0 37.5%

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

       1. +-commutative 37.5%

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

   11. Simplified 37.5%

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

   if -4.79999999999999982 < y < 5.8e13

   1. Initial program 100.0%

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

      1. add-log-exp 84.0%

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

   3. Applied egg-rr 84.0%

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

      1. add-cube-cbrt 83.9%

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

      2. pow3 83.9%

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

      3. log-pow 84.0%

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

      4. pow1/3 84.0%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 84.0%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.9%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.9%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in y around 0 99.8%

      \[\leadsto \color{blue}{1 + \left(x + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot {y}^{2}\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 99.8%

          \[\leadsto 1 + \left(x + \left(\color{blue}{\left(-y \cdot z\right)} + -0.5 \cdot {y}^{2}\right)\right) \]

       2. distribute-rgt-neg-out 99.8%

          \[\leadsto 1 + \left(x + \left(\color{blue}{y \cdot \left(-z\right)} + -0.5 \cdot {y}^{2}\right)\right) \]

       3. associate-+r+ 99.8%

          \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot \left(-z\right)\right) + -0.5 \cdot {y}^{2}\right)} \]

       4. distribute-rgt-neg-out 99.8%

          \[\leadsto 1 + \left(\left(x + \color{blue}{\left(-y \cdot z\right)}\right) + -0.5 \cdot {y}^{2}\right) \]

       5. sub-neg 99.8%

          \[\leadsto 1 + \left(\color{blue}{\left(x - y \cdot z\right)} + -0.5 \cdot {y}^{2}\right) \]

       6. unpow2 99.8%

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

   11. Simplified 99.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 58000000000000:\\ \;\;\;\;1 + \left(\left(x - y \cdot z\right) + -0.5 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 5: 69.4% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+33}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+180}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.4e+33)
   (+ x 1.0)
   (if (<= y 3.1e+180) (+ 1.0 (- x (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.4e+33) {
		tmp = x + 1.0;
	} else if (y <= 3.1e+180) {
		tmp = 1.0 + (x - (y * z));
	} 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 (y <= (-8.4d+33)) then
        tmp = x + 1.0d0
    else if (y <= 3.1d+180) then
        tmp = 1.0d0 + (x - (y * z))
    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 (y <= -8.4e+33) {
		tmp = x + 1.0;
	} else if (y <= 3.1e+180) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.4e+33:
		tmp = x + 1.0
	elif y <= 3.1e+180:
		tmp = 1.0 + (x - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.4e+33)
		tmp = Float64(x + 1.0);
	elseif (y <= 3.1e+180)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.4e+33)
		tmp = x + 1.0;
	elseif (y <= 3.1e+180)
		tmp = 1.0 + (x - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.4e+33], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 3.1e+180], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4000000000000002e33 or 3.09999999999999998e180 < y

   1. Initial program 99.9%

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

      1. add-log-exp 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. add-cube-cbrt 99.1%

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

      2. pow3 99.1%

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

      3. log-pow 99.1%

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

      4. pow1/3 99.2%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 99.6%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.7%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 32.3%

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

      1. *-commutative 32.3%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 32.3%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in y around 0 39.2%

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

       1. +-commutative 39.2%

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

   11. Simplified 39.2%

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

   if -8.4000000000000002e33 < y < 3.09999999999999998e180

   1. Initial program 100.0%

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

      1. add-log-exp 87.5%

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

   3. Applied egg-rr 87.5%

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

      1. add-cube-cbrt 87.4%

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

      2. pow3 87.4%

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

      3. log-pow 87.4%

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

      4. pow1/3 87.4%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 87.5%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.8%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 91.6%

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

      1. *-commutative 91.6%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 91.6%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in y around 0 84.2%

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

       1. mul-1-neg 84.2%

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

       2. sub-neg 84.2%

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

   11. Simplified 84.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+33}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+180}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 6: 62.4% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z -1e+222) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+222) {
		tmp = y * -z;
	} 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 <= (-1d+222)) then
        tmp = y * -z
    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 <= -1e+222) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e+222:
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e+222)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1e+222)
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e+222], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e222

   1. Initial program 99.9%

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

      1. add-log-exp 46.3%

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

   3. Applied egg-rr 46.3%

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

      1. add-cube-cbrt 45.4%

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

      2. pow3 45.5%

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

      3. log-pow 45.7%

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

      4. pow1/3 45.8%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 46.2%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.2%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.2%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 71.3%

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

      1. *-commutative 71.3%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 71.3%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in y around inf 58.6%

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

       1. mul-1-neg 58.6%

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

       2. distribute-rgt-neg-out 58.6%

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

   11. Simplified 58.6%

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

   if -1e222 < z

   1. Initial program 99.9%

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

      1. add-log-exp 94.2%

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

   3. Applied egg-rr 94.2%

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

      1. add-cube-cbrt 94.0%

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

      2. pow3 93.9%

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

      3. log-pow 94.0%

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

      4. pow1/3 94.0%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

      5. log-pow 94.2%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

      6. add-log-exp 99.8%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

   6. Taylor expanded in y around 0 71.7%

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

      1. *-commutative 71.7%

         \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   8. Simplified 71.7%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

   9. Taylor expanded in y around 0 63.2%

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

       1. +-commutative 63.2%

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

   11. Simplified 63.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7: 62.2% 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. Step-by-step derivation

   1. add-log-exp 91.6%

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

3. Applied egg-rr 91.6%

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

   1. add-cube-cbrt 91.3%

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

   2. pow3 91.3%

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

   3. log-pow 91.3%

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

   4. pow1/3 91.4%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

   5. log-pow 91.6%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

   6. add-log-exp 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

5. Applied egg-rr 99.8%

   \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

6. Taylor expanded in y around 0 71.7%

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

   1. *-commutative 71.7%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

8. Simplified 71.7%

   \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

9. Taylor expanded in y around 0 60.5%

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

    1. +-commutative 60.5%

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

11. Simplified 60.5%

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

12. Final simplification 60.5%

    \[\leadsto x + 1 \]

Alternative 8: 43.5% 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. Step-by-step derivation

   1. add-log-exp 91.6%

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

3. Applied egg-rr 91.6%

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

   1. add-cube-cbrt 91.3%

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

   2. pow3 91.3%

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

   3. log-pow 91.3%

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

   4. pow1/3 91.4%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \log \color{blue}{\left({\left(e^{\sin y}\right)}^{0.3333333333333333}\right)}\right) \]

   5. log-pow 91.6%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(e^{\sin y}\right)\right)}\right) \]

   6. add-log-exp 99.8%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \left(0.3333333333333333 \cdot \color{blue}{\sin y}\right)\right) \]

5. Applied egg-rr 99.8%

   \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(3 \cdot \left(0.3333333333333333 \cdot \sin y\right)\right)} \]

6. Taylor expanded in y around 0 71.7%

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

   1. *-commutative 71.7%

      \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

8. Simplified 71.7%

   \[\leadsto \left(x + \cos y\right) - z \cdot \left(3 \cdot \color{blue}{\left(y \cdot 0.3333333333333333\right)}\right) \]

9. Taylor expanded in x around inf 43.7%

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

10. Final simplification 43.7%

    \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(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))))