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

Percentage Accurate: 99.9% → 99.9%

Time: 9.4s

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. Final simplification 99.9%

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

Alternative 2: 81.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+139}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+60} \lor \neg \left(z \leq 3 \cdot 10^{+138}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -1.9e+139)
     t_0
     (if (<= z 4.8e+36)
       (+ x (cos y))
       (if (or (<= z 2.1e+60) (not (<= z 3e+138)))
         t_0
         (+ x (- 1.0 (* y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -1.9e+139) {
		tmp = t_0;
	} else if (z <= 4.8e+36) {
		tmp = x + cos(y);
	} else if ((z <= 2.1e+60) || !(z <= 3e+138)) {
		tmp = t_0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) * -z
    if (z <= (-1.9d+139)) then
        tmp = t_0
    else if (z <= 4.8d+36) then
        tmp = x + cos(y)
    else if ((z <= 2.1d+60) .or. (.not. (z <= 3d+138))) then
        tmp = t_0
    else
        tmp = x + (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -1.9e+139) {
		tmp = t_0;
	} else if (z <= 4.8e+36) {
		tmp = x + Math.cos(y);
	} else if ((z <= 2.1e+60) || !(z <= 3e+138)) {
		tmp = t_0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -1.9e+139:
		tmp = t_0
	elif z <= 4.8e+36:
		tmp = x + math.cos(y)
	elif (z <= 2.1e+60) or not (z <= 3e+138):
		tmp = t_0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -1.9e+139)
		tmp = t_0;
	elseif (z <= 4.8e+36)
		tmp = Float64(x + cos(y));
	elseif ((z <= 2.1e+60) || !(z <= 3e+138))
		tmp = t_0;
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -1.9e+139)
		tmp = t_0;
	elseif (z <= 4.8e+36)
		tmp = x + cos(y);
	elseif ((z <= 2.1e+60) || ~((z <= 3e+138)))
		tmp = t_0;
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.9e+139], t$95$0, If[LessEqual[z, 4.8e+36], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.1e+60], N[Not[LessEqual[z, 3e+138]], $MachinePrecision]], t$95$0, N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e139 or 4.79999999999999985e36 < z < 2.1000000000000001e60 or 3.0000000000000001e138 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 82.0%

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

      1. associate-*r* 82.0%

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

      2. neg-mul-1 82.0%

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

      3. *-commutative 82.0%

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

   4. Simplified 82.0%

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

   if -1.9e139 < z < 4.79999999999999985e36

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.4%

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

      3. associate--l+ 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in z around 0 93.9%

      \[\leadsto \color{blue}{\left(\cos y + x\right) \cdot {1}^{0.3333333333333333}} \]
   5. Step-by-step derivation

      1. pow-base-1 93.9%

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

      2. *-rgt-identity 93.9%

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

   6. Simplified 93.9%

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

   if 2.1000000000000001e60 < z < 3.0000000000000001e138

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 70.6%

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

      1. associate-+r+ 70.6%

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

      2. +-commutative 70.6%

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

      3. mul-1-neg 70.6%

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

      4. unsub-neg 70.6%

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

   4. Simplified 70.6%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+139}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+60} \lor \neg \left(z \leq 3 \cdot 10^{+138}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 3: 99.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -18 \lor \neg \left(z \leq 1.15\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -18.0) (not (<= z 1.15)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -18.0) || !(z <= 1.15)) {
		tmp = (x + 1.0) - (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 <= (-18.0d0)) .or. (.not. (z <= 1.15d0))) then
        tmp = (x + 1.0d0) - (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 <= -18.0) || !(z <= 1.15)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -18.0) or not (z <= 1.15):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -18.0) || !(z <= 1.15))
		tmp = Float64(Float64(x + 1.0) - 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 <= -18.0) || ~((z <= 1.15)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -18.0], N[Not[LessEqual[z, 1.15]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - 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 < -18 or 1.1499999999999999 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. +-commutative 97.9%

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

   4. Simplified 97.9%

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

   if -18 < z < 1.1499999999999999

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.4%

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

      3. associate--l+ 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in z around 0 99.4%

      \[\leadsto \color{blue}{\left(\cos y + x\right) \cdot {1}^{0.3333333333333333}} \]
   5. Step-by-step derivation

      1. pow-base-1 99.4%

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

      2. *-rgt-identity 99.4%

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

   6. Simplified 99.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18 \lor \neg \left(z \leq 1.15\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 4: 93.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -125000000000 \lor \neg \left(z \leq 26\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -125000000000.0) (not (<= z 26.0)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -125000000000.0) || !(z <= 26.0)) {
		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 <= (-125000000000.0d0)) .or. (.not. (z <= 26.0d0))) 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 <= -125000000000.0) || !(z <= 26.0)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -125000000000.0) or not (z <= 26.0):
		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 <= -125000000000.0) || !(z <= 26.0))
		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 <= -125000000000.0) || ~((z <= 26.0)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -125000000000.0], N[Not[LessEqual[z, 26.0]], $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 < -1.25e11 or 26 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 89.7%

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

   if -1.25e11 < z < 26

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.4%

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

      3. associate--l+ 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in z around 0 98.7%

      \[\leadsto \color{blue}{\left(\cos y + x\right) \cdot {1}^{0.3333333333333333}} \]
   5. Step-by-step derivation

      1. pow-base-1 98.7%

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

      2. *-rgt-identity 98.7%

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

   6. Simplified 98.7%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -125000000000 \lor \neg \left(z \leq 26\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 80.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -450000 \lor \neg \left(y \leq 0.0003\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -450000.0) (not (<= y 0.0003)))
   (+ x (cos y))
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -450000.0) || !(y <= 0.0003)) {
		tmp = x + cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-450000.0d0)) .or. (.not. (y <= 0.0003d0))) then
        tmp = x + cos(y)
    else
        tmp = x + (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -450000.0) || !(y <= 0.0003)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -450000.0) or not (y <= 0.0003):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -450000.0) || !(y <= 0.0003))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -450000.0) || ~((y <= 0.0003)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -450000.0], N[Not[LessEqual[y, 0.0003]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e5 or 2.99999999999999974e-4 < y

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.0%

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

      2. pow3 98.1%

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

      3. associate--l+ 98.1%

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

   3. Applied egg-rr 98.1%

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

   4. Taylor expanded in z around 0 57.3%

      \[\leadsto \color{blue}{\left(\cos y + x\right) \cdot {1}^{0.3333333333333333}} \]
   5. Step-by-step derivation

      1. pow-base-1 57.3%

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

      2. *-rgt-identity 57.3%

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

   6. Simplified 57.3%

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

   if -4.5e5 < y < 2.99999999999999974e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.7%

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

      1. associate-+r+ 98.7%

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

      2. +-commutative 98.7%

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

      3. mul-1-neg 98.7%

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

      4. unsub-neg 98.7%

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

   4. Simplified 98.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -450000 \lor \neg \left(y \leq 0.0003\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 6: 70.1% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -175000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+77}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -175000000.0)
   (+ x 1.0)
   (if (<= y 7.5e+77) (+ x (- 1.0 (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -175000000.0) {
		tmp = x + 1.0;
	} else if (y <= 7.5e+77) {
		tmp = x + (1.0 - (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 <= (-175000000.0d0)) then
        tmp = x + 1.0d0
    else if (y <= 7.5d+77) then
        tmp = x + (1.0d0 - (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 <= -175000000.0) {
		tmp = x + 1.0;
	} else if (y <= 7.5e+77) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -175000000.0:
		tmp = x + 1.0
	elif y <= 7.5e+77:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -175000000.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 7.5e+77)
		tmp = Float64(x + Float64(1.0 - 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 <= -175000000.0)
		tmp = x + 1.0;
	elseif (y <= 7.5e+77)
		tmp = x + (1.0 - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -175000000.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 7.5e+77], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e8 or 7.49999999999999955e77 < y

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.0%

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

      2. pow3 98.0%

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

      3. associate--l+ 98.0%

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

   3. Applied egg-rr 98.0%

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

   4. Taylor expanded in y around 0 39.2%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(1 + x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 39.2%

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

      2. *-lft-identity 39.2%

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

   6. Simplified 39.2%

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

   if -1.75e8 < y < 7.49999999999999955e77

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.7%

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

      1. associate-+r+ 90.7%

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

      2. +-commutative 90.7%

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

      3. mul-1-neg 90.7%

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

      4. unsub-neg 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -175000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+77}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7: 62.5% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+188} \lor \neg \left(z \leq 9 \cdot 10^{+142}\right):\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e+188) (not (<= z 9e+142))) (- 1.0 (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e+188) || !(z <= 9e+142)) {
		tmp = 1.0 - (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 <= (-4.2d+188)) .or. (.not. (z <= 9d+142))) then
        tmp = 1.0d0 - (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 <= -4.2e+188) || !(z <= 9e+142)) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e+188) or not (z <= 9e+142):
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e+188) || !(z <= 9e+142))
		tmp = Float64(1.0 - 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 ((z <= -4.2e+188) || ~((z <= 9e+142)))
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e+188], N[Not[LessEqual[z, 9e+142]], $MachinePrecision]], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999973e188 or 8.9999999999999998e142 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 89.1%

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

   3. Taylor expanded in y around 0 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   if -4.19999999999999973e188 < z < 8.9999999999999998e142

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.4%

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

      3. associate--l+ 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in y around 0 72.7%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(1 + x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 72.7%

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

      2. *-lft-identity 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+188} \lor \neg \left(z \leq 9 \cdot 10^{+142}\right):\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8: 61.2% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+209} \lor \neg \left(z \leq 1.05 \cdot 10^{+143}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e+209) (not (<= z 1.05e+143))) (* z (- y)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e+209) || !(z <= 1.05e+143)) {
		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 <= (-2.8d+209)) .or. (.not. (z <= 1.05d+143))) 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 <= -2.8e+209) || !(z <= 1.05e+143)) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e+209) or not (z <= 1.05e+143):
		tmp = z * -y
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e+209) || !(z <= 1.05e+143))
		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 <= -2.8e+209) || ~((z <= 1.05e+143)))
		tmp = z * -y;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e+209], N[Not[LessEqual[z, 1.05e+143]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000013e209 or 1.04999999999999994e143 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 82.4%

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

      1. associate-*r* 82.4%

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

      2. neg-mul-1 82.4%

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

      3. *-commutative 82.4%

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

   4. Simplified 82.4%

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

   5. Taylor expanded in y around 0 40.6%

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

      1. mul-1-neg 40.6%

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

      2. distribute-rgt-neg-in 40.6%

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

   7. Simplified 40.6%

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

   if -2.80000000000000013e209 < z < 1.04999999999999994e143

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.4%

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

      3. associate--l+ 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in y around 0 71.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(1 + x\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 71.8%

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

      2. *-lft-identity 71.8%

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

   6. Simplified 71.8%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+209} \lor \neg \left(z \leq 1.05 \cdot 10^{+143}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 60.7% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00011:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.00011) x (if (<= x 5.5e-13) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00011) {
		tmp = x;
	} else if (x <= 5.5e-13) {
		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 <= (-0.00011d0)) then
        tmp = x
    else if (x <= 5.5d-13) 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 <= -0.00011) {
		tmp = x;
	} else if (x <= 5.5e-13) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.00011:
		tmp = x
	elif x <= 5.5e-13:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.00011)
		tmp = x;
	elseif (x <= 5.5e-13)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.00011)
		tmp = x;
	elseif (x <= 5.5e-13)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.00011], x, If[LessEqual[x, 5.5e-13], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.10000000000000004e-4 or 5.49999999999999979e-13 < x

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 58.7%

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

      2. pow2 58.7%

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

   3. Applied egg-rr 58.7%

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

   4. Taylor expanded in x around inf 73.3%

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

   if -1.10000000000000004e-4 < x < 5.49999999999999979e-13

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.1%

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

   3. Taylor expanded in y around 0 39.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00011:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 61.7% 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-cube-cbrt 98.3%

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

   2. pow3 98.3%

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

   3. associate--l+ 98.3%

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

3. Applied egg-rr 98.3%

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

4. Taylor expanded in y around 0 57.7%

   \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(1 + x\right)} \]
5. Step-by-step derivation

   1. pow-base-1 57.7%

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

   2. *-lft-identity 57.7%

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

6. Simplified 57.7%

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

7. Final simplification 57.7%

   \[\leadsto x + 1 \]

Alternative 11: 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. Taylor expanded in x around 0 60.7%

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

3. Taylor expanded in y around 0 20.1%

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

4. Final simplification 20.1%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023195 
(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))))