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

Percentage Accurate: 99.9% → 99.9%

Time: 12.8s

Alternatives: 10

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

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

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(x + Float64(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[(x + N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-7} \lor \neg \left(x \leq 4 \cdot 10^{-53}\right):\\ \;\;\;\;x + \left(1 - z \cdot \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{\cos y}{z} - \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.4e-7) (not (<= x 4e-53)))
   (+ x (- 1.0 (* z (sin y))))
   (* z (- (/ (cos y) z) (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e-7) || !(x <= 4e-53)) {
		tmp = x + (1.0 - (z * sin(y)));
	} else {
		tmp = z * ((cos(y) / z) - sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3.4d-7)) .or. (.not. (x <= 4d-53))) then
        tmp = x + (1.0d0 - (z * sin(y)))
    else
        tmp = z * ((cos(y) / z) - sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e-7) || !(x <= 4e-53)) {
		tmp = x + (1.0 - (z * Math.sin(y)));
	} else {
		tmp = z * ((Math.cos(y) / z) - Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.4e-7) or not (x <= 4e-53):
		tmp = x + (1.0 - (z * math.sin(y)))
	else:
		tmp = z * ((math.cos(y) / z) - math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.4e-7) || !(x <= 4e-53))
		tmp = Float64(x + Float64(1.0 - Float64(z * sin(y))));
	else
		tmp = Float64(z * Float64(Float64(cos(y) / z) - sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.4e-7) || ~((x <= 4e-53)))
		tmp = x + (1.0 - (z * sin(y)));
	else
		tmp = z * ((cos(y) / z) - sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.4e-7], N[Not[LessEqual[x, 4e-53]], $MachinePrecision]], N[(x + N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(N[Cos[y], $MachinePrecision] / z), $MachinePrecision] - N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.39999999999999974e-7 or 4.00000000000000012e-53 < x

   1. Initial program 99.9%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in y around 0 98.8%

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

   7. Taylor expanded in z around 0 98.8%

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

      1. mul-1-neg 98.8%

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

      2. unsub-neg 98.8%

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

   9. Simplified 98.8%

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

   if -3.39999999999999974e-7 < x < 4.00000000000000012e-53

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in x around 0 99.8%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-7} \lor \neg \left(x \leq 4 \cdot 10^{-53}\right):\\ \;\;\;\;x + \left(1 - z \cdot \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{\cos y}{z} - \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3000000000 \lor \neg \left(z \leq 3.1 \cdot 10^{-6}\right):\\ \;\;\;\;x + \left(1 - z \cdot \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3000000000.0) (not (<= z 3.1e-6)))
   (+ x (- 1.0 (* z (sin y))))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3000000000.0) || !(z <= 3.1e-6)) {
		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 <= (-3000000000.0d0)) .or. (.not. (z <= 3.1d-6))) 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 <= -3000000000.0) || !(z <= 3.1e-6)) {
		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 <= -3000000000.0) or not (z <= 3.1e-6):
		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 <= -3000000000.0) || !(z <= 3.1e-6))
		tmp = Float64(x + Float64(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 <= -3000000000.0) || ~((z <= 3.1e-6)))
		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, -3000000000.0], N[Not[LessEqual[z, 3.1e-6]], $MachinePrecision]], N[(x + N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e9 or 3.1e-6 < z

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in y around 0 98.6%

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

   7. Taylor expanded in z around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. unsub-neg 98.7%

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

   9. Simplified 98.7%

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

   if -3e9 < z < 3.1e-6

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. +-commutative 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3000000000 \lor \neg \left(z \leq 3.1 \cdot 10^{-6}\right):\\ \;\;\;\;x + \left(1 - z \cdot \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -62000000000 \lor \neg \left(z \leq 3.9 \cdot 10^{+62}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -62000000000.0) (not (<= z 3.9e+62)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -62000000000.0) || !(z <= 3.9e+62)) {
		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 <= (-62000000000.0d0)) .or. (.not. (z <= 3.9d+62))) 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 <= -62000000000.0) || !(z <= 3.9e+62)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -62000000000.0) or not (z <= 3.9e+62):
		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 <= -62000000000.0) || !(z <= 3.9e+62))
		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 <= -62000000000.0) || ~((z <= 3.9e+62)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -62000000000.0], N[Not[LessEqual[z, 3.9e+62]], $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 < -6.2e10 or 3.9e62 < z

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 91.1%

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

      1. associate-*r* 91.1%

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

      2. neg-mul-1 91.1%

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

      3. *-commutative 91.1%

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

   7. Simplified 91.1%

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

   if -6.2e10 < z < 3.9e62

   1. Initial program 99.9%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 96.8%

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

      1. +-commutative 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -62000000000 \lor \neg \left(z \leq 3.9 \cdot 10^{+62}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.96 \lor \neg \left(y \leq 16000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.96) (not (<= y 16000000.0)))
   (+ x (cos y))
   (+ x (+ 1.0 (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.96) || !(y <= 16000000.0)) {
		tmp = x + cos(y);
	} else {
		tmp = x + (1.0 + (y * ((y * -0.5) - 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 <= (-0.96d0)) .or. (.not. (y <= 16000000.0d0))) then
        tmp = x + cos(y)
    else
        tmp = x + (1.0d0 + (y * ((y * (-0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.96) || !(y <= 16000000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.96) or not (y <= 16000000.0):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 + (y * ((y * -0.5) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.96) || !(y <= 16000000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(x + Float64(1.0 + Float64(y * Float64(Float64(y * -0.5) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.96) || ~((y <= 16000000.0)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.96], N[Not[LessEqual[y, 16000000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.95999999999999996 or 1.6e7 < y

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 52.3%

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

      1. +-commutative 52.3%

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

   7. Simplified 52.3%

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

   if -0.95999999999999996 < y < 1.6e7

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.96 \lor \neg \left(y \leq 16000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+141}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e-5)
   (+ x 1.0)
   (if (<= y 1.2e+141) (+ x (- 1.0 (* y z))) (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e-5) {
		tmp = x + 1.0;
	} else if (y <= 1.2e+141) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9d-5)) then
        tmp = x + 1.0d0
    else if (y <= 1.2d+141) then
        tmp = x + (1.0d0 - (y * z))
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e-5) {
		tmp = x + 1.0;
	} else if (y <= 1.2e+141) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e-5:
		tmp = x + 1.0
	elif y <= 1.2e+141:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e-5)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.2e+141)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e-5)
		tmp = x + 1.0;
	elseif (y <= 1.2e+141)
		tmp = x + (1.0 - (y * z));
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e-5], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.2e+141], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Cos[y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000057e-5

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 44.1%

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

   if -9.00000000000000057e-5 < y < 1.19999999999999999e141

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in y around 0 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-+r+ 85.4%

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

      3. mul-1-neg 85.4%

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

      4. *-commutative 85.4%

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

      5. unsub-neg 85.4%

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

      6. *-commutative 85.4%

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

   8. Simplified 85.4%

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

   if 1.19999999999999999e141 < y

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

      1. add-sqr-sqrt 58.5%

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

      2. pow2 58.5%

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

   6. Applied egg-rr 58.5%

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

      1. add-log-exp 22.8%

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

      2. +-commutative 22.8%

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

      3. sub-neg 22.8%

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

      4. associate-+l+ 22.8%

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

      5. unpow2 22.8%

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

      6. add-sqr-sqrt 35.9%

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

      7. distribute-lft-neg-in 35.9%

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

      8. add-sqr-sqrt 23.2%

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

      9. sqrt-unprod 35.0%

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

      10. sqr-neg 35.0%

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

      11. sqrt-unprod 11.8%

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

      12. add-sqr-sqrt 32.5%

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

   8. Applied egg-rr 32.5%

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

   9. Taylor expanded in z around 0 34.1%

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

   10. Taylor expanded in x around 0 34.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+141}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+150} \lor \neg \left(z \leq 8.2 \cdot 10^{+155}\right):\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.9e+150) (not (<= z 8.2e+155))) (- x (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.9e+150) || !(z <= 8.2e+155)) {
		tmp = 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 ((z <= (-5.9d+150)) .or. (.not. (z <= 8.2d+155))) then
        tmp = 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 ((z <= -5.9e+150) || !(z <= 8.2e+155)) {
		tmp = x - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.9e+150) or not (z <= 8.2e+155):
		tmp = x - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.9e+150) || !(z <= 8.2e+155))
		tmp = 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 ((z <= -5.9e+150) || ~((z <= 8.2e+155)))
		tmp = x - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.9e+150], N[Not[LessEqual[z, 8.2e+155]], $MachinePrecision]], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.90000000000000023e150 or 8.1999999999999996e155 < z

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 97.1%

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

      1. associate-*r* 97.1%

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

      2. neg-mul-1 97.1%

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

      3. *-commutative 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in y around 0 53.5%

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

      1. mul-1-neg 53.5%

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

      2. *-commutative 53.5%

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

      3. distribute-rgt-neg-in 53.5%

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

   10. Simplified 53.5%

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

   if -5.90000000000000023e150 < z < 8.1999999999999996e155

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 70.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+150} \lor \neg \left(z \leq 8.2 \cdot 10^{+155}\right):\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.2% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e-5) (+ x 1.0) (+ x (- 1.0 (* y z)))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9d-5)) then
        tmp = x + 1.0d0
    else
        tmp = x + (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e-5) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e-5:
		tmp = x + 1.0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e-5)
		tmp = Float64(x + 1.0);
	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 <= -9e-5)
		tmp = x + 1.0;
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000057e-5

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 44.1%

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

   if -9.00000000000000057e-5 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in y around 0 72.6%

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

      1. +-commutative 72.6%

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

      2. associate-+r+ 72.6%

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

      3. mul-1-neg 72.6%

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

      4. *-commutative 72.6%

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

      5. unsub-neg 72.6%

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

      6. *-commutative 72.6%

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

   8. Simplified 72.6%

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

4. Final simplification 66.1%

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

Alternative 9: 61.6% 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. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 57.8%

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

6. Final simplification 57.8%

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

Alternative 10: 42.6% 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. associate--l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 38.1%

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

6. Final simplification 38.1%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(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))))