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

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. cancel-sign-sub-inv 99.9%

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

   2. +-commutative 99.9%

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

   3. distribute-lft-neg-out 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. sin-neg 99.9%

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

   6. fma-def 99.9%

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

   7. sin-neg 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 90.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.49:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.7e+24)
   x
   (if (<= x 0.49) (- (cos y) (* z (sin y))) (+ x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.7e+24) {
		tmp = x;
	} else if (x <= 0.49) {
		tmp = cos(y) - (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 (x <= (-2.7d+24)) then
        tmp = x
    else if (x <= 0.49d0) then
        tmp = cos(y) - (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 (x <= -2.7e+24) {
		tmp = x;
	} else if (x <= 0.49) {
		tmp = Math.cos(y) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.7e+24:
		tmp = x
	elif x <= 0.49:
		tmp = math.cos(y) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.7e+24)
		tmp = x;
	elseif (x <= 0.49)
		tmp = Float64(cos(y) - 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 (x <= -2.7e+24)
		tmp = x;
	elseif (x <= 0.49)
		tmp = cos(y) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.7e+24], x, If[LessEqual[x, 0.49], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e24

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 81.3%

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

   if -2.7e24 < x < 0.48999999999999999

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 96.8%

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

   if 0.48999999999999999 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 85.5%

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

      1. +-commutative 85.5%

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

   4. Simplified 85.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.49:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 3: 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 4: 81.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+154} \lor \neg \left(z \leq 2.4 \cdot 10^{+85}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+154) (not (<= z 2.4e+85))) (* z (- (sin y))) (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+154) || !(z <= 2.4e+85)) {
		tmp = 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 <= (-6d+154)) .or. (.not. (z <= 2.4d+85))) then
        tmp = 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 <= -6e+154) || !(z <= 2.4e+85)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e+154) or not (z <= 2.4e+85):
		tmp = z * -math.sin(y)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e+154) || !(z <= 2.4e+85))
		tmp = Float64(z * Float64(-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 <= -6e+154) || ~((z <= 2.4e+85)))
		tmp = z * -sin(y);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e+154], N[Not[LessEqual[z, 2.4e+85]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000052e154 or 2.39999999999999997e85 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 75.0%

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

      1. neg-mul-1 75.0%

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

      2. *-commutative 75.0%

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

      3. distribute-rgt-neg-in 75.0%

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

   4. Simplified 75.0%

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

   if -6.00000000000000052e154 < z < 2.39999999999999997e85

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 91.5%

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

      1. +-commutative 91.5%

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

   4. Simplified 91.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+154} \lor \neg \left(z \leq 2.4 \cdot 10^{+85}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+27} \lor \neg \left(y \leq 6.8 \cdot 10^{-7}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+27) (not (<= y 6.8e-7)))
   (+ x (cos y))
   (+ 1.0 (- x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+27) || !(y <= 6.8e-7)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x - (z * 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 <= (-2.4d+27)) .or. (.not. (y <= 6.8d-7))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x - (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+27) || !(y <= 6.8e-7)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+27) or not (y <= 6.8e-7):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x - (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+27) || !(y <= 6.8e-7))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x - Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4e+27) || ~((y <= 6.8e-7)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x - (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+27], N[Not[LessEqual[y, 6.8e-7]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999998e27 or 6.79999999999999948e-7 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 59.4%

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

      1. +-commutative 59.4%

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

   4. Simplified 59.4%

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

   if -2.39999999999999998e27 < y < 6.79999999999999948e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.6%

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

      1. mul-1-neg 97.6%

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

      2. unsub-neg 97.6%

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

   4. Simplified 97.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+27} \lor \neg \left(y \leq 6.8 \cdot 10^{-7}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z \cdot y\right)\\ \end{array} \]

Alternative 6: 73.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-8} \lor \neg \left(x \leq 2.75 \cdot 10^{-12}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-8) (not (<= x 2.75e-12))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-8) || !(x <= 2.75e-12)) {
		tmp = x + 1.0;
	} else {
		tmp = cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3.8d-8)) .or. (.not. (x <= 2.75d-12))) then
        tmp = x + 1.0d0
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-8) || !(x <= 2.75e-12)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-8) or not (x <= 2.75e-12):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-8) || !(x <= 2.75e-12))
		tmp = Float64(x + 1.0);
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.8e-8) || ~((x <= 2.75e-12)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-8], N[Not[LessEqual[x, 2.75e-12]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000028e-8 or 2.7500000000000002e-12 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.4%

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

      1. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   if -3.80000000000000028e-8 < x < 2.7500000000000002e-12

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.3%

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

      2. pow3 99.3%

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

   3. Applied egg-rr 99.3%

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

      1. rem-cube-cbrt 99.8%

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

      2. *-commutative 99.8%

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

      3. add-sqr-sqrt 51.6%

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

      4. associate-*r* 51.6%

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

   5. Applied egg-rr 51.6%

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

   6. Taylor expanded in x around 0 99.1%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   7. Step-by-step derivation

      1. *-commutative 99.1%

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

   8. Simplified 99.1%

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

   9. Taylor expanded in z around 0 57.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-8} \lor \neg \left(x \leq 2.75 \cdot 10^{-12}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]

Alternative 7: 70.4% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+27} \lor \neg \left(y \leq 42000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) + y \cdot \left(y \cdot -0.5 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+27) (not (<= y 42000000.0)))
   (+ x 1.0)
   (+ (+ x 1.0) (* y (- (* y -0.5) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+27) || !(y <= 42000000.0)) {
		tmp = x + 1.0;
	} 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 <= (-2.4d+27)) .or. (.not. (y <= 42000000.0d0))) then
        tmp = x + 1.0d0
    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 <= -2.4e+27) || !(y <= 42000000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = (x + 1.0) + (y * ((y * -0.5) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+27) or not (y <= 42000000.0):
		tmp = x + 1.0
	else:
		tmp = (x + 1.0) + (y * ((y * -0.5) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+27) || !(y <= 42000000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(Float64(x + 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 <= -2.4e+27) || ~((y <= 42000000.0)))
		tmp = x + 1.0;
	else
		tmp = (x + 1.0) + (y * ((y * -0.5) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+27], N[Not[LessEqual[y, 42000000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999998e27 or 4.2e7 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 41.9%

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

      1. +-commutative 41.9%

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

   4. Simplified 41.9%

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

   if -2.39999999999999998e27 < y < 4.2e7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. associate-+r+ 96.0%

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

      2. +-commutative 96.0%

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

      3. +-commutative 96.0%

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

      4. mul-1-neg 96.0%

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

      5. unsub-neg 96.0%

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

      6. *-commutative 96.0%

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

      7. unpow2 96.0%

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

      8. associate-*l* 96.0%

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

      9. distribute-lft-out-- 96.0%

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

   4. Simplified 96.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+27} \lor \neg \left(y \leq 42000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) + y \cdot \left(y \cdot -0.5 - z\right)\\ \end{array} \]

Alternative 8: 70.3% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+29} \lor \neg \left(y \leq 4.5 \cdot 10^{+65}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.9e+29) (not (<= y 4.5e+65)))
   (+ x 1.0)
   (+ 1.0 (- x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e+29) || !(y <= 4.5e+65)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (z * 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 <= (-5.9d+29)) .or. (.not. (y <= 4.5d+65))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x - (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e+29) || !(y <= 4.5e+65)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.9e+29) or not (y <= 4.5e+65):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.9e+29) || !(y <= 4.5e+65))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x - Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.9e+29) || ~((y <= 4.5e+65)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x - (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.9e+29], N[Not[LessEqual[y, 4.5e+65]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8999999999999999e29 or 4.5e65 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 40.4%

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

      1. +-commutative 40.4%

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

   4. Simplified 40.4%

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

   if -5.8999999999999999e29 < y < 4.5e65

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.7%

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

      1. mul-1-neg 92.7%

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

      2. unsub-neg 92.7%

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

   4. Simplified 92.7%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+29} \lor \neg \left(y \leq 4.5 \cdot 10^{+65}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z \cdot y\right)\\ \end{array} \]

Alternative 9: 66.6% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-79}:\\ \;\;\;\;1 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e+17) x (if (<= x 6.5e-79) (- 1.0 (* z y)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e+17) {
		tmp = x;
	} else if (x <= 6.5e-79) {
		tmp = 1.0 - (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 (x <= (-1.5d+17)) then
        tmp = x
    else if (x <= 6.5d-79) then
        tmp = 1.0d0 - (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 (x <= -1.5e+17) {
		tmp = x;
	} else if (x <= 6.5e-79) {
		tmp = 1.0 - (z * y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e+17:
		tmp = x
	elif x <= 6.5e-79:
		tmp = 1.0 - (z * y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e+17)
		tmp = x;
	elseif (x <= 6.5e-79)
		tmp = Float64(1.0 - Float64(z * y));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e+17)
		tmp = x;
	elseif (x <= 6.5e-79)
		tmp = 1.0 - (z * y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e+17], x, If[LessEqual[x, 6.5e-79], N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5e17

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 79.0%

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

   if -1.5e17 < x < 6.5000000000000003e-79

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 41.8%

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

      1. associate-+r+ 41.8%

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

      2. +-commutative 41.8%

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

      3. +-commutative 41.8%

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

      4. mul-1-neg 41.8%

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

      5. unsub-neg 41.8%

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

      6. *-commutative 41.8%

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

      7. unpow2 41.8%

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

      8. associate-*l* 41.8%

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

      9. distribute-lft-out-- 41.9%

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

   4. Simplified 41.9%

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

   5. Taylor expanded in x around 0 41.1%

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

   6. Taylor expanded in y around 0 42.1%

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

      1. associate-*r* 42.1%

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

      2. *-commutative 42.1%

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

      3. mul-1-neg 42.1%

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

   8. Simplified 42.1%

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

   9. Taylor expanded in z around 0 42.1%

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

       1. mul-1-neg 42.1%

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

       2. sub-neg 42.1%

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

   11. Simplified 42.1%

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

   if 6.5000000000000003e-79 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.2%

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

      1. +-commutative 80.2%

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

   4. Simplified 80.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-79}:\\ \;\;\;\;1 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 10: 61.3% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -82000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.48:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -82000000000.0) x (if (<= x 0.48) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -82000000000.0) {
		tmp = x;
	} else if (x <= 0.48) {
		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 <= (-82000000000.0d0)) then
        tmp = x
    else if (x <= 0.48d0) 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 <= -82000000000.0) {
		tmp = x;
	} else if (x <= 0.48) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -82000000000.0:
		tmp = x
	elif x <= 0.48:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -82000000000.0)
		tmp = x;
	elseif (x <= 0.48)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -82000000000.0)
		tmp = x;
	elseif (x <= 0.48)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -82000000000.0], x, If[LessEqual[x, 0.48], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.2e10 or 0.47999999999999998 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 81.5%

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

   if -8.2e10 < x < 0.47999999999999998

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.3%

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

      1. associate-+r+ 43.3%

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

      2. +-commutative 43.3%

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

      3. +-commutative 43.3%

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

      4. mul-1-neg 43.3%

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

      5. unsub-neg 43.3%

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

      6. *-commutative 43.3%

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

      7. unpow2 43.3%

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

      8. associate-*l* 43.3%

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

      9. distribute-lft-out-- 43.4%

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

   4. Simplified 43.4%

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

   5. Taylor expanded in x around 0 41.8%

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

   6. Taylor expanded in y around 0 42.9%

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

      1. associate-*r* 42.9%

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

      2. *-commutative 42.9%

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

      3. mul-1-neg 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in z around 0 35.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -82000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.48:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 62.3% 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. Taylor expanded in y around 0 61.1%

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

   1. +-commutative 61.1%

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

4. Simplified 61.1%

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

5. Final simplification 61.1%

   \[\leadsto x + 1 \]

Alternative 12: 22.2% 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 y around 0 50.5%

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

   1. associate-+r+ 50.5%

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

   2. +-commutative 50.5%

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

   3. +-commutative 50.5%

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

   4. mul-1-neg 50.5%

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

   5. unsub-neg 50.5%

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

   6. *-commutative 50.5%

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

   7. unpow2 50.5%

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

   8. associate-*l* 50.5%

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

   9. distribute-lft-out-- 50.6%

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

4. Simplified 50.6%

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

5. Taylor expanded in x around 0 22.0%

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

6. Taylor expanded in y around 0 22.8%

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

   1. associate-*r* 22.8%

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

   2. *-commutative 22.8%

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

   3. mul-1-neg 22.8%

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

8. Simplified 22.8%

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

9. Taylor expanded in z around 0 17.8%

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

10. Final simplification 17.8%

    \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023334 
(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))))