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

Percentage Accurate: 99.9% → 99.9%

Time: 6.5s

Alternatives: 9

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: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -3200000000 \lor \neg \left(y \leq 1.8 \cdot 10^{+42}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (or (<= y -3200000000.0) (not (<= y 1.8e+42))) t_0 (- t_0 (* y z)))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if ((y <= -3200000000.0) || !(y <= 1.8e+42)) {
		tmp = t_0;
	} else {
		tmp = t_0 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + cos(y)
    if ((y <= (-3200000000.0d0)) .or. (.not. (y <= 1.8d+42))) then
        tmp = t_0
    else
        tmp = t_0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.cos(y);
	double tmp;
	if ((y <= -3200000000.0) || !(y <= 1.8e+42)) {
		tmp = t_0;
	} else {
		tmp = t_0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	tmp = 0
	if (y <= -3200000000.0) or not (y <= 1.8e+42):
		tmp = t_0
	else:
		tmp = t_0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if ((y <= -3200000000.0) || !(y <= 1.8e+42))
		tmp = t_0;
	else
		tmp = Float64(t_0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	tmp = 0.0;
	if ((y <= -3200000000.0) || ~((y <= 1.8e+42)))
		tmp = t_0;
	else
		tmp = t_0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -3200000000.0], N[Not[LessEqual[y, 1.8e+42]], $MachinePrecision]], t$95$0, N[(t$95$0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e9 or 1.8e42 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.1%

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

   3. Taylor expanded in z around 0 72.0%

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

   if -3.2e9 < y < 1.8e42

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3200000000 \lor \neg \left(y \leq 1.8 \cdot 10^{+42}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \]

Alternative 3: 81.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -125000000 \lor \neg \left(y \leq 7.5 \cdot 10^{-11}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -125000000.0) (not (<= y 7.5e-11)))
   (+ x (cos y))
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -125000000.0) || !(y <= 7.5e-11)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-125000000.0d0)) .or. (.not. (y <= 7.5d-11))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -125000000.0) || !(y <= 7.5e-11)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -125000000.0) or not (y <= 7.5e-11):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -125000000.0) || !(y <= 7.5e-11))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -125000000.0) || ~((y <= 7.5e-11)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -125000000.0], N[Not[LessEqual[y, 7.5e-11]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e8 or 7.5e-11 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 44.2%

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

   3. Taylor expanded in z around 0 71.3%

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

   if -1.25e8 < y < 7.5e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-neg-out 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. distribute-rgt-neg-out 99.9%

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

      6. sub-neg 99.9%

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

      7. associate-+r- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -125000000 \lor \neg \left(y \leq 7.5 \cdot 10^{-11}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 4: 69.8% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+29}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e+22)
   (+ x 1.0)
   (if (<= y 6.2e+29) (+ 1.0 (+ x (* y (- (* y -0.5) z)))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+22) {
		tmp = x + 1.0;
	} else if (y <= 6.2e+29) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - 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 <= (-1.5d+22)) then
        tmp = x + 1.0d0
    else if (y <= 6.2d+29) then
        tmp = 1.0d0 + (x + (y * ((y * (-0.5d0)) - 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 <= -1.5e+22) {
		tmp = x + 1.0;
	} else if (y <= 6.2e+29) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e+22:
		tmp = x + 1.0
	elif y <= 6.2e+29:
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e+22)
		tmp = Float64(x + 1.0);
	elseif (y <= 6.2e+29)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.5e+22)
		tmp = x + 1.0;
	elseif (y <= 6.2e+29)
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e+22], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 6.2e+29], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e22 or 6.1999999999999998e29 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 42.0%

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

   3. Taylor expanded in y around 0 46.2%

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

      1. +-commutative 46.2%

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

   5. Simplified 46.2%

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

   if -1.5e22 < y < 6.1999999999999998e29

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.3%

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

   3. Taylor expanded in y around 0 95.6%

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

      1. mul-1-neg 95.6%

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

      2. distribute-rgt-neg-out 95.6%

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

      3. +-commutative 95.6%

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

      4. distribute-rgt-neg-out 95.6%

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

      5. unsub-neg 95.6%

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

      6. fma-def 95.6%

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

      7. unpow2 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in y around 0 95.6%

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

      1. associate-+r+ 95.6%

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

      2. +-commutative 95.6%

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

      3. +-commutative 95.6%

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

      4. mul-1-neg 95.6%

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

      5. sub-neg 95.6%

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

      6. unpow2 95.6%

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

      7. associate-*r* 95.6%

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

      8. *-commutative 95.6%

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

      9. distribute-rgt-out-- 95.6%

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

      10. *-commutative 95.6%

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

   8. Simplified 95.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+29}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 5: 69.9% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4100000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+58}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4100000000.0)
   (+ x 1.0)
   (if (<= y 2.7e+58) (+ 1.0 (- x (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4100000000.0) {
		tmp = x + 1.0;
	} else if (y <= 2.7e+58) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4100000000.0d0)) then
        tmp = x + 1.0d0
    else if (y <= 2.7d+58) then
        tmp = 1.0d0 + (x - (y * z))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4100000000.0) {
		tmp = x + 1.0;
	} else if (y <= 2.7e+58) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4100000000.0:
		tmp = x + 1.0
	elif y <= 2.7e+58:
		tmp = 1.0 + (x - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4100000000.0)
		tmp = Float64(x + 1.0);
	elseif (y <= 2.7e+58)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4100000000.0)
		tmp = x + 1.0;
	elseif (y <= 2.7e+58)
		tmp = 1.0 + (x - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4100000000.0], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 2.7e+58], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e9 or 2.7000000000000001e58 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 43.1%

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

   3. Taylor expanded in y around 0 46.4%

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

      1. +-commutative 46.4%

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

   5. Simplified 46.4%

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

   if -4.1e9 < y < 2.7000000000000001e58

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.0%

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

   3. Taylor expanded in y around 0 96.7%

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

      1. mul-1-neg 96.7%

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

      2. distribute-rgt-neg-out 96.7%

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

      3. +-commutative 96.7%

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

      4. associate-+r+ 96.7%

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

      5. distribute-rgt-neg-out 96.7%

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

      6. sub-neg 96.7%

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

      7. associate-+r- 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4100000000:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+58}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 6: 67.0% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-11}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-19}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.8e-11) (+ x 1.0) (if (<= x 8e-19) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e-11) {
		tmp = x + 1.0;
	} else if (x <= 8e-19) {
		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 (x <= (-2.8d-11)) then
        tmp = x + 1.0d0
    else if (x <= 8d-19) 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 (x <= -2.8e-11) {
		tmp = x + 1.0;
	} else if (x <= 8e-19) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8e-11:
		tmp = x + 1.0
	elif x <= 8e-19:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e-11)
		tmp = Float64(x + 1.0);
	elseif (x <= 8e-19)
		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 (x <= -2.8e-11)
		tmp = x + 1.0;
	elseif (x <= 8e-19)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e-11], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 8e-19], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e-11 or 7.9999999999999998e-19 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.9%

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

   3. Taylor expanded in y around 0 84.4%

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

      1. +-commutative 84.4%

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

   5. Simplified 84.4%

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

   if -2.8e-11 < x < 7.9999999999999998e-19

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 61.8%

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

   3. Taylor expanded in y around 0 48.5%

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

      1. mul-1-neg 48.5%

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

      2. distribute-rgt-neg-out 48.5%

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

      3. +-commutative 48.5%

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

      4. distribute-rgt-neg-out 48.5%

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

      5. unsub-neg 48.5%

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

      6. fma-def 48.5%

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

      7. unpow2 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in z around inf 49.9%

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

      1. associate-*r* 49.9%

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

      2. neg-mul-1 49.9%

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

      3. *-commutative 49.9%

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

   8. Simplified 49.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-11}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-19}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7: 61.9% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.95 \cdot 10^{+217}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.95e+217) (+ x 1.0) (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.95e+217) {
		tmp = x + 1.0;
	} else {
		tmp = 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 (z <= 1.95d+217) then
        tmp = x + 1.0d0
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.95e+217) {
		tmp = x + 1.0;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.95e+217:
		tmp = x + 1.0
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.95e+217)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.95e+217)
		tmp = x + 1.0;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.95e+217], N[(x + 1.0), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.94999999999999997e217

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.7%

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

   3. Taylor expanded in y around 0 68.0%

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

      1. +-commutative 68.0%

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

   5. Simplified 68.0%

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

   if 1.94999999999999997e217 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 60.4%

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

   3. Taylor expanded in y around inf 42.1%

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

      1. mul-1-neg 42.1%

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

      2. distribute-rgt-neg-out 42.1%

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

   5. Simplified 42.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.95 \cdot 10^{+217}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 8: 61.3% 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 70.8%

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

3. Taylor expanded in y around 0 64.1%

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

   1. +-commutative 64.1%

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

5. Simplified 64.1%

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

6. Final simplification 64.1%

   \[\leadsto x + 1 \]

Alternative 9: 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. Taylor expanded in y around 0 70.8%

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

3. Taylor expanded in x around inf 45.6%

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

4. Final simplification 45.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(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))))