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

Percentage Accurate: 99.9% → 99.9%

Time: 9.6s

Alternatives: 10

Speedup: N/A×

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. Final simplification 99.9%

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

Alternative 2: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+32}:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+41}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.16e+32)
   (- x (* z (sin y)))
   (if (<= z 1.25e+41) (+ x (cos y)) (fma (sin y) (- z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e+32) {
		tmp = x - (z * sin(y));
	} else if (z <= 1.25e+41) {
		tmp = x + cos(y);
	} else {
		tmp = fma(sin(y), -z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.16e+32)
		tmp = Float64(x - Float64(z * sin(y)));
	elseif (z <= 1.25e+41)
		tmp = Float64(x + cos(y));
	else
		tmp = fma(sin(y), Float64(-z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.16e+32], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+41], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * (-z) + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.16e32

   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. Taylor expanded in z around inf 84.9%

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

      1. neg-mul-1 84.9%

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

      2. *-commutative 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in x around 0 84.9%

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

      1. neg-mul-1 84.9%

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

      2. sub-neg 84.9%

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

   9. Simplified 84.9%

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

   if -1.16e32 < z < 1.25000000000000006e41

   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. Taylor expanded in z around 0 97.3%

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

      1. +-commutative 97.3%

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

   6. Simplified 97.3%

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

   if 1.25000000000000006e41 < z

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. neg-mul-1 86.8%

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

      2. *-commutative 86.8%

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

      3. distribute-rgt-neg-in 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in x around 0 86.8%

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

      1. neg-mul-1 86.8%

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

      2. +-commutative 86.8%

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

      3. *-commutative 86.8%

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

      4. distribute-rgt-neg-in 86.8%

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

      5. neg-mul-1 86.8%

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

      6. fma-def 86.9%

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

      7. neg-mul-1 86.9%

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

   9. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+32}:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+41}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \end{array} \]

Alternative 3: 81.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+104}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+95} \lor \neg \left(z \leq 1.65 \cdot 10^{+67}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -2.1e+169)
     t_0
     (if (<= z -1.12e+104)
       (- (+ x 1.0) (* y z))
       (if (or (<= z -1.5e+95) (not (<= z 1.65e+67))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -2.1e+169) {
		tmp = t_0;
	} else if (z <= -1.12e+104) {
		tmp = (x + 1.0) - (y * z);
	} else if ((z <= -1.5e+95) || !(z <= 1.65e+67)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) * -z
    if (z <= (-2.1d+169)) then
        tmp = t_0
    else if (z <= (-1.12d+104)) then
        tmp = (x + 1.0d0) - (y * z)
    else if ((z <= (-1.5d+95)) .or. (.not. (z <= 1.65d+67))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -2.1e+169) {
		tmp = t_0;
	} else if (z <= -1.12e+104) {
		tmp = (x + 1.0) - (y * z);
	} else if ((z <= -1.5e+95) || !(z <= 1.65e+67)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -2.1e+169:
		tmp = t_0
	elif z <= -1.12e+104:
		tmp = (x + 1.0) - (y * z)
	elif (z <= -1.5e+95) or not (z <= 1.65e+67):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -2.1e+169)
		tmp = t_0;
	elseif (z <= -1.12e+104)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	elseif ((z <= -1.5e+95) || !(z <= 1.65e+67))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -2.1e+169)
		tmp = t_0;
	elseif (z <= -1.12e+104)
		tmp = (x + 1.0) - (y * z);
	elseif ((z <= -1.5e+95) || ~((z <= 1.65e+67)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.1e+169], t$95$0, If[LessEqual[z, -1.12e+104], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.5e+95], N[Not[LessEqual[z, 1.65e+67]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1000000000000001e169 or -1.12000000000000003e104 < z < -1.49999999999999996e95 or 1.6500000000000001e67 < z

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 88.1%

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

      1. neg-mul-1 88.1%

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

      2. *-commutative 88.1%

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

      3. distribute-rgt-neg-in 88.1%

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

   6. Simplified 88.1%

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

   7. Taylor expanded in x around 0 88.1%

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

      1. neg-mul-1 88.1%

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

      2. +-commutative 88.1%

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

      3. *-commutative 88.1%

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

      4. distribute-rgt-neg-in 88.1%

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

      5. neg-mul-1 88.1%

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

      6. fma-def 88.1%

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

      7. neg-mul-1 88.1%

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

   9. Simplified 88.1%

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

   10. Taylor expanded in z around inf 69.1%

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

       1. mul-1-neg 69.1%

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

       2. *-commutative 69.1%

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

       3. distribute-rgt-neg-in 69.1%

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

   12. Simplified 69.1%

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

   if -2.1000000000000001e169 < z < -1.12000000000000003e104

   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. Taylor expanded in y around 0 74.7%

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

      1. mul-1-neg 74.7%

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

   6. Simplified 74.7%

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

      1. associate-+r+ 74.7%

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

      2. unsub-neg 74.7%

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

      3. *-commutative 74.7%

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

   8. Applied egg-rr 74.7%

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

   if -1.49999999999999996e95 < z < 1.6500000000000001e67

   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. Taylor expanded in z around 0 93.8%

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

      1. +-commutative 93.8%

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

   6. Simplified 93.8%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+169}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+104}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+95} \lor \neg \left(z \leq 1.65 \cdot 10^{+67}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 4: 93.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+32} \lor \neg \left(z \leq 3.1 \cdot 10^{+40}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+32) (not (<= z 3.1e+40)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+32) || !(z <= 3.1e+40)) {
		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 <= (-6d+32)) .or. (.not. (z <= 3.1d+40))) 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 <= -6e+32) || !(z <= 3.1e+40)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e+32) or not (z <= 3.1e+40):
		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 <= -6e+32) || !(z <= 3.1e+40))
		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 <= -6e+32) || ~((z <= 3.1e+40)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e+32], N[Not[LessEqual[z, 3.1e+40]], $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 < -6e32 or 3.0999999999999998e40 < z

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 85.8%

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

      1. neg-mul-1 85.8%

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

      2. *-commutative 85.8%

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

      3. distribute-rgt-neg-in 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in x around 0 85.8%

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

      1. neg-mul-1 85.8%

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

      2. sub-neg 85.8%

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

   9. Simplified 85.8%

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

   if -6e32 < z < 3.0999999999999998e40

   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. Taylor expanded in z around 0 97.3%

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

      1. +-commutative 97.3%

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

   6. Simplified 97.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+32} \lor \neg \left(z \leq 3.1 \cdot 10^{+40}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5: 79.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-7} \lor \neg \left(y \leq 2400\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-7) (not (<= y 2400.0)))
   (+ x (cos y))
   (- (+ x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-7) || !(y <= 2400.0)) {
		tmp = x + cos(y);
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.4d-7)) .or. (.not. (y <= 2400.0d0))) then
        tmp = x + cos(y)
    else
        tmp = (x + 1.0d0) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-7) || !(y <= 2400.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-7) or not (y <= 2400.0):
		tmp = x + math.cos(y)
	else:
		tmp = (x + 1.0) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-7) || !(y <= 2400.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e-7) || ~((y <= 2400.0)))
		tmp = x + cos(y);
	else
		tmp = (x + 1.0) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-7], N[Not[LessEqual[y, 2400.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999974e-7 or 2400 < 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. Taylor expanded in z around 0 65.5%

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

      1. +-commutative 65.5%

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

   6. Simplified 65.5%

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

   if -3.39999999999999974e-7 < y < 2400

   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. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

   6. Simplified 99.2%

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

      1. associate-+r+ 99.2%

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

      2. unsub-neg 99.2%

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

      3. *-commutative 99.2%

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

   8. Applied egg-rr 99.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-7} \lor \neg \left(y \leq 2400\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \]

Alternative 6: 68.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-22}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e-19) (- (+ x 1.0) (* y z)) (if (<= x 3.9e-22) (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e-19) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 3.9e-22) {
		tmp = cos(y);
	} 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 <= (-3.2d-19)) then
        tmp = (x + 1.0d0) - (y * z)
    else if (x <= 3.9d-22) then
        tmp = cos(y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e-19) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 3.9e-22) {
		tmp = Math.cos(y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.2e-19:
		tmp = (x + 1.0) - (y * z)
	elif x <= 3.9e-22:
		tmp = math.cos(y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e-19)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	elseif (x <= 3.9e-22)
		tmp = cos(y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.2e-19)
		tmp = (x + 1.0) - (y * z);
	elseif (x <= 3.9e-22)
		tmp = cos(y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e-19], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e-22], N[Cos[y], $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999982e-19

   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. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

   6. Simplified 75.9%

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

      1. associate-+r+ 75.9%

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

      2. unsub-neg 75.9%

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

      3. *-commutative 75.9%

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

   8. Applied egg-rr 75.9%

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

   if -3.19999999999999982e-19 < x < 3.89999999999999998e-22

   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. Taylor expanded in z around 0 70.6%

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

      1. +-commutative 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in x around 0 70.6%

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

   if 3.89999999999999998e-22 < x

   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. Taylor expanded in x around inf 82.4%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-22}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 68.7% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+42} \lor \neg \left(y \leq 18000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.05e+42) (not (<= y 18000.0)))
   (+ x 1.0)
   (- (+ x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e+42) || !(y <= 18000.0)) {
		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 <= (-2.05d+42)) .or. (.not. (y <= 18000.0d0))) 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 <= -2.05e+42) || !(y <= 18000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.05e+42) or not (y <= 18000.0):
		tmp = x + 1.0
	else:
		tmp = (x + 1.0) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.05e+42) || !(y <= 18000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.05e+42) || ~((y <= 18000.0)))
		tmp = x + 1.0;
	else
		tmp = (x + 1.0) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.05e+42], N[Not[LessEqual[y, 18000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e42 or 18000 < 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. Taylor expanded in y around 0 38.7%

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

   if -2.05e42 < y < 18000

   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. Taylor expanded in y around 0 95.2%

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

      1. mul-1-neg 95.2%

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

   6. Simplified 95.2%

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

      1. associate-+r+ 95.2%

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

      2. unsub-neg 95.2%

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

      3. *-commutative 95.2%

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

   8. Applied egg-rr 95.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+42} \lor \neg \left(y \leq 18000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \]

Alternative 8: 65.4% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-12}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-14}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35e-12) (+ x 1.0) (if (<= x 4.4e-14) (- 1.0 (* y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35e-12) {
		tmp = x + 1.0;
	} else if (x <= 4.4e-14) {
		tmp = 1.0 - (y * z);
	} 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 <= (-1.35d-12)) then
        tmp = x + 1.0d0
    else if (x <= 4.4d-14) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35e-12) {
		tmp = x + 1.0;
	} else if (x <= 4.4e-14) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.35e-12:
		tmp = x + 1.0
	elif x <= 4.4e-14:
		tmp = 1.0 - (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35e-12)
		tmp = Float64(x + 1.0);
	elseif (x <= 4.4e-14)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.35e-12)
		tmp = x + 1.0;
	elseif (x <= 4.4e-14)
		tmp = 1.0 - (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35e-12], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 4.4e-14], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3499999999999999e-12

   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. Taylor expanded in y around 0 77.6%

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

   if -1.3499999999999999e-12 < x < 4.4000000000000002e-14

   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. Taylor expanded in y around 0 50.4%

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

      1. mul-1-neg 50.4%

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

   6. Simplified 50.4%

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

   7. Taylor expanded in x around 0 50.4%

      \[\leadsto \color{blue}{1 - y \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 50.4%

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

   9. Simplified 50.4%

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

   if 4.4000000000000002e-14 < x

   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. Taylor expanded in x around inf 83.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-12}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-14}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 60.7% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. 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. Taylor expanded in y around 0 61.6%

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

5. Final simplification 61.6%

   \[\leadsto x + 1 \]

Alternative 10: 42.7% 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. Taylor expanded in x around inf 40.8%

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

5. Final simplification 40.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023315 
(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))))