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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(x + N[(N[Sin[y], $MachinePrecision] * (-z) + 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. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. *-commutative 99.9%

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

   5. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) - (sin(y) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 3: 81.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\sin y \cdot z\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+192}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+161}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+72} \lor \neg \left(z \leq 1.45 \cdot 10^{+165}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (sin y) z))))
   (if (<= z -2.6e+192)
     t_0
     (if (<= z -7.8e+161)
       (+ x (- 1.0 (* y z)))
       (if (or (<= z -5.4e+72) (not (<= z 1.45e+165))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = -(sin(y) * z);
	double tmp;
	if (z <= -2.6e+192) {
		tmp = t_0;
	} else if (z <= -7.8e+161) {
		tmp = x + (1.0 - (y * z));
	} else if ((z <= -5.4e+72) || !(z <= 1.45e+165)) {
		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 <= (-2.6d+192)) then
        tmp = t_0
    else if (z <= (-7.8d+161)) then
        tmp = x + (1.0d0 - (y * z))
    else if ((z <= (-5.4d+72)) .or. (.not. (z <= 1.45d+165))) 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 <= -2.6e+192) {
		tmp = t_0;
	} else if (z <= -7.8e+161) {
		tmp = x + (1.0 - (y * z));
	} else if ((z <= -5.4e+72) || !(z <= 1.45e+165)) {
		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 <= -2.6e+192:
		tmp = t_0
	elif z <= -7.8e+161:
		tmp = x + (1.0 - (y * z))
	elif (z <= -5.4e+72) or not (z <= 1.45e+165):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(sin(y) * z))
	tmp = 0.0
	if (z <= -2.6e+192)
		tmp = t_0;
	elseif (z <= -7.8e+161)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	elseif ((z <= -5.4e+72) || !(z <= 1.45e+165))
		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 <= -2.6e+192)
		tmp = t_0;
	elseif (z <= -7.8e+161)
		tmp = x + (1.0 - (y * z));
	elseif ((z <= -5.4e+72) || ~((z <= 1.45e+165)))
		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, -2.6e+192], t$95$0, If[LessEqual[z, -7.8e+161], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5.4e+72], N[Not[LessEqual[z, 1.45e+165]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.60000000000000003e192 or -7.8000000000000004e161 < z < -5.4000000000000001e72 or 1.45000000000000003e165 < z

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 97.5%

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

      1. mul-1-neg 97.5%

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

      2. *-commutative 97.5%

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

      3. distribute-rgt-neg-in 97.5%

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

   7. Simplified 97.5%

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

      1. distribute-rgt-neg-out 97.5%

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

      2. unsub-neg 97.5%

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

   9. Applied egg-rr 97.5%

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

   10. Taylor expanded in x around 0 78.1%

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

       1. mul-1-neg 78.1%

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

       2. *-commutative 78.1%

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

       3. distribute-rgt-neg-in 78.1%

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

   12. Simplified 78.1%

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

   if -2.60000000000000003e192 < z < -7.8000000000000004e161

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

   7. Simplified 79.2%

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

   if -5.4000000000000001e72 < z < 1.45000000000000003e165

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 93.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+192}:\\ \;\;\;\;-\sin y \cdot z\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+161}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+72} \lor \neg \left(z \leq 1.45 \cdot 10^{+165}\right):\\ \;\;\;\;-\sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+71} \lor \neg \left(z \leq 2.35 \cdot 10^{+76}\right):\\ \;\;\;\;x - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.15e+71) (not (<= z 2.35e+76)))
   (- x (* (sin y) z))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e+71) || !(z <= 2.35e+76)) {
		tmp = x - (sin(y) * z);
	} 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 <= (-2.15d+71)) .or. (.not. (z <= 2.35d+76))) then
        tmp = x - (sin(y) * z)
    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 <= -2.15e+71) || !(z <= 2.35e+76)) {
		tmp = x - (Math.sin(y) * z);
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.15e+71) or not (z <= 2.35e+76):
		tmp = x - (math.sin(y) * z)
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.15e+71) || !(z <= 2.35e+76))
		tmp = Float64(x - Float64(sin(y) * z));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.15e+71) || ~((z <= 2.35e+76)))
		tmp = x - (sin(y) * z);
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.15e+71], N[Not[LessEqual[z, 2.35e+76]], $MachinePrecision]], N[(x - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.14999999999999992e71 or 2.3500000000000002e76 < z

   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. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 93.9%

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

      1. mul-1-neg 93.9%

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

      2. *-commutative 93.9%

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

      3. distribute-rgt-neg-in 93.9%

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

   7. Simplified 93.9%

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

      1. distribute-rgt-neg-out 93.9%

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

      2. unsub-neg 93.9%

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

   9. Applied egg-rr 93.9%

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

   if -2.14999999999999992e71 < z < 2.3500000000000002e76

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 96.7%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+71} \lor \neg \left(z \leq 2.35 \cdot 10^{+76}\right):\\ \;\;\;\;x - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+27} \lor \neg \left(y \leq 6.7 \cdot 10^{-6}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9e+27) (not (<= y 6.7e-6)))
   (+ x (cos y))
   (+ x (+ 1.0 (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9e+27) || !(y <= 6.7e-6)) {
		tmp = x + cos(y);
	} else {
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-9d+27)) .or. (.not. (y <= 6.7d-6))) then
        tmp = x + cos(y)
    else
        tmp = x + (1.0d0 + (y * ((y * (-0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9e+27) || !(y <= 6.7e-6)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9e+27) or not (y <= 6.7e-6):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 + (y * ((y * -0.5) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9e+27) || !(y <= 6.7e-6))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(x + Float64(1.0 + Float64(y * Float64(Float64(y * -0.5) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9e+27) || ~((y <= 6.7e-6)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 + (y * ((y * -0.5) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9e+27], N[Not[LessEqual[y, 6.7e-6]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999998e27 or 6.7e-6 < y

   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. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 60.9%

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

   if -8.9999999999999998e27 < y < 6.7e-6

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.5%

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

      1. +-commutative 98.5%

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

      2. mul-1-neg 98.5%

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

      3. unsub-neg 98.5%

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

      4. *-commutative 98.5%

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

      5. unpow2 98.5%

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

      6. associate-*l* 98.5%

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

      7. distribute-lft-out-- 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+27} \lor \neg \left(y \leq 6.7 \cdot 10^{-6}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.8% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+33} \lor \neg \left(y \leq 530000000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+33) (not (<= y 530000000000.0)))
   (+ x 1.0)
   (+ x (+ 1.0 (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+33) || !(y <= 530000000000.0)) {
		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 <= (-6.5d+33)) .or. (.not. (y <= 530000000000.0d0))) 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 <= -6.5e+33) || !(y <= 530000000000.0)) {
		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 <= -6.5e+33) or not (y <= 530000000000.0):
		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 <= -6.5e+33) || !(y <= 530000000000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(x + Float64(1.0 + Float64(y * Float64(Float64(y * -0.5) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e+33) || ~((y <= 530000000000.0)))
		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, -6.5e+33], N[Not[LessEqual[y, 530000000000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(x + N[(1.0 + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999993e33 or 5.3e11 < y

   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. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 37.1%

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

   if -6.49999999999999993e33 < y < 5.3e11

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.1%

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

      1. +-commutative 97.1%

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

      2. mul-1-neg 97.1%

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

      3. unsub-neg 97.1%

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

      4. *-commutative 97.1%

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

      5. unpow2 97.1%

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

      6. associate-*l* 97.1%

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

      7. distribute-lft-out-- 97.1%

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

   7. Simplified 97.1%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+33} \lor \neg \left(y \leq 530000000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.8% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+34} \lor \neg \left(y \leq 6.7 \cdot 10^{-6}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+34) (not (<= y 6.7e-6))) (+ x 1.0) (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+34) || !(y <= 6.7e-6)) {
		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 <= (-1.8d+34)) .or. (.not. (y <= 6.7d-6))) 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 <= -1.8e+34) || !(y <= 6.7e-6)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e+34) or not (y <= 6.7e-6):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e+34) || !(y <= 6.7e-6))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e+34) || ~((y <= 6.7e-6)))
		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, -1.8e+34], N[Not[LessEqual[y, 6.7e-6]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e34 or 6.7e-6 < y

   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. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 38.7%

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

   if -1.8e34 < y < 6.7e-6

   1. Initial program 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.4%

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

      1. mul-1-neg 97.4%

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

      2. unsub-neg 97.4%

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

   7. Simplified 97.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+34} \lor \neg \left(y \leq 6.7 \cdot 10^{-6}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.4% 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. cancel-sign-sub-inv 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. *-commutative 99.9%

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

   5. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 60.5%

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

6. Final simplification 60.5%

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

Alternative 9: 42.4% 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. cancel-sign-sub-inv 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. *-commutative 99.9%

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

   5. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 66.0%

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

   1. mul-1-neg 66.0%

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

   2. *-commutative 66.0%

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

   3. distribute-rgt-neg-in 66.0%

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

7. Simplified 66.0%

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

8. Taylor expanded in x around inf 39.1%

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

9. Final simplification 39.1%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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))))