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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(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 + sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(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 + sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(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 + sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 81.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(1, z, \sin y\right)\\ t_1 := \left(x + \sin y\right) + z \cdot \cos y\\ \mathbf{if}\;t\_1 \leq -50000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_1 \leq -0.1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-25}:\\ \;\;\;\;\left(z + y\right) + x\\ \mathbf{elif}\;t\_1 \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma 1.0 z (sin y))) (t_1 (+ (+ x (sin y)) (* z (cos y)))))
   (if (<= t_1 -50000000.0)
     (+ z x)
     (if (<= t_1 -0.1)
       t_0
       (if (<= t_1 2e-25) (+ (+ z y) x) (if (<= t_1 1.0) t_0 (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(1.0, z, sin(y));
	double t_1 = (x + sin(y)) + (z * cos(y));
	double tmp;
	if (t_1 <= -50000000.0) {
		tmp = z + x;
	} else if (t_1 <= -0.1) {
		tmp = t_0;
	} else if (t_1 <= 2e-25) {
		tmp = (z + y) + x;
	} else if (t_1 <= 1.0) {
		tmp = t_0;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(1.0, z, sin(y))
	t_1 = Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
	tmp = 0.0
	if (t_1 <= -50000000.0)
		tmp = Float64(z + x);
	elseif (t_1 <= -0.1)
		tmp = t_0;
	elseif (t_1 <= 2e-25)
		tmp = Float64(Float64(z + y) + x);
	elseif (t_1 <= 1.0)
		tmp = t_0;
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 * z + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000.0], N[(z + x), $MachinePrecision], If[LessEqual[t$95$1, -0.1], t$95$0, If[LessEqual[t$95$1, 2e-25], N[(N[(z + y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1.0], t$95$0, N[(z + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -5e7 or 1 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if -5e7 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -0.10000000000000001 or 2.00000000000000008e-25 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 98.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.7

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 98.7

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

   7. Applied rewrites 98.7%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(1, z, \color{blue}{\sin y}\right) \]
   9. Step-by-step derivation

      1. lower-sin.f64 97.8

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

   10. Applied rewrites 97.8%

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

   if -0.10000000000000001 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 2.00000000000000008e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \sin y\right) + z \cdot \cos y \leq -50000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;\left(x + \sin y\right) + z \cdot \cos y \leq -0.1:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y\right)\\ \mathbf{elif}\;\left(x + \sin y\right) + z \cdot \cos y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;\left(z + y\right) + x\\ \mathbf{elif}\;\left(x + \sin y\right) + z \cdot \cos y \leq 1:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+80} \lor \neg \left(z \leq 9 \cdot 10^{+121}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e+80) (not (<= z 9e+121)))
   (* z (cos y))
   (fma 1.0 z (+ (sin y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e+80) || !(z <= 9e+121)) {
		tmp = z * cos(y);
	} else {
		tmp = fma(1.0, z, (sin(y) + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e+80) || !(z <= 9e+121))
		tmp = Float64(z * cos(y));
	else
		tmp = fma(1.0, z, Float64(sin(y) + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e+80], N[Not[LessEqual[z, 9e+121]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 * z + N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000004e80 or 9.0000000000000007e121 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 59.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 59.6

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 59.6

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

   7. Applied rewrites 59.6%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-cos.f64 83.8

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

   10. Applied rewrites 83.8%

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

   if -2.30000000000000004e80 < z < 9.0000000000000007e121

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 96.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 96.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 96.8

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

   7. Applied rewrites 96.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+80} \lor \neg \left(z \leq 9 \cdot 10^{+121}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+164} \lor \neg \left(y \leq 1.4 \cdot 10^{+120}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e+164) (not (<= y 1.4e+120))) (* z (cos y)) (+ (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e+164) || !(y <= 1.4e+120)) {
		tmp = z * cos(y);
	} else {
		tmp = (z + y) + 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 ((y <= (-2.9d+164)) .or. (.not. (y <= 1.4d+120))) then
        tmp = z * cos(y)
    else
        tmp = (z + y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e+164) || !(y <= 1.4e+120)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = (z + y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.9e+164) or not (y <= 1.4e+120):
		tmp = z * math.cos(y)
	else:
		tmp = (z + y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.9e+164) || !(y <= 1.4e+120))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(Float64(z + y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.9e+164) || ~((y <= 1.4e+120)))
		tmp = z * cos(y);
	else
		tmp = (z + y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.9e+164], N[Not[LessEqual[y, 1.4e+120]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(z + y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999999e164 or 1.4e120 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 55.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 55.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 55.0

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

   7. Applied rewrites 55.0%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-cos.f64 51.0

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

   10. Applied rewrites 51.0%

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

   if -2.8999999999999999e164 < y < 1.4e120

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 84.3

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

   5. Applied rewrites 84.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+164} \lor \neg \left(y \leq 1.4 \cdot 10^{+120}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.2% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+21}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 70:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, -0.5, 1\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.12e+21)
   (+ z x)
   (if (<= y 70.0) (fma (fma (* z y) -0.5 1.0) y (+ z x)) (- x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.12e+21) {
		tmp = z + x;
	} else if (y <= 70.0) {
		tmp = fma(fma((z * y), -0.5, 1.0), y, (z + x));
	} else {
		tmp = x - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.12e+21)
		tmp = Float64(z + x);
	elseif (y <= 70.0)
		tmp = fma(fma(Float64(z * y), -0.5, 1.0), y, Float64(z + x));
	else
		tmp = Float64(x - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.12e+21], N[(z + x), $MachinePrecision], If[LessEqual[y, 70.0], N[(N[(N[(z * y), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(x - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e21

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 36.0

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

   5. Applied rewrites 36.0%

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

   if -1.12e21 < y < 70

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if 70 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 44.4

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

   5. Applied rewrites 44.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.1%

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \color{blue}{x}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 46.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+21}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 70:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, -0.5, 1\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.8% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-137} \lor \neg \left(x \leq 5.5 \cdot 10^{-169}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.6e-137) (not (<= x 5.5e-169))) (+ z x) (+ z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e-137) || !(x <= 5.5e-169)) {
		tmp = z + x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7.6d-137)) .or. (.not. (x <= 5.5d-169))) then
        tmp = z + x
    else
        tmp = z + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e-137) || !(x <= 5.5e-169)) {
		tmp = z + x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.6e-137) or not (x <= 5.5e-169):
		tmp = z + x
	else:
		tmp = z + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.6e-137) || !(x <= 5.5e-169))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.6e-137) || ~((x <= 5.5e-169)))
		tmp = z + x;
	else
		tmp = z + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.6e-137], N[Not[LessEqual[x, 5.5e-169]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.59999999999999997e-137 or 5.4999999999999994e-169 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 73.8

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

   5. Applied rewrites 73.8%

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

   if -7.59999999999999997e-137 < x < 5.4999999999999994e-169

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 57.6

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-137} \lor \neg \left(x \leq 5.5 \cdot 10^{-169}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.4% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-13} \lor \neg \left(x \leq 1.22 \cdot 10^{-33}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.6e-13) (not (<= x 1.22e-33))) x (+ z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.6e-13) || !(x <= 1.22e-33)) {
		tmp = x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8.6d-13)) .or. (.not. (x <= 1.22d-33))) then
        tmp = x
    else
        tmp = z + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.6e-13) || !(x <= 1.22e-33)) {
		tmp = x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.6e-13) or not (x <= 1.22e-33):
		tmp = x
	else:
		tmp = z + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.6e-13) || !(x <= 1.22e-33))
		tmp = x;
	else
		tmp = Float64(z + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.6e-13) || ~((x <= 1.22e-33)))
		tmp = x;
	else
		tmp = z + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.6e-13], N[Not[LessEqual[x, 1.22e-33]], $MachinePrecision]], x, N[(z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5999999999999997e-13 or 1.22e-33 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 82.8

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

   5. Applied rewrites 82.8%

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

   7. Applied rewrites 41.8%

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

   8. Taylor expanded in x around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(x \cdot {\left(\sqrt{-1}\right)}^{2}\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 72.7%

       \[\leadsto x \]

   if -8.5999999999999997e-13 < x < 1.22e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-13} \lor \neg \left(x \leq 1.22 \cdot 10^{-33}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.9% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 106:\\ \;\;\;\;\left(z + y\right) + x\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 106.0) (+ (+ z y) x) (- x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 106.0) {
		tmp = (z + y) + x;
	} else {
		tmp = x - 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 <= 106.0d0) then
        tmp = (z + y) + x
    else
        tmp = x - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 106.0) {
		tmp = (z + y) + x;
	} else {
		tmp = x - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 106.0:
		tmp = (z + y) + x
	else:
		tmp = x - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 106.0)
		tmp = Float64(Float64(z + y) + x);
	else
		tmp = Float64(x - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 106.0)
		tmp = (z + y) + x;
	else
		tmp = x - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 106.0], N[(N[(z + y), $MachinePrecision] + x), $MachinePrecision], N[(x - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 106

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 78.6

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

   5. Applied rewrites 78.6%

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

   if 106 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 44.4

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

   5. Applied rewrites 44.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.1%

      \[\leadsto \mathsf{fma}\left(\frac{z}{x}, \color{blue}{x}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 46.4%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 106:\\ \;\;\;\;\left(z + y\right) + x\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.9% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{+36}:\\ \;\;\;\;\left(z + y\right) + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.7e+36) (+ (+ z y) x) (+ z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.7e+36) {
		tmp = (z + y) + x;
	} else {
		tmp = z + 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 (y <= 2.7d+36) then
        tmp = (z + y) + x
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.7e+36) {
		tmp = (z + y) + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.7e+36:
		tmp = (z + y) + x
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.7e+36)
		tmp = Float64(Float64(z + y) + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.7e+36)
		tmp = (z + y) + x;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.7e+36], N[(N[(z + y), $MachinePrecision] + x), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.7000000000000001e36

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 76.9

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

   5. Applied rewrites 76.9%

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

   if 2.7000000000000001e36 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 46.1

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

   5. Applied rewrites 46.1%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{+36}:\\ \;\;\;\;\left(z + y\right) + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.4% accurate, 212.0× 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%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 65.5

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

5. Applied rewrites 65.5%

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

7. Applied rewrites 32.6%

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

8. Taylor expanded in x around -inf

   \[\leadsto -1 \cdot \color{blue}{\left(x \cdot {\left(\sqrt{-1}\right)}^{2}\right)} \]
9. Step-by-step derivation

10. Applied rewrites 43.3%

    \[\leadsto x \]

11. Final simplification 43.3%

    \[\leadsto x \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024326 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))