Linear.Quaternion:$cexp from linear-1.19.1.3

Average Accuracy: 99.8% → 99.8%

Time: 7.3s

Precision: binary64

Cost: 6720

Math

\[x \cdot \frac{\sin y}{y} \]

↓

\[x \cdot \frac{\sin y}{y} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))

↓

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))

C

double code(double x, double y) {
	return x * (sin(y) / y);
}

↓

double code(double x, double y) {
	return x * (sin(y) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (sin(y) / y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (sin(y) / y)
end function

Java

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

↓

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

Python

def code(x, y):
	return x * (math.sin(y) / y)

↓

def code(x, y):
	return x * (math.sin(y) / y)

Julia

function code(x, y)
	return Float64(x * Float64(sin(y) / y))
end

↓

function code(x, y)
	return Float64(x * Float64(sin(y) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (sin(y) / y);
end

↓

function tmp = code(x, y)
	tmp = x * (sin(y) / y);
end

Wolfram

code[x_, y_] := N[(x * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(x * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]

2. Final simplification 99.8%

   \[\leadsto x \cdot \frac{\sin y}{y} \]

Alternatives

Alternative 1
Accuracy	63.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -45000 \lor \neg \left(y \leq 2.3\right):\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \end{array} \]

Alternative 2
Accuracy	63.5%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -45000 \lor \neg \left(y \leq 2.5\right):\\ \;\;\;\;\left(1 + x \cdot \frac{y}{y}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \end{array} \]

Alternative 3
Accuracy	63.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -0.0035 \lor \neg \left(y \leq 0.003\right):\\ \;\;\;\;y \cdot \frac{1}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	61.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+96} \lor \neg \left(y \leq 2.45 \cdot 10^{-51}\right):\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Accuracy	62.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+73} \lor \neg \left(y \leq 0.001\right):\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	63.8%
Cost	576

\[\frac{x}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)} \]

Alternative 7
Accuracy	52.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023126 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))