Linear.Quaternion:$cexp from linear-1.19.1.3

Average Error: 0.1 → 0.1

Time: 5.4s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	0.1
Cost	6720

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

Alternative 2
Error	23.4
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \lor \neg \left(y \leq 6800000\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \end{array} \]

Alternative 3
Error	23.4
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \lor \neg \left(y \leq 6800000\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.16666666666666666\right)\right)\\ \end{array} \]

Alternative 4
Error	23.6
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \lor \neg \left(y \leq 2.4\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	24.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+89} \lor \neg \left(y \leq 1.05 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	23.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -400000000000 \lor \neg \left(y \leq 3.6 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x + 1\right) + -1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	24.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) + -1\\ \end{array} \]

Alternative 8
Error	23.4
Cost	576

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

Alternative 9
Error	30.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023031 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))