Linear.Quaternion:$cexp from linear-1.19.1.3

Average Error: 0.1 → 0.2

Time: 4.8s

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 0.2

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

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.1
Cost	6720

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

Alternative 2
Error	22.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+19}:\\ \;\;\;\;6 \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 105000000000:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{6}{y \cdot y}\\ \end{array} \]

Alternative 3
Error	22.6
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -6200000000:\\ \;\;\;\;6 \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 105000000000:\\ \;\;\;\;x + -0.16666666666666666 \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{6}{y \cdot y}\\ \end{array} \]

Alternative 4
Error	22.8
Cost	712

\[\begin{array}{l} t_0 := 6 \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;y \leq -2.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	22.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.5:\\ \;\;\;\;6 \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{6}{y \cdot y}\\ \end{array} \]

Alternative 6
Error	22.6
Cost	576

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

Alternative 7
Error	30.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))