Linear.Quaternion:$cexp from linear-1.19.1.3

Average Error: 0.1 → 0.1

Time: 12.7s

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	23.0
Cost	832

\[\frac{\frac{1}{y}}{\frac{1}{y} + y \cdot 0.16666666666666666} \cdot x \]

Alternative 3
Error	23.1
Cost	712

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

Alternative 4
Error	23.0
Cost	704

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

Alternative 5
Error	23.4
Cost	648

\[\begin{array}{l} t_0 := -1 + \left(1 - \left(-x\right)\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	24.1
Cost	584

\[\begin{array}{l} t_0 := \frac{x}{y} \cdot y\\ \mathbf{if}\;y \leq -2 \cdot 10^{+97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	23.4
Cost	584

\[\begin{array}{l} t_0 := \frac{y}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -3 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	30.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023064 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))