Linear.Quaternion:$cexp from linear-1.19.1.3

Average Error: 0.1 → 0.1

Time: 5.5s

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 0.1

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

2. Final simplification 0.1

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

Alternatives

Alternative 1
Error	0.5
Cost	6984

\[\begin{array}{l} t_0 := \frac{\sin y}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -3.7577645386439 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.1728532471958 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.1
Cost	6720

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

Alternative 3
Error	23.8
Cost	840

\[\begin{array}{l} t_0 := y \cdot \left(\left(1 + \frac{x}{y}\right) + -1\right)\\ \mathbf{if}\;y \leq -2.2916894560475174 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.026398485657958 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	23.6
Cost	704

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

Alternative 5
Error	24.2
Cost	584

\[\begin{array}{l} t_0 := \frac{y}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -1.2105375778933525 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.9331722059281635 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	23.9
Cost	584

\[\begin{array}{l} t_0 := \left(x + 1\right) + -1\\ \mathbf{if}\;y \leq -22751751.198026627:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.026398485657958 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	31.2
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))