Linear.Quaternion:$cexp from linear-1.19.1.3

Average Error: 0.1 → 0.1

Time: 4.7s

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	23.0
Cost	840

\[\begin{array}{l} t_0 := 6 \cdot \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 550:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	23.2
Cost	712

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

Alternative 3
Error	23.1
Cost	712

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

Alternative 4
Error	23.4
Cost	584

\[\begin{array}{l} t_0 := 1 + \left(x + -1\right)\\ \mathbf{if}\;y \leq -3.1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	23.0
Cost	576

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

Alternative 6
Error	30.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022330 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))