Linear.Quaternion:$ccos from linear-1.19.1.3

Average Error: 0.0 → 0.0

Time: 9.8s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sin(x) * (sinh(y) / y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sin(x) * (sinh(y) / y)
end function

Java

public static double code(double x, double y) {
	return Math.sin(x) * (Math.sinh(y) / y);
}

↓

public static double code(double x, double y) {
	return Math.sin(x) * (Math.sinh(y) / y);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.5
Cost	20041

\[\begin{array}{l} \mathbf{if}\;\sin x \leq -1 \cdot 10^{-7} \lor \neg \left(\sin x \leq 2 \cdot 10^{-45}\right):\\ \;\;\;\;\sin x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\sinh y \cdot 2\right) \cdot \frac{x}{y}}{2}\\ \end{array} \]

Alternative 2
Error	0.5
Cost	20041

\[\begin{array}{l} \mathbf{if}\;\sin x \leq -1 \cdot 10^{-7} \lor \neg \left(\sin x \leq 2 \cdot 10^{-45}\right):\\ \;\;\;\;\sin x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sinh y \cdot 2}}}{2}\\ \end{array} \]

Alternative 3
Error	0.9
Cost	6976

\[\sin x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right) \]

Alternative 4
Error	1.2
Cost	6464

\[\sin x \]

Alternative 5
Error	31.2
Cost	1088

\[\frac{x \cdot \left(2 + \left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot 0.016666666666666666 + 0.3333333333333333\right)\right)}{2} \]

Alternative 6
Error	31.3
Cost	576

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

Alternative 7
Error	31.3
Cost	576

\[x + x \cdot \left(0.16666666666666666 \cdot \left(y \cdot y\right)\right) \]

Alternative 8
Error	31.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023018 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))