Linear.Quaternion:$csinh from linear-1.19.1.3

Percentage Accurate: 99.9% → 99.9%

Time: 6.9s

Precision: binary64

Cost: 13120

• 48.8% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	99.9%
Target	99.9%
Herbie	99.9%

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

Derivation

1. Initial program 99.9%

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

2. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\frac{\sin y \cdot \cosh x}{y}} \]
   Step-by-step derivation

   [Start] 99.9%	\[ \cosh x \cdot \frac{\sin y}{y} \]
   *-commutative [=>] 99.9%	\[ \color{blue}{\frac{\sin y}{y} \cdot \cosh x} \]
   associate-*l/ [=>] 99.9%	\[ \color{blue}{\frac{\sin y \cdot \cosh x}{y}} \]

3. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	99.9%
Cost	13120

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

Alternative 2
Accuracy	86.8%
Cost	13124

\[\begin{array}{l} \mathbf{if}\;\cosh x \leq 1.00001:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \]

Alternative 3
Accuracy	99.9%
Cost	13120

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

Alternative 4
Accuracy	93.2%
Cost	7761

\[\begin{array}{l} t_0 := \sin y \cdot \left(\frac{1}{y} + 0.5 \cdot \frac{x \cdot x}{y}\right)\\ \mathbf{if}\;x \leq -7.3 \cdot 10^{+133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -25:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 0.41 \lor \neg \left(x \leq 1.35 \cdot 10^{+154}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \]

Alternative 5
Accuracy	62.4%
Cost	6596

\[\begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+167}:\\ \;\;\;\;\cosh x\\ \mathbf{else}:\\ \;\;\;\;1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 6
Accuracy	32.4%
Cost	448

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

Alternative 7
Accuracy	32.3%
Cost	448

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

Alternative 8
Accuracy	26.7%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023165 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))