Linear.Quaternion:$csinh from linear-1.19.1.3

Average Error: 0.2 → 0.2

Time: 10.1s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.2
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Alternatives

Alternative 1
Error	1.4
Cost	13252

\[\begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;t_0 \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \]

Alternative 2
Error	0.8
Cost	7368

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\cosh x\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y \cdot \left(1 + 0.5 \cdot \left(x \cdot x\right)\right)}{y}\\ \end{array} \]

Alternative 3
Error	31.4
Cost	6464

\[\cosh x \]

Alternative 4
Error	32.0
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023187 
(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)))