Linear.Quaternion:$csinh from linear-1.19.1.3

Average Accuracy: 99.8% → 99.8%

Time: 11.6s

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	99.8%
Target	99.8%
Herbie	99.8%

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	98.4%
Cost	7104

\[\sin y \cdot \frac{1 + x \cdot \left(x \cdot 0.5\right)}{y} \]

Alternative 2
Accuracy	98.5%
Cost	7104

\[\frac{1 + x \cdot \left(x \cdot 0.5\right)}{\frac{y}{\sin y}} \]

Alternative 3
Accuracy	98.1%
Cost	6592

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

Alternative 4
Accuracy	52.3%
Cost	704

\[\frac{\frac{1}{y}}{\frac{1}{y} + y \cdot 0.16666666666666666} \]

Alternative 5
Accuracy	51.3%
Cost	448

\[1 + x \cdot \left(x \cdot 0.5\right) \]

Alternative 6
Accuracy	51.0%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023137 
(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)))