Linear.Quaternion:$csinh from linear-1.19.1.3

Average Error: 0.1 → 0.1

Time: 10.4s

Precision: binary64

Cost: 13120

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	0.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 31.8

   \[\leadsto \cosh x \cdot \color{blue}{\left(\frac{\sqrt{\sin y}}{y} \cdot \sqrt{\sin y}\right)} \]

3. Applied egg-rr 0.8

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{\sin y}{\frac{y}{\cosh x}}}\right)}^{3}} \]

4. Applied egg-rr 0.1

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

5. Final simplification 0.1

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

Alternatives

Alternative 1
Error	0.1
Cost	13120

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

Alternative 2
Error	1.0
Cost	7104

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

Alternative 3
Error	1.3
Cost	6592

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

Alternative 4
Error	30.2
Cost	1216

\[\frac{\frac{1}{y} + 0.5 \cdot \frac{x \cdot x}{y}}{\frac{1}{y} + y \cdot 0.16666666666666666} \]

Alternative 5
Error	31.1
Cost	960

\[\frac{\frac{1}{y} + 0.5 \cdot \frac{x \cdot x}{y}}{\frac{1}{y}} \]

Alternative 6
Error	31.1
Cost	448

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

Alternative 7
Error	31.2
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023046 
(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)))