Linear.Quaternion:$csin from linear-1.19.1.3

Average Error: 0.02% → 0.06%

Time: 6.0s

Precision: binary64

Cost: 13376

Math

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

↓

\[\cos x \cdot \frac{\frac{1}{y}}{\frac{1}{\sinh y}} \]

FPCore

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

↓

(FPCore (x y) :precision binary64 (* (cos x) (/ (/ 1.0 y) (/ 1.0 (sinh y)))))

C

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

↓

double code(double x, double y) {
	return cos(x) * ((1.0 / y) / (1.0 / sinh(y)));
}

Fortran

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

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = cos(x) * ((1.0d0 / y) / (1.0d0 / sinh(y)))
end function

Java

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

↓

public static double code(double x, double y) {
	return Math.cos(x) * ((1.0 / y) / (1.0 / Math.sinh(y)));
}

Python

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

↓

def code(x, y):
	return math.cos(x) * ((1.0 / y) / (1.0 / math.sinh(y)))

Julia

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

↓

function code(x, y)
	return Float64(cos(x) * Float64(Float64(1.0 / y) / Float64(1.0 / sinh(y))))
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = cos(x) * ((1.0 / y) / (1.0 / sinh(y)));
end

Wolfram

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

↓

code[x_, y_] := N[(N[Cos[x], $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] / N[(1.0 / N[Sinh[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.02

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

2. Applied egg-rr 50.12

   \[\leadsto \cos x \cdot \color{blue}{\left(\frac{1}{\sqrt{y}} \cdot \frac{\sinh y}{\sqrt{y}}\right)} \]

3. Applied egg-rr 0.06

   \[\leadsto \cos x \cdot \color{blue}{\frac{\frac{1}{y}}{\frac{1}{\sinh y}}} \]

4. Final simplification 0.06

   \[\leadsto \cos x \cdot \frac{\frac{1}{y}}{\frac{1}{\sinh y}} \]

Alternatives

Alternative 1
Error	0.02%
Cost	13120

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

Alternative 2
Error	1.1%
Cost	6976

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

Alternative 3
Error	1.66%
Cost	6464

\[\cos x \]

Reproduce

herbie shell --seed 2023103 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))