Linear.Quaternion:$ccosh from linear-1.19.1.3

Average Error: 13.7 → 0.1

Time: 8.9s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	13.7
Target	0.2
Herbie	0.1

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

Derivation

1. Initial program 13.7

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

2. Applied egg-rr 0.1

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	16.3
Cost	6728

\[\begin{array}{l} t_0 := x \cdot \left(\left(1 + \frac{y}{x}\right) + -1\right)\\ \mathbf{if}\;x \leq -3.738586295927389 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.805425793411015 \cdot 10^{+61}:\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	1.2
Cost	6720

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

Alternative 3
Error	16.8
Cost	840

\[\begin{array}{l} t_0 := x \cdot \left(\left(1 + \frac{y}{x}\right) + -1\right)\\ \mathbf{if}\;x \leq -3.738586295927389 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.805425793411015 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	16.9
Cost	584

\[\begin{array}{l} t_0 := \left(y + 1\right) + -1\\ \mathbf{if}\;x \leq -3.738586295927389 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.805425793411015 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	31.1
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

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

  (/ (* (sin x) (sinh y)) x))