?

Average Error: 21.93% → 0.19%
Time: 9.7s
Precision: binary64
Cost: 13120

?

\[\frac{\sin x \cdot \sinh y}{x} \]
↓
\[\frac{\sinh y}{\frac{x}{\sin x}} \]
(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))
↓
(FPCore (x y) :precision binary64 (/ (sinh y) (/ x (sin x))))
double code(double x, double y) {
	return (sin(x) * sinh(y)) / x;
}
↓
double code(double x, double y) {
	return sinh(y) / (x / sin(x));
}

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 = sinh(y) / (x / sin(x))
end function

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.sinh(y) / (x / Math.sin(x));
}

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

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

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

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

\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sinh y}{\frac{x}{\sin x}}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original21.93%
Target0.38%
Herbie0.19%
\[\sin x \cdot \frac{\sinh y}{x} \]

Derivation?

  1. Initial program 21.93

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

  2. Simplified0.19

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

    [Start]21.93

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

    *-commutative [=>]21.93

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

    associate-/l* [=>]0.19

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

  3. Final simplification0.19

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

Alternatives

Alternative 1
Error0.38%
Cost13120
\[\sin x \cdot \frac{\sinh y}{x} \]
Alternative 2
Error2.25%
Cost6720
\[\sin x \cdot \frac{y}{x} \]
Alternative 3
Error2.14%
Cost6720
\[y \cdot \frac{\sin x}{x} \]
Alternative 4
Error2.15%
Cost6720
\[\frac{y}{\frac{x}{\sin x}} \]
Alternative 5
Error26.04%
Cost841
\[\begin{array}{l} \mathbf{if}\;x \leq -2700000000000 \lor \neg \left(x \leq 7600\right):\\ \;\;\;\;6 \cdot \frac{\frac{y}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \]
Alternative 6
Error26.04%
Cost841
\[\begin{array}{l} \mathbf{if}\;x \leq -5600000000000 \lor \neg \left(x \leq 7600\right):\\ \;\;\;\;6 \cdot \frac{\frac{y}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \end{array} \]
Alternative 7
Error26.18%
Cost704
\[\frac{y}{x \cdot \left(x \cdot 0.16666666666666666 + \frac{1}{x}\right)} \]
Alternative 8
Error28.4%
Cost320
\[x \cdot \frac{y}{x} \]
Alternative 9
Error48.75%
Cost64
\[y \]

Error

Reproduce?

herbie shell --seed 2023115 
(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))