Average Error: 14.3 → 0.2

Time: 10.8s

Precision: binary64

Cost: 13120

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	14.3
Target	0.2
Herbie	0.2

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

Derivation

Initial program 14.3
\[\frac{\sin x \cdot \sinh y}{x} \]
Simplified0.2
\[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
Proof
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) x)): 0 points increase in error, 0 points decrease in error
(Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) x)): 89 points increase in error, 13 points decrease in error
Final simplification0.2
\[\leadsto \sin x \cdot \frac{\sinh y}{x} \]

Alternatives

Alternative 1
Error	0.8
Cost	13120

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

Alternative 2
Error	1.5
Cost	7104

\[\frac{\sin x}{x \cdot \left(\frac{1}{y} + y \cdot -0.16666666666666666\right)} \]

Alternative 3
Error	1.4
Cost	7104

\[\frac{\sin x}{-0.16666666666666666 \cdot \left(x \cdot y\right) + \frac{x}{y}} \]

Alternative 4
Error	1.1
Cost	6720

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

Alternative 5
Error	16.4
Cost	584

\[\begin{array}{l} t_0 := \left(y + 1\right) + -1\\ \mathbf{if}\;x \leq -2643.833281426483:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4124695972440483300:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	16.6
Cost	320

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

Alternative 7
Error	30.9
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022316 
(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))