Linear.Quaternion:$ccos from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Precision: binary64

Cost: 13120

• 50.2% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	13120

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

Alternative 2
Accuracy	73.6%
Cost	7376

\[\begin{array}{l} t_0 := 0.16666666666666666 \cdot \left(y \cdot \left(\sin x \cdot y\right)\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+208}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.015:\\ \;\;\;\;x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 10^{+19}:\\ \;\;\;\;\sin x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+211}:\\ \;\;\;\;0.16666666666666666 \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	75.6%
Cost	7113

\[\begin{array}{l} \mathbf{if}\;y \leq -2.45 \lor \neg \left(y \leq 2.45\right):\\ \;\;\;\;\sin x \cdot \left(0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin x\\ \end{array} \]

Alternative 4
Accuracy	75.9%
Cost	6976

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

Alternative 5
Accuracy	71.5%
Cost	6729

\[\begin{array}{l} \mathbf{if}\;y \leq -0.03 \lor \neg \left(y \leq 6 \cdot 10^{+25}\right):\\ \;\;\;\;x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin x\\ \end{array} \]

Alternative 6
Accuracy	41.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2.45 \lor \neg \left(y \leq 2.45\right):\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Accuracy	47.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2.45 \lor \neg \left(y \leq 2.45\right):\\ \;\;\;\;0.16666666666666666 \cdot \left(x \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Accuracy	47.6%
Cost	576

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

Alternative 9
Accuracy	26.2%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))