Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 9.9s

Precision: binary64

Cost: 13120

• 49.9% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

function tmp = code(x, y)
	tmp = cos(x) * (sinh(y) / 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[Sinh[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	13120

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

Alternative 2
Accuracy	83.2%
Cost	13452

\[\begin{array}{l} t_0 := 0.16666666666666666 \cdot \left(y \cdot y\right)\\ t_1 := \sqrt[3]{{y}^{6} \cdot 0.004629629629629629}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+54}:\\ \;\;\;\;\cos x \cdot \left(1 + t_0\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(-0.08333333333333333, y \cdot \left(x \cdot x\right), y \cdot 0.16666666666666666\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;\left(1 - \left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot 0.027777777777777776\right)\right) \cdot \frac{1}{1 - t_0}\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot \left(\cos x \cdot y\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	84.3%
Cost	7508

\[\begin{array}{l} t_0 := 0.16666666666666666 \cdot \left(y \cdot \left(\cos x \cdot y\right)\right)\\ t_1 := \left(1 - \left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot 0.027777777777777776\right)\right) \cdot \frac{1}{1 - 0.16666666666666666 \cdot \left(y \cdot y\right)}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -270000000000:\\ \;\;\;\;y \cdot \left(-0.08333333333333333 \cdot \left(y \cdot \left(x \cdot x\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+30}:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Accuracy	84.7%
Cost	7508

\[\begin{array}{l} t_0 := 0.16666666666666666 \cdot \left(y \cdot \left(\cos x \cdot y\right)\right)\\ t_1 := 0.16666666666666666 \cdot \left(y \cdot y\right)\\ t_2 := \left(1 - \left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot 0.027777777777777776\right)\right) \cdot \frac{1}{1 - t_1}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -150000000000:\\ \;\;\;\;y \cdot \left(-0.08333333333333333 \cdot \left(y \cdot \left(x \cdot x\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+60}:\\ \;\;\;\;\cos x \cdot \left(1 + t_1\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	84.7%
Cost	7508

\[\begin{array}{l} t_0 := 0.16666666666666666 \cdot \left(y \cdot \left(\cos x \cdot y\right)\right)\\ t_1 := 0.16666666666666666 \cdot \left(y \cdot y\right)\\ t_2 := \left(1 - \left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot 0.027777777777777776\right)\right) \cdot \frac{1}{1 - t_1}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -270000000000:\\ \;\;\;\;y \cdot \mathsf{fma}\left(-0.08333333333333333, y \cdot \left(x \cdot x\right), y \cdot 0.16666666666666666\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+60}:\\ \;\;\;\;\cos x \cdot \left(1 + t_1\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Accuracy	78.4%
Cost	6992

\[\begin{array}{l} t_0 := 0.16666666666666666 \cdot \left(y \cdot y\right)\\ t_1 := \left(1 - \left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot 0.027777777777777776\right)\right) \cdot \frac{1}{1 - t_0}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -180000000000:\\ \;\;\;\;y \cdot \left(-0.08333333333333333 \cdot \left(y \cdot \left(x \cdot x\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+30}:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Accuracy	55.1%
Cost	2136

\[\begin{array}{l} t_0 := 0.16666666666666666 \cdot \left(y \cdot y\right)\\ t_1 := y \cdot \left(-0.08333333333333333 \cdot \left(y \cdot \left(x \cdot x\right)\right)\right)\\ t_2 := \left(1 - \left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot 0.027777777777777776\right)\right) \cdot \frac{1}{1 - t_0}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -210000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Accuracy	48.1%
Cost	708

\[\begin{array}{l} \mathbf{if}\;x \leq 3.9 \cdot 10^{+118}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-0.08333333333333333 \cdot \left(y \cdot \left(x \cdot x\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	47.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-7} \lor \neg \left(y \leq 235000000000\right):\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10
Accuracy	47.2%
Cost	448

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

Alternative 11
Accuracy	28.5%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))