Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 22.7s

Precision: binary64

Cost: 13120

• Unsound rule application detected in e-graph. Results may not be sound.

• could not determine a ground truth

  1. x = 1.5004564603928934e-240
  2. y = -1.593288660425601e+149

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	97.9%
Cost	13636

\[\begin{array}{l} t_0 := \frac{\sinh y}{y}\\ \mathbf{if}\;t_0 \leq 50:\\ \;\;\;\;\cos x \cdot \left(0.16666666666666666 \cdot \left(y \cdot y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	97.6%
Cost	13252

\[\begin{array}{l} t_0 := \frac{\sinh y}{y}\\ \mathbf{if}\;t_0 \leq 1.0000001:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Accuracy	94.2%
Cost	6464

\[\cos x \]

Alternative 5
Accuracy	52.7%
Cost	448

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

Alternative 6
Accuracy	52.4%
Cost	192

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

Alternative 7
Accuracy	5.3%
Cost	64

\[-3 \]

Alternative 8
Accuracy	6.3%
Cost	64

\[-1 \]

Alternative 9
Accuracy	10.6%
Cost	64

\[0.004629629629629629 \]

Alternative 10
Accuracy	11.3%
Cost	64

\[0.027777777777777776 \]

Alternative 11
Accuracy	11.8%
Cost	64

\[0.0625 \]

Alternative 12
Accuracy	12.3%
Cost	64

\[0.125 \]

Alternative 13
Accuracy	12.5%
Cost	64

\[0.16666666666666666 \]

Alternative 14
Accuracy	13.0%
Cost	64

\[0.25 \]

Alternative 15
Accuracy	13.3%
Cost	64

\[0.3333333333333333 \]

Alternative 16
Accuracy	14.1%
Cost	64

\[0.5 \]

Alternative 17
Accuracy	15.9%
Cost	64

\[1.1666666666666667 \]

Reproduce

herbie shell --seed 2023277 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))