Average Error: 33.0 → 33.0
Time: 7.3s
Precision: binary64
\[\frac{\left(2 \cdot x - 3 \cdot \sin x\right) + x \cdot \cos x}{2 \cdot {x}^{5}}\]
↓
\[\frac{\left(2 \cdot x - 3 \cdot \sin x\right) + x \cdot \cos x}{2 \cdot {x}^{5}}\]
\frac{\left(2 \cdot x - 3 \cdot \sin x\right) + x \cdot \cos x}{2 \cdot {x}^{5}}
↓
\frac{\left(2 \cdot x - 3 \cdot \sin x\right) + x \cdot \cos x}{2 \cdot {x}^{5}}
double code(double x) {
	return ((double) (((double) (((double) (((double) (2.0 * x)) - ((double) (3.0 * ((double) sin(x)))))) + ((double) (x * ((double) cos(x)))))) / ((double) (2.0 * ((double) pow(x, 5.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) (2.0 * x)) - ((double) (3.0 * ((double) sin(x)))))) + ((double) (x * ((double) cos(x)))))) / ((double) (2.0 * ((double) pow(x, 5.0))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 33.0

    \[\frac{\left(2 \cdot x - 3 \cdot \sin x\right) + x \cdot \cos x}{2 \cdot {x}^{5}}\]

  2. Final simplification33.0

    \[\leadsto \frac{\left(2 \cdot x - 3 \cdot \sin x\right) + x \cdot \cos x}{2 \cdot {x}^{5}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (+ (- (* 2 x) (* 3 (sin x))) (* x (cos x))) (* 2 (pow x 5)))"
  :precision binary64
  (/ (+ (- (* 2.0 x) (* 3.0 (sin x))) (* x (cos x))) (* 2.0 (pow x 5.0))))