(sin (- (- (* (+ x 1) (+ x 1)) (* x (+ x 1))) 1))

Average Error: 59.2 → 59.2

Time: 2.8s

Precision: binary64

Math

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

↓

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

C

double code(double x) {
	return ((double) sin(((double) (((double) (((double) (((double) (x + 1.0)) * ((double) (x + 1.0)))) - ((double) (x * ((double) (x + 1.0)))))) - 1.0))));
}

↓

double code(double x) {
	return ((double) sin(((double) (((double) (((double) (((double) (x + 1.0)) * ((double) (x + 1.0)))) - ((double) (x * ((double) (x + 1.0)))))) - 1.0))));
}

Error

Bits error versus x

Derivation

1. Initial program 59.2

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

2. Final simplification 59.2

   \[\leadsto \sin \left(\left(\left(x + 1\right) \cdot \left(x + 1\right) - x \cdot \left(x + 1\right)\right) - 1\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sin (- (- (* (+ x 1) (+ x 1)) (* x (+ x 1))) 1))"
  :precision binary64
  (sin (- (- (* (+ x 1.0) (+ x 1.0)) (* x (+ x 1.0))) 1.0)))