Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
\[\left(\left(\sin x \cdot \sin x - \cos x \cdot \cos x\right) - \left(2 \cdot \sin x\right) \cdot \sin x\right) - 1\]
↓
\[\left(\left(\sin x \cdot \sin x - \cos x \cdot \cos x\right) - \left(2 \cdot \sin x\right) \cdot \sin x\right) - 1\]
\left(\left(\sin x \cdot \sin x - \cos x \cdot \cos x\right) - \left(2 \cdot \sin x\right) \cdot \sin x\right) - 1
↓
\left(\left(\sin x \cdot \sin x - \cos x \cdot \cos x\right) - \left(2 \cdot \sin x\right) \cdot \sin x\right) - 1
double code(double x) {
	return ((double) (((double) (((double) (((double) (((double) sin(x)) * ((double) sin(x)))) - ((double) (((double) cos(x)) * ((double) cos(x)))))) - ((double) (((double) (2.0 * ((double) sin(x)))) * ((double) sin(x)))))) - 1.0));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) (((double) sin(x)) * ((double) sin(x)))) - ((double) (((double) cos(x)) * ((double) cos(x)))))) - ((double) (((double) (2.0 * ((double) sin(x)))) * ((double) sin(x)))))) - 1.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\left(\sin x \cdot \sin x - \cos x \cdot \cos x\right) - \left(2 \cdot \sin x\right) \cdot \sin x\right) - 1\]

  2. Final simplification0.0

    \[\leadsto \left(\left(\sin x \cdot \sin x - \cos x \cdot \cos x\right) - \left(2 \cdot \sin x\right) \cdot \sin x\right) - 1\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (- (- (* (sin x) (sin x)) (* (cos x) (cos x))) (* (* 2 (sin x)) (sin x))) 1)"
  :precision binary64
  (- (- (- (* (sin x) (sin x)) (* (cos x) (cos x))) (* (* 2.0 (sin x)) (sin x))) 1.0))