Average Error: 25.8 → 25.8
Time: 3.2s
Precision: binary64
\[\left(1 - \sqrt{1 - {x}^{2}}\right) - x \cdot \sin^{-1} x\]
↓
\[\left(1 - \sqrt{1 - {x}^{2}}\right) - x \cdot \sin^{-1} x\]
\left(1 - \sqrt{1 - {x}^{2}}\right) - x \cdot \sin^{-1} x
↓
\left(1 - \sqrt{1 - {x}^{2}}\right) - x \cdot \sin^{-1} x
double code(double x) {
	return ((double) (((double) (1.0 - ((double) sqrt(((double) (1.0 - ((double) pow(x, 2.0)))))))) - ((double) (x * ((double) asin(x))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) sqrt(((double) (1.0 - ((double) pow(x, 2.0)))))))) - ((double) (x * ((double) asin(x))))));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 25.8

    \[\left(1 - \sqrt{1 - {x}^{2}}\right) - x \cdot \sin^{-1} x\]

  2. Final simplification25.8

    \[\leadsto \left(1 - \sqrt{1 - {x}^{2}}\right) - x \cdot \sin^{-1} x\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (- 1 (sqrt (- 1 (pow x 2)))) (* x (asin x)))"
  :precision binary64
  (- (- 1.0 (sqrt (- 1.0 (pow x 2.0)))) (* x (asin x))))