Average Error: 30.8 → 30.8
Time: 2.0s
Precision: binary64
\[\frac{\sin \left(x + 1.00000000000000008 \cdot 10^{-5}\right) - \sin x}{1.00000000000000008 \cdot 10^{-5}}\]
↓
\[\frac{\sin \left(x + 1.00000000000000008 \cdot 10^{-5}\right) - \sin x}{1.00000000000000008 \cdot 10^{-5}}\]
\frac{\sin \left(x + 1.00000000000000008 \cdot 10^{-5}\right) - \sin x}{1.00000000000000008 \cdot 10^{-5}}
↓
\frac{\sin \left(x + 1.00000000000000008 \cdot 10^{-5}\right) - \sin x}{1.00000000000000008 \cdot 10^{-5}}
double code(double x) {
	return ((double) (((double) (((double) sin(((double) (x + 1e-05)))) - ((double) sin(x)))) / 1e-05));
}
↓
double code(double x) {
	return ((double) (((double) (((double) sin(((double) (x + 1e-05)))) - ((double) sin(x)))) / 1e-05));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.8

    \[\frac{\sin \left(x + 1.00000000000000008 \cdot 10^{-5}\right) - \sin x}{1.00000000000000008 \cdot 10^{-5}}\]

  2. Final simplification30.8

    \[\leadsto \frac{\sin \left(x + 1.00000000000000008 \cdot 10^{-5}\right) - \sin x}{1.00000000000000008 \cdot 10^{-5}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (- (sin (+ x 1e-05)) (sin x)) 1e-05)"
  :precision binary64
  (/ (- (sin (+ x 1e-05)) (sin x)) 1e-05))