Average Error: 0.4 → 0.4
Time: 4.1s
Precision: binary64
\[\mathsf{erf}\left(\left(\sin x\right)\right) + \log \left(\tan^{-1} x\right)\]
↓
\[\mathsf{erf}\left(\left(\sin x\right)\right) + \log \left(\tan^{-1} x\right)\]
\mathsf{erf}\left(\left(\sin x\right)\right) + \log \left(\tan^{-1} x\right)
↓
\mathsf{erf}\left(\left(\sin x\right)\right) + \log \left(\tan^{-1} x\right)
double code(double x) {
	return ((double) (((double) erf(((double) sin(x)))) + ((double) log(((double) atan(x))))));
}
↓
double code(double x) {
	return ((double) (((double) erf(((double) sin(x)))) + ((double) log(((double) atan(x))))));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\mathsf{erf}\left(\left(\sin x\right)\right) + \log \left(\tan^{-1} x\right)\]

  2. Final simplification0.4

    \[\leadsto \mathsf{erf}\left(\left(\sin x\right)\right) + \log \left(\tan^{-1} x\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (erf (sin x)) (log (atan x)))"
  :precision binary64
  (+ (erf (sin x)) (log (atan x))))