Average Error: 61.3 → 0.5
Time: 12.9s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) log(((double) (1.0 - x)))) / ((double) log(((double) (1.0 + x))))));
}

↓
double code(double x) {
	return ((double) (((double) (((double) log(1.0)) + ((double) (((double) (x * ((double) (((double) (x * ((double) (-0.5 / 1.0)))) / 1.0)))) - ((double) (1.0 * x)))))) / ((double) (((double) (1.0 * x)) + ((double) (((double) log(1.0)) + ((double) (-0.5 * ((double) (((double) (x / 1.0)) * ((double) (x / 1.0))))))))))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original61.3
Target0.3
Herbie0.5
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Derivation
  1. Initial program 61.3
    \[\]
  2. Taylor expanded around 0 60.4
    \[\leadsto \]
  3. Simplified60.4
    \[\leadsto \]
  4. Taylor expanded around 0 0.5
    \[\leadsto \]
  5. Simplified0.5
    \[\leadsto \]
  6. Final simplification0.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "qlog (example 3.10)"
  :precision binary64
  :pre (and (< -1.0 x) (< x 1.0))

  :herbie-target
  (neg (+ (+ (+ 1.0 x) (/ (* x x) 2.0)) (* 0.4166666666666667 (pow x 3.0))))

  (/ (log (- 1.0 x)) (log (+ 1.0 x))))