neg log

Average Error: 0.0 → 0.0

Time: 1.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[-\log \left(\frac{1}{x} - 1\right)\]

↓

\[-\log \left(\frac{1}{x} - 1\right)\]

C

double f(double x) {
        double r1481 = 1.0;
        double r1482 = x;
        double r1483 = r1481 / r1482;
        double r1484 = r1483 - r1481;
        double r1485 = log(r1484);
        double r1486 = -r1485;
        return r1486;
}

↓

double f(double x) {
        double r1487 = 1.0;
        double r1488 = x;
        double r1489 = r1487 / r1488;
        double r1490 = r1489 - r1487;
        double r1491 = log(r1490);
        double r1492 = -r1491;
        return r1492;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[-\log \left(\frac{1}{x} - 1\right)\]

2. Final simplification 0.0

   \[\leadsto -\log \left(\frac{1}{x} - 1\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))