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 r1479 = 1.0;
        double r1480 = x;
        double r1481 = r1479 / r1480;
        double r1482 = r1481 - r1479;
        double r1483 = log(r1482);
        double r1484 = -r1483;
        return r1484;
}

↓

double f(double x) {
        double r1485 = 1.0;
        double r1486 = x;
        double r1487 = r1485 / r1486;
        double r1488 = r1487 - r1485;
        double r1489 = log(r1488);
        double r1490 = -r1489;
        return r1490;
}

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 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))