Random Jason Timeout Test 004

Average Error: 34.1 → 33.7

Time: 14.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = -2.147009436181225e-259
  2. c = 1.0551194375545526e+290

Math

\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

↓

\[\sqrt{\left(\left(\sqrt{\cosh c} \cdot \left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\cosh c} \cdot \left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

C

double f(double a, double c) {
        double r15500 = c;
        double r15501 = cosh(r15500);
        double r15502 = a;
        double r15503 = log1p(r15502);
        double r15504 = fmod(r15501, r15503);
        return r15504;
}

↓

double f(double a, double c) {
        double r15505 = c;
        double r15506 = cosh(r15505);
        double r15507 = sqrt(r15506);
        double r15508 = -1.0;
        double r15509 = r15508 * r15505;
        double r15510 = exp(r15509);
        double r15511 = exp(r15505);
        double r15512 = r15510 + r15511;
        double r15513 = sqrt(r15512);
        double r15514 = 0.5;
        double r15515 = sqrt(r15514);
        double r15516 = r15513 * r15515;
        double r15517 = r15507 * r15516;
        double r15518 = a;
        double r15519 = log1p(r15518);
        double r15520 = fmod(r15517, r15519);
        double r15521 = sqrt(r15520);
        double r15522 = r15521 * r15521;
        return r15522;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.1

   \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
2. Using strategy rm

3. Applied add-sqr-sqrt 34.1

   \[\leadsto \left(\color{blue}{\left(\sqrt{\cosh c} \cdot \sqrt{\cosh c}\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

4. Taylor expanded around inf 34.0

   \[\leadsto \left(\left(\sqrt{\cosh c} \cdot \color{blue}{\left(\sqrt{e^{c} + e^{-c}} \cdot \sqrt{\frac{1}{2}}\right)}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

5. Simplified 34.0

   \[\leadsto \left(\left(\sqrt{\cosh c} \cdot \color{blue}{\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
6. Using strategy rm

7. Applied add-sqr-sqrt 33.7

   \[\leadsto \color{blue}{\sqrt{\left(\left(\sqrt{\cosh c} \cdot \left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\cosh c} \cdot \left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

8. Final simplification 33.7

   \[\leadsto \sqrt{\left(\left(\sqrt{\cosh c} \cdot \left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\cosh c} \cdot \left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))