Random Jason Timeout Test 004

Average Error: 34.2 → 34.1

Time: 40.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.2076870027320673e+232
  2. c = -1.231501630887623e+236

Math

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

↓

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

C

double f(double a, double c) {
        double r21526 = c;
        double r21527 = cosh(r21526);
        double r21528 = a;
        double r21529 = log1p(r21528);
        double r21530 = fmod(r21527, r21529);
        return r21530;
}

↓

double f(double a, double c) {
        double r21531 = -1.0;
        double r21532 = c;
        double r21533 = r21531 * r21532;
        double r21534 = exp(r21533);
        double r21535 = exp(r21532);
        double r21536 = r21534 + r21535;
        double r21537 = sqrt(r21536);
        double r21538 = 0.5;
        double r21539 = sqrt(r21538);
        double r21540 = r21537 * r21539;
        double r21541 = cosh(r21532);
        double r21542 = sqrt(r21541);
        double r21543 = r21540 * r21542;
        double r21544 = a;
        double r21545 = log1p(r21544);
        double r21546 = fmod(r21543, r21545);
        return r21546;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.2

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

3. Applied add-sqr-sqrt 34.2

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

4. Taylor expanded around inf 34.1

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

5. Simplified 34.1

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

7. Applied add-sqr-sqrt 33.8

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

9. Applied add-sqr-sqrt 33.8

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

10. Applied sqrt-prod 33.8

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

11. Applied associate-*r* 33.8

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

12. Final simplification 34.1

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

Reproduce

herbie shell --seed 2019291 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))