Average Error: 34.3 → 34.3
Time: 30.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[e^{\sqrt[3]{\left(\log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right) \cdot \left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right)}}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.3

    \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
  2. Using strategy rm

  3. Applied add-exp-log34.3

    \[\leadsto \color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube34.3

    \[\leadsto e^{\color{blue}{\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt34.3

    \[\leadsto e^{\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}}}\]

  8. Applied log-prod34.3

    \[\leadsto e^{\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}}}\]

  9. Final simplification34.3

    \[\leadsto e^{\sqrt[3]{\left(\log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right) \cdot \left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right)}}\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 27.9s)Debug log

sample807.0ms

Algorithm
intervals

simplify15.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

14.0ms
(fmod (cosh c) (log1p a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize24.0ms

Local error

Found 1 expressions with local error:

41.4b
(fmod (cosh c) (log1p a))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 9
Calls

1 calls. Slowest were:

1.0ms
(fmod (cosh c) (log1p a))

series35.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

35.0ms
(fmod (cosh c) (log1p a))

simplify9.0ms

Counts
3 → 12
Calls

3 calls. Slowest were:

3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))

prune324.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 36.3b

localize13.0ms

Local error

Found 3 expressions with local error:

41.4b
(fmod (cosh c) (log1p a))
1.6b
(log (fmod (cosh c) (log1p a)))
0.6b
(exp (log (fmod (cosh c) (log1p a))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
3 → 40
Calls

3 calls. Slowest were:

4.0ms
(exp (log (fmod (cosh c) (log1p a))))
3.0ms
(log (fmod (cosh c) (log1p a)))
0.0ms
(fmod (cosh c) (log1p a))

series43.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

33.0ms
(log (fmod (cosh c) (log1p a)))
5.0ms
(exp (log (fmod (cosh c) (log1p a))))
4.0ms
(fmod (cosh c) (log1p a))

simplify172.0ms

Counts
21 → 49
Calls

21 calls. Slowest were:

19.0ms
(exp (log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a))))))
18.0ms
(exp (* (cbrt (log (fmod (cosh c) (log1p a)))) (cbrt (log (fmod (cosh c) (log1p a))))))
18.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))

prune581.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 36.3b

localize11.0ms

Local error

Found 4 expressions with local error:

41.4b
(fmod (cosh c) (log1p a))
41.4b
(fmod (cosh c) (log1p a))
41.4b
(fmod (cosh c) (log1p a))
1.6b
(log (fmod (cosh c) (log1p a)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
4 → 41
Calls

4 calls. Slowest were:

1.0ms
(log (fmod (cosh c) (log1p a)))
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))

series30.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

22.0ms
(log (fmod (cosh c) (log1p a)))
3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))

simplify80.0ms

Counts
16 → 53
Calls

16 calls. Slowest were:

13.0ms
(log (sqrt (fmod (cosh c) (log1p a))))
9.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
5.0ms
(fmod (cosh c) (log1p a))

prune828.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 36.3b

localize49.0ms

Local error

Found 4 expressions with local error:

41.4b
(fmod (cosh c) (log1p a))
41.4b
(fmod (cosh c) (log1p a))
41.4b
(fmod (cosh c) (log1p a))
41.4b
(fmod (cosh c) (log1p a))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
4 → 36
Calls

4 calls. Slowest were:

0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))

series18.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

5.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))

simplify62.0ms

Counts
12 → 48
Calls

12 calls. Slowest were:

6.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))

prune786.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 36.3b

regimes562.0ms

Accuracy

0% (0.0b remaining)

Error of 34.3b against oracle of 34.3b and baseline of 34.3b

bsearch2.0ms

end0.0ms

sample23.4s

Algorithm
intervals