Average Error: 34.3 → 34.3
Time: 29.1s
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 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 27.0s)Debug log

sample845.0ms

Algorithm
intervals

simplify8.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

8.0ms
(fmod (cosh c) (log1p a))

prune8.0ms

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 → 7
Calls

1 calls. Slowest were:

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

series40.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

40.0ms
(fmod (cosh c) (log1p a))

simplify17.0ms

Counts
3 → 10
Calls

3 calls. Slowest were:

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

prune134.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 36.3b

localize11.0ms

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 → 34
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))

series33.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

25.0ms
(log (fmod (cosh c) (log1p a)))
5.0ms
(fmod (cosh c) (log1p a))
3.0ms
(exp (log (fmod (cosh c) (log1p a))))

simplify109.0ms

Counts
21 → 43
Calls

21 calls. Slowest were:

21.0ms
(exp (* (cbrt (log (fmod (cosh c) (log1p a)))) (cbrt (log (fmod (cosh c) (log1p a))))))
14.0ms
(exp (log (sqrt (fmod (cosh c) (log1p a)))))
9.0ms
(exp (log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a))))))

prune569.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 36.3b

localize23.0ms

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)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
4 → 33
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))

series40.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

29.0ms
(log (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))

simplify73.0ms

Counts
16 → 45
Calls

16 calls. Slowest were:

19.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
9.0ms
(log (fmod (cosh c) (log1p a)))
7.0ms
(log (sqrt (fmod (cosh c) (log1p a))))

prune726.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 36.3b

localize24.0ms

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))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
4 → 28
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:

7.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))

simplify48.0ms

Counts
12 → 40
Calls

12 calls. Slowest were:

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

prune692.0ms

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

bsearch4.0ms

end0.0ms

sample23.0s

Algorithm
intervals