Average Error: 34.7 → 34.7
Time: 34.9s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[e^{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.7

    \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]

  2. Initial simplification34.7

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

  4. Applied add-exp-log34.7

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

  6. Applied add-cube-cbrt34.7

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

  7. Final simplification34.7

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

Reproduce

herbie shell --seed 2018362 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 4.5s)Debug log

start699.0ms

Algorithm
intervals

setup440.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize25.0ms

Local error

Found 1 expressions with local error:

37.9b
(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))

series16.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

16.0ms
(fmod (cosh c) (log1p a))

simplify15.0ms

Counts
3 → 10
Calls

3 calls. Slowest were:

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

prune148.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 33.5b

localize11.0ms

Local error

Found 3 expressions with local error:

37.9b
(fmod (cosh c) (log1p a))
1.3b
(log (fmod (cosh c) (log1p a)))
0.6b
(exp (log (fmod (cosh c) (log1p a))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
3 → 34
Calls

3 calls. Slowest were:

4.0ms
(exp (log (fmod (cosh c) (log1p a))))
3.0ms
(fmod (cosh c) (log1p a))
2.0ms
(log (fmod (cosh c) (log1p a)))

series30.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

22.0ms
(log (fmod (cosh c) (log1p a)))
5.0ms
(fmod (cosh c) (log1p a))
3.0ms
(exp (log (fmod (cosh c) (log1p a))))

simplify176.0ms

Counts
21 → 43
Calls

21 calls. Slowest were:

20.0ms
(exp (* (cbrt (log (fmod (cosh c) (log1p a)))) (cbrt (log (fmod (cosh c) (log1p a))))))
20.0ms
(exp (log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a))))))
16.0ms
(exp (log (sqrt (fmod (cosh c) (log1p a)))))

prune702.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 33.5b

localize26.0ms

Local error

Found 4 expressions with local error:

37.9b
(fmod (cosh c) (log1p a))
37.9b
(fmod (cosh c) (log1p a))
37.9b
(fmod (cosh c) (log1p a))
1.3b
(log (fmod (cosh c) (log1p a)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
4 → 33
Calls

4 calls. Slowest were:

2.0ms
(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:

26.0ms
(log (fmod (cosh c) (log1p a)))
5.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))

simplify99.0ms

Counts
16 → 45
Calls

16 calls. Slowest were:

10.0ms
(log (fmod (cosh c) (log1p a)))
9.0ms
(log (fmod (cosh c) (log1p a)))
9.0ms
(log (fmod (cosh c) (log1p a)))

prune742.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 33.5b

localize12.0ms

Local error

Found 4 expressions with local error:

37.9b
(fmod (cosh c) (log1p a))
37.9b
(fmod (cosh c) (log1p a))
37.9b
(fmod (cosh c) (log1p a))
37.9b
(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))

series12.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

4.0ms
(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))

simplify47.0ms

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))

prune673.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 33.5b

regimes533.0ms

Accuracy

0% (0.0b remaining)

Error of 34.7b against oracle of 34.6b and baseline of 34.7b

bsearch2.0ms