Average Error: 34.0 → 33.6
Time: 37.9s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\left(\left(\cosh c\right) \bmod \left(\left(\sqrt[3]{\log_* (1 + a)} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}}\right)\right) \cdot e^{\log \left(\sqrt[3]{\sqrt[3]{\log_* (1 + a)} \cdot \sqrt[3]{\log_* (1 + a)}}\right)}\right)\right) \cdot \sqrt[3]{\log_* (1 + a)}\right)\right)\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.0

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

  3. Applied add-cube-cbrt33.7

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

  5. Applied add-cube-cbrt33.7

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

  6. Applied cbrt-prod33.6

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

  8. Applied add-exp-log33.6

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

  10. Applied add-cube-cbrt33.6

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

  11. Final simplification33.6

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

Reproduce

herbie shell --seed 2019004 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 30.4s)Debug log

sample1.1s

Algorithm
intervals

simplify34.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

33.0ms
(fmod (cosh c) (log1p a))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize26.0ms

Local error

Found 2 expressions with local error:

40.6b
(fmod (cosh c) (log1p a))
0.0b
(log1p a)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 14
Calls

2 calls. Slowest were:

2.0ms
(fmod (cosh c) (log1p a))
0.0ms
(log1p a)

series19.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

16.0ms
(fmod (cosh c) (log1p a))
3.0ms
(log1p a)

simplify19.0ms

Counts
6 → 20
Calls

6 calls. Slowest were:

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

prune297.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.0b

localize30.0ms

Local error

Found 4 expressions with local error:

40.7b
(fmod (cosh c) (* (* (cbrt (log1p a)) (cbrt (log1p a))) (cbrt (log1p a))))
0.6b
(cbrt (log1p a))
0.6b
(cbrt (log1p a))
0.6b
(cbrt (log1p a))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
4 → 40
Calls

4 calls. Slowest were:

2.0ms
(cbrt (log1p a))
1.0ms
(cbrt (log1p a))
1.0ms
(cbrt (log1p a))

series535.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

203.0ms
(cbrt (log1p a))
185.0ms
(cbrt (log1p a))
142.0ms
(cbrt (log1p a))
5.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (cbrt (log1p a))) (cbrt (log1p a))))

simplify46.0ms

Counts
21 → 52
Calls

21 calls. Slowest were:

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

prune762.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 34.1b

localize32.0ms

Local error

Found 4 expressions with local error:

40.7b
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))) (cbrt (cbrt (log1p a))))) (cbrt (log1p a))))
0.6b
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
0.6b
(cbrt (cbrt (log1p a)))
0.6b
(cbrt (log1p a))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 41
Calls

4 calls. Slowest were:

3.0ms
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
1.0ms
(cbrt (cbrt (log1p a)))
1.0ms
(cbrt (log1p a))

series521.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

200.0ms
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
178.0ms
(cbrt (cbrt (log1p a)))
140.0ms
(cbrt (log1p a))
3.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))) (cbrt (cbrt (log1p a))))) (cbrt (log1p a))))

simplify48.0ms

Counts
22 → 53
Calls

22 calls. Slowest were:

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

prune858.0ms

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 33.3b

localize44.0ms

Local error

Found 4 expressions with local error:

40.7b
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))))) (cbrt (cbrt (log1p a))))) (cbrt (log1p a))))
2.6b
(exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))))
0.6b
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
0.6b
(cbrt (cbrt (log1p a)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
4 → 47
Calls

4 calls. Slowest were:

9.0ms
(exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))))
5.0ms
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
1.0ms
(cbrt (cbrt (log1p a)))

series547.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

199.0ms
(exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))))
172.0ms
(cbrt (cbrt (log1p a)))
170.0ms
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
5.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))))) (cbrt (cbrt (log1p a))))) (cbrt (log1p a))))

simplify96.0ms

Counts
29 → 59
Calls

29 calls. Slowest were:

11.0ms
(exp (log (* (cbrt (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))) (cbrt (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))))))
7.0ms
(exp (* (cbrt (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))))) (cbrt (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))))))
5.0ms
(fmod (cosh c) (log1p a))

prune1.0s

Pruning

44 alts after pruning (44 fresh and 0 done)

Merged error: 32.8b

regimes1.8s

Accuracy

0% (2.5b remaining)

Error of 33.6b against oracle of 31.1b and baseline of 33.6b

bsearch2.0ms

end0.0ms

sample22.6s

Algorithm
intervals