Average Error: 34.4 → 34.4
Time: 27.4s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[e^{\sqrt[3]{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}} \cdot \left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.4

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

  3. Applied add-exp-log34.4

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

  5. Applied add-cube-cbrt34.4

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

  7. Applied add-cube-cbrt34.4

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

  8. Final simplification34.4

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

Reproduce

herbie shell --seed 2019018 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 25.7s)Debug log

sample547.0ms

Algorithm
intervals
Results
373.0ms208×body10240exit
61.0ms76×body1280valid
32.0ms84×body80valid
25.0ms50×body640valid
15.0ms183×body80nan
10.0ms31×body320valid
8.0ms4×body2560valid
3.0ms12×body160valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(fmod (cosh c) (log1p a))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize15.0ms

Local error

Found 1 expressions with local error:

39.8b
(fmod (cosh c) (log1p a))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
1×add-log-exp
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×*-un-lft-identity
1×pow1
1×add-sqr-sqrt
Counts
1 → 7
Calls
1 calls:
Slowest
1.0ms
(fmod (cosh c) (log1p a))

series14.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
13.0ms
(fmod (cosh c) (log1p a))

simplify9.0ms

Counts
3 → 10
Calls
3 calls:
Slowest
4.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))

prune144.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 35.1b

localize14.0ms

Local error

Found 3 expressions with local error:

39.8b
(fmod (cosh c) (log1p a))
0.7b
(log (fmod (cosh c) (log1p a)))
0.5b
(exp (log (fmod (cosh c) (log1p a))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×add-cube-cbrt
6×*-un-lft-identity
6×log-prod
6×add-sqr-sqrt
5×pow1
4×add-exp-log
4×exp-prod
3×add-log-exp
3×exp-sum
3×add-cbrt-cube
2×log-pow
1×rem-exp-log
1×rem-log-exp
Counts
3 → 34
Calls
3 calls:
Slowest
4.0ms
(exp (log (fmod (cosh c) (log1p a))))
3.0ms
(log (fmod (cosh c) (log1p a)))
0.0ms
(fmod (cosh c) (log1p a))

series45.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
35.0ms
(log (fmod (cosh c) (log1p a)))
5.0ms
(exp (log (fmod (cosh c) (log1p a))))
5.0ms
(fmod (cosh c) (log1p a))

simplify174.0ms

Counts
21 → 43
Calls
21 calls:
Slowest
19.0ms
(exp (* (cbrt (log (fmod (cosh c) (log1p a)))) (cbrt (log (fmod (cosh c) (log1p a))))))
18.0ms
(exp (log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a))))))
18.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
17.0ms
(exp (log (sqrt (fmod (cosh c) (log1p a)))))
15.0ms
(exp (sqrt (log (fmod (cosh c) (log1p a)))))

prune607.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 35.1b

localize23.0ms

Local error

Found 4 expressions with local error:

39.8b
(fmod (cosh c) (log1p a))
39.8b
(fmod (cosh c) (log1p a))
39.8b
(fmod (cosh c) (log1p a))
0.7b
(log (fmod (cosh c) (log1p a)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
5×add-cube-cbrt
5×add-exp-log
5×*-un-lft-identity
5×pow1
5×add-sqr-sqrt
4×add-log-exp
4×add-cbrt-cube
3×log-prod
1×log-pow
1×rem-log-exp
Counts
4 → 33
Calls
4 calls:
Slowest
1.0ms
(log (fmod (cosh c) (log1p a)))
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))

series45.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
30.0ms
(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))

simplify83.0ms

Counts
16 → 45
Calls
16 calls:
Slowest
15.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
14.0ms
(log (sqrt (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))

prune709.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 35.1b

localize11.0ms

Local error

Found 4 expressions with local error:

39.8b
(fmod (cosh c) (log1p a))
39.8b
(fmod (cosh c) (log1p a))
39.8b
(fmod (cosh c) (log1p a))
39.8b
(fmod (cosh c) (log1p a))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
4×add-cube-cbrt
4×add-exp-log
4×add-cbrt-cube
4×*-un-lft-identity
4×pow1
4×add-sqr-sqrt
Counts
4 → 28
Calls
4 calls:
Slowest
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))

series11.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))

simplify53.0ms

Counts
12 → 40
Calls
12 calls:
Slowest
7.0ms
(fmod (cosh c) (log1p a))
6.0ms
(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))

prune709.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 35.1b

regimes413.0ms

Accuracy

0% (0.0b remaining)

Error of 34.4b against oracle of 34.3b and baseline of 34.4b

bsearch2.0ms

end0.0ms

sample22.0s

Algorithm
intervals
Results
15.8s7628×body10240exit
2.7s2301×body1280valid
1.2s1568×body640valid
482.0ms5142×body80nan
372.0ms186×body2560valid
368.0ms2741×body80valid
367.0ms781×body320valid
144.0ms414×body160valid
26.0ms9×body5120valid