Average Error: 34.1 → 34.1
Time: 30.5s
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 34.1

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

  3. Applied add-exp-log34.1

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

  5. Applied add-cube-cbrt34.1

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

  7. Applied add-cube-cbrt34.1

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

  8. Final simplification34.1

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

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 28.1s)Debug log

sample653.0ms

Algorithm
intervals
Results
699×(pre true 80)
243×(body exit 10240)
200×(body nan 80)
91×(body real 80)
67×(body real 1280)
54×(body real 640)
22×(body real 320)
16×(body real 160)
5×(body real 2560)
1×(body real 5120)

simplify14.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
14.0ms
(fmod (cosh c) (log1p a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize25.0ms

Local error

Found 1 expressions with local error:

38.2b
(fmod (cosh c) (log1p a))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
1×add-log-exp
1×log1p-expm1-u
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×*-un-lft-identity
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 9
Calls
1 calls:
Slowest
1.0ms
(fmod (cosh c) (log1p a))

series17.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
16.0ms
(fmod (cosh c) (log1p a))

simplify16.0ms

Counts
3 → 12
Calls
3 calls:
Slowest
5.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))

prune189.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 33.8b

localize5.0ms

Local error

Found 3 expressions with local error:

38.2b
(fmod (cosh c) (log1p a))
0.9b
(log (fmod (cosh c) (log1p a)))
0.5b
(exp (log (fmod (cosh c) (log1p a))))

rewrite4.0ms

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×log1p-expm1-u
3×exp-sum
3×add-cbrt-cube
3×expm1-log1p-u
2×log-pow
1×rem-exp-log
1×rem-log-exp
Counts
3 → 40
Calls
3 calls:
Slowest
2.0ms
(exp (log (fmod (cosh c) (log1p a))))
2.0ms
(log (fmod (cosh c) (log1p a)))
0.0ms
(fmod (cosh c) (log1p a))

series41.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
33.0ms
(log (fmod (cosh c) (log1p a)))
4.0ms
(exp (log (fmod (cosh c) (log1p a))))
4.0ms
(fmod (cosh c) (log1p a))

simplify563.0ms

Counts
21 → 49
Calls
21 calls:
Slowest
424.0ms
(exp (sqrt (log (fmod (cosh c) (log1p a)))))
19.0ms
(exp (* (cbrt (log (fmod (cosh c) (log1p a)))) (cbrt (log (fmod (cosh c) (log1p a))))))
19.0ms
(exp (log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a))))))
17.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
15.0ms
(exp (log (sqrt (fmod (cosh c) (log1p a)))))

prune604.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 33.8b

localize11.0ms

Local error

Found 4 expressions with local error:

38.2b
(fmod (cosh c) (log1p a))
38.2b
(fmod (cosh c) (log1p a))
38.2b
(fmod (cosh c) (log1p a))
0.9b
(log (fmod (cosh c) (log1p a)))

rewrite2.0ms

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×log1p-expm1-u
4×add-cbrt-cube
4×expm1-log1p-u
3×log-prod
1×log-pow
1×rem-log-exp
Counts
4 → 41
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))

series26.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
19.0ms
(log (fmod (cosh c) (log1p a)))
3.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))

simplify62.0ms

Counts
16 → 53
Calls
16 calls:
Slowest
10.0ms
(log (sqrt (fmod (cosh c) (log1p a))))
9.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
5.0ms
(log (fmod (cosh c) (log1p a)))
5.0ms
(log (fmod (cosh c) (log1p a)))
5.0ms
(log (fmod (cosh c) (log1p a)))

prune873.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 33.8b

localize21.0ms

Local error

Found 4 expressions with local error:

38.2b
(fmod (cosh c) (log1p a))
38.2b
(fmod (cosh c) (log1p a))
38.2b
(fmod (cosh c) (log1p a))
38.2b
(fmod (cosh c) (log1p a))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
4×log1p-expm1-u
4×add-cube-cbrt
4×add-exp-log
4×add-cbrt-cube
4×*-un-lft-identity
4×pow1
4×expm1-log1p-u
4×add-sqr-sqrt
Counts
4 → 36
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))

series16.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
4.0ms
(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))

simplify51.0ms

Counts
12 → 48
Calls
12 calls:
Slowest
5.0ms
(fmod (cosh c) (log1p a))
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))

prune780.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 33.8b

regimes809.0ms

Accuracy

0% (0.0b remaining)

Error of 34.1b against oracle of 34.0b and baseline of 34.1b

bsearch2.0ms

end0.0ms

sample23.3s

Algorithm
intervals
Results
21228×(pre true 80)
7918×(body exit 10240)
5310×(body nan 80)
2791×(body real 80)
2295×(body real 1280)
1628×(body real 640)
715×(body real 320)
398×(body real 160)
164×(body real 2560)
9×(body real 5120)