Average Error: 34.6 → 34.6
Time: 24.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\left(\left(\sqrt[3]{\left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\right)\right) \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.6

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

  3. Applied add-cube-cbrt34.6

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

  5. Applied add-cube-cbrt34.6

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

  6. Applied associate-*l*34.6

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

  8. Applied add-cube-cbrt34.6

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

  9. Final simplification34.6

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

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 22.8s)Debug log

sample668.0ms

Algorithm
intervals
Results
521.0ms238×body10240exit
67.0ms79×body1280valid
23.0ms46×body640valid
15.0ms175×body80nan
11.0ms100×body80valid
7.0ms20×body320valid
3.0ms10×body160valid
2.0ms1×body2560valid

simplify8.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
8.0ms
(fmod (cosh c) (log1p a))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize13.0ms

Local error

Found 1 expressions with local error:

36.3b
(fmod (cosh c) (log1p a))

rewrite2.0ms

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))

series29.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
29.0ms
(fmod (cosh c) (log1p a))

simplify13.0ms

Counts
3 → 12
Calls
3 calls:
Slowest
5.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))

prune156.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 32.0b

localize11.0ms

Local error

Found 4 expressions with local error:

36.3b
(fmod (cosh c) (log1p a))
36.3b
(fmod (cosh c) (log1p a))
0.1b
(* (sqrt (fmod (cosh c) (log1p a))) (sqrt (fmod (cosh c) (log1p a))))
0.0b
(sqrt (fmod (cosh c) (log1p a)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
9×add-cube-cbrt
9×*-un-lft-identity
9×pow1
6×add-exp-log
6×associate-*l*
6×associate-*r*
6×add-cbrt-cube
5×pow1/2
4×add-log-exp
4×log1p-expm1-u
4×expm1-log1p-u
2×pow-prod-up
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×sqrt-unprod
1×pow-plus
1×rem-square-sqrt
1×rem-sqrt-square
1×pow2
Counts
4 → 64
Calls
4 calls:
Slowest
13.0ms
(* (sqrt (fmod (cosh c) (log1p a))) (sqrt (fmod (cosh c) (log1p a))))
2.0ms
(sqrt (fmod (cosh c) (log1p a)))
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))

series33.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
18.0ms
(sqrt (fmod (cosh c) (log1p a)))
5.0ms
(fmod (cosh c) (log1p a))
5.0ms
(* (sqrt (fmod (cosh c) (log1p a))) (sqrt (fmod (cosh c) (log1p a))))
5.0ms
(fmod (cosh c) (log1p a))

simplify308.0ms

Counts
39 → 76
Calls
39 calls:
Slowest
50.0ms
(* (* (* (sqrt (fmod (cosh c) (log1p a))) (sqrt (fmod (cosh c) (log1p a)))) (sqrt (fmod (cosh c) (log1p a)))) (* (* (sqrt (fmod (cosh c) (log1p a))) (sqrt (fmod (cosh c) (log1p a)))) (sqrt (fmod (cosh c) (log1p a)))))
17.0ms
(+ (log (sqrt (fmod (cosh c) (log1p a)))) (log (sqrt (fmod (cosh c) (log1p a)))))
16.0ms
(sqrt (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
15.0ms
(* (sqrt (fmod (cosh c) (log1p a))) (sqrt (fmod (cosh c) (log1p a))))
15.0ms
(* (fmod (cosh c) (log1p a)) (fmod (cosh c) (log1p a)))

prune969.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 32.0b

localize17.0ms

Local error

Found 4 expressions with local error:

36.3b
(fmod (cosh c) (log1p a))
36.3b
(fmod (cosh c) (log1p a))
36.3b
(fmod (cosh c) (log1p a))
0.0b
(* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-cube-cbrt
8×*-un-lft-identity
8×add-sqr-sqrt
6×add-exp-log
6×associate-*l*
6×associate-*r*
6×cbrt-prod
4×add-log-exp
4×log1p-expm1-u
4×pow1/3
4×add-cbrt-cube
4×expm1-log1p-u
2×pow-prod-up
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 57
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (fmod (cosh c) (log1p a))) (cbrt (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))

series74.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(* (cbrt (fmod (cosh c) (log1p a))) (cbrt (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))

simplify194.0ms

Counts
32 → 69
Calls
32 calls:
Slowest
16.0ms
(pow (pow (fmod (cosh c) (log1p a)) 2) 1/3)
13.0ms
(cbrt (cbrt (fmod (cosh c) (log1p a))))
9.0ms
(pow (pow (fmod (cosh c) (log1p a)) 2) 1/3)
9.0ms
(cbrt (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
9.0ms
(cbrt (sqrt (fmod (cosh c) (log1p a))))

prune913.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.0b

localize15.0ms

Local error

Found 4 expressions with local error:

36.3b
(fmod (cosh c) (log1p a))
36.3b
(fmod (cosh c) (log1p a))
36.3b
(fmod (cosh c) (log1p a))
36.3b
(fmod (cosh c) (log1p a))

rewrite1.0ms

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))

series10.0ms

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

simplify35.0ms

Counts
12 → 48
Calls
12 calls:
Slowest
5.0ms
(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))
2.0ms
(fmod (cosh c) (log1p a))

prune708.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.0b

regimes598.0ms

Accuracy

0% (0.1b remaining)

Error of 34.6b against oracle of 34.5b and baseline of 34.6b

bsearch2.0ms

end0.0ms

sample18.0s

Algorithm
intervals
Results
13.1s7758×body10240exit
2.2s2418×body1280valid
792.0ms1535×body640valid
488.0ms778×body320valid
435.0ms5336×body80nan
285.0ms2713×body80valid
219.0ms150×body2560valid
81.0ms400×body160valid
11.0ms6×body5120valid