Average Error: 34.6 → 34.6
Time: 24.5s
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 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 23.1s)Debug log

sample766.0ms

Algorithm
intervals
Results
558.0ms238×body10240exit
94.0ms79×body1280valid
32.0ms46×body640valid
21.0ms175×body80nan
15.0ms100×body80valid
9.0ms20×body320valid
4.0ms10×body160valid
3.0ms1×body2560valid

simplify38.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
37.0ms
(fmod (cosh c) (log1p a))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize16.0ms

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×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))

series10.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
9.0ms
(fmod (cosh c) (log1p a))

simplify9.0ms

Counts
3 → 10
Calls
3 calls:
Slowest
3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))

prune115.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 32.0b

localize7.0ms

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)))

rewrite10.0ms

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
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 → 56
Calls
4 calls:
Slowest
8.0ms
(* (sqrt (fmod (cosh c) (log1p a))) (sqrt (fmod (cosh c) (log1p a))))
1.0ms
(sqrt (fmod (cosh c) (log1p a)))
0.0ms
(fmod (cosh c) (log1p a))
0.0ms
(fmod (cosh c) (log1p a))

series21.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
12.0ms
(sqrt (fmod (cosh c) (log1p a)))
3.0ms
(* (sqrt (fmod (cosh c) (log1p a))) (sqrt (fmod (cosh c) (log1p a))))
3.0ms
(fmod (cosh c) (log1p a))
3.0ms
(fmod (cosh c) (log1p a))

simplify305.0ms

Counts
39 → 68
Calls
39 calls:
Slowest
34.0ms
(* (* (* (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)))))
16.0ms
(sqrt (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
16.0ms
(sqrt (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
16.0ms
(* (cbrt (sqrt (fmod (cosh c) (log1p a)))) (cbrt (sqrt (fmod (cosh c) (log1p a)))))
15.0ms
(sqrt (sqrt (fmod (cosh c) (log1p a))))

prune810.0ms

Pruning

14 alts after pruning (13 fresh and 1 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))
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×pow1/3
4×add-cbrt-cube
2×pow-prod-up
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 49
Calls
4 calls:
Slowest
10.0ms
(* (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))

series89.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
75.0ms
(* (cbrt (fmod (cosh c) (log1p a))) (cbrt (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))

simplify214.0ms

Counts
32 → 61
Calls
32 calls:
Slowest
16.0ms
(* (cbrt (cbrt (fmod (cosh c) (log1p a)))) (cbrt (cbrt (fmod (cosh c) (log1p a)))))
15.0ms
(pow (pow (fmod (cosh c) (log1p a)) 2) 1/3)
14.0ms
(cbrt (sqrt (fmod (cosh c) (log1p a))))
14.0ms
(sqrt (cbrt (fmod (cosh c) (log1p a))))
12.0ms
(cbrt (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))

prune715.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.0b

localize29.0ms

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))

rewrite2.0ms

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))

series17.0ms

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))

simplify64.0ms

Counts
12 → 40
Calls
12 calls:
Slowest
5.0ms
(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))
5.0ms
(fmod (cosh c) (log1p a))

prune620.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.0b

regimes687.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample18.5s

Algorithm
intervals
Results
13.6s7758×body10240exit
2.3s2418×body1280valid
821.0ms1535×body640valid
520.0ms5336×body80nan
310.0ms2713×body80valid
230.0ms778×body320valid
229.0ms150×body2560valid
85.0ms400×body160valid
12.0ms6×body5120valid