Average Error: 34.0 → 34.0
Time: 29.8s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.0

    \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]

  2. Final simplification34.0

    \[\leadsto \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]

Reproduce

herbie shell --seed 2019010 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 27.5s)Debug log

sample1.1s

Algorithm
intervals

simplify8.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize12.0ms

Local error

Found 1 expressions with local error:

39.6b
(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))

series10.0ms

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

simplify8.0ms

Counts
3 → 12
Calls
3 calls:
Slowest
3.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))

prune179.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 35.0b

localize7.0ms

Local error

Found 3 expressions with local error:

39.6b
(fmod (cosh c) (log1p a))
1.3b
(log (fmod (cosh c) (log1p a)))
0.7b
(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))

series27.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
22.0ms
(log (fmod (cosh c) (log1p a)))
3.0ms
(exp (log (fmod (cosh c) (log1p a))))
3.0ms
(fmod (cosh c) (log1p a))

simplify112.0ms

Counts
21 → 49
Calls
21 calls:
Slowest
22.0ms
(exp (* (cbrt (log (fmod (cosh c) (log1p a)))) (cbrt (log (fmod (cosh c) (log1p a))))))
12.0ms
(log (sqrt (fmod (cosh c) (log1p a))))
10.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
10.0ms
(exp (log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a))))))
8.0ms
(exp (log (sqrt (fmod (cosh c) (log1p a)))))

prune622.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 35.0b

localize11.0ms

Local error

Found 4 expressions with local error:

39.6b
(fmod (cosh c) (log1p a))
39.6b
(fmod (cosh c) (log1p a))
39.6b
(fmod (cosh c) (log1p a))
1.3b
(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))

series27.0ms

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))

simplify97.0ms

Counts
16 → 53
Calls
16 calls:
Slowest
10.0ms
(log (fmod (cosh c) (log1p a)))
10.0ms
(log (fmod (cosh c) (log1p a)))
9.0ms
(log (* (cbrt (fmod (cosh c) (log1p a))) (cbrt (fmod (cosh c) (log1p a)))))
9.0ms
(fmod (cosh c) (log1p a))
8.0ms
(log (sqrt (fmod (cosh c) (log1p a))))

prune934.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 35.0b

localize21.0ms

Local error

Found 4 expressions with local error:

39.6b
(fmod (cosh c) (log1p a))
39.6b
(fmod (cosh c) (log1p a))
39.6b
(fmod (cosh c) (log1p a))
39.6b
(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))

series19.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
5.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))
5.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))

simplify69.0ms

Counts
12 → 48
Calls
12 calls:
Slowest
8.0ms
(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))

prune692.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 35.0b

regimes638.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample22.9s

Algorithm
intervals