Average Error: 34.1 → 33.7
Time: 34.4s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\left(\left(\cosh c\right) \bmod \left(\sqrt[3]{\log_* (1 + a)} \cdot \left(\left(\sqrt[3]{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)} \cdot \sqrt[3]{\log_* (1 + a)}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\log_* (1 + a)}} \cdot \sqrt[3]{\sqrt[3]{\log_* (1 + a)}}\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\log_* (1 + a)}} \cdot \sqrt[3]{\sqrt[3]{\log_* (1 + a)}}\right)\right) \cdot \sqrt[3]{\log_* (1 + a)}\right)\right)\right)\]

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-cube-cbrt33.7

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

  5. Applied add-cube-cbrt33.7

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

  7. Applied add-cbrt-cube33.7

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

  9. Applied add-cube-cbrt33.7

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

  10. Applied cbrt-prod33.7

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

  11. Applied cbrt-prod33.7

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

  12. Final simplification33.7

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

Reproduce

herbie shell --seed 2019021 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 29.1s)Debug log

sample745.0ms

Algorithm
intervals
Results
500.0ms260×body10240exit
69.0ms72×body1280valid
45.0ms78×body80valid
44.0ms184×body80nan
33.0ms57×body640valid
11.0ms31×body320valid
8.0ms4×body2560valid
4.0ms15×body160valid

simplify13.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(fmod (cosh c) (log1p a))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize12.0ms

Local error

Found 3 expressions with local error:

41.3b
(fmod (cosh c) (log1p a))
0.0b
(log1p a)
0.0b
(cosh c)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
3×add-cube-cbrt
3×add-exp-log
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×add-sqr-sqrt
1×cosh-def
Counts
3 → 22
Calls
3 calls:
Slowest
1.0ms
(fmod (cosh c) (log1p a))
1.0ms
(cosh c)
0.0ms
(log1p a)

series90.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
78.0ms
(cosh c)
10.0ms
(fmod (cosh c) (log1p a))
2.0ms
(log1p a)

simplify108.0ms

Counts
9 → 31
Calls
9 calls:
Slowest
40.0ms
(* 1/2 (+ (exp (* -1 c)) (exp c)))
24.0ms
(+ (* 1/2 (pow c 2)) (+ (* 1/24 (pow c 4)) 1))
21.0ms
(* 1/2 (+ (exp c) (exp (- c))))
6.0ms
(fmod (cosh c) (log1p a))
6.0ms
(fmod (cosh c) (log1p a))

prune350.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 35.3b

localize21.0ms

Local error

Found 4 expressions with local error:

41.3b
(fmod (cosh c) (* (* (cbrt (log1p a)) (cbrt (log1p a))) (cbrt (log1p a))))
0.6b
(cbrt (log1p a))
0.6b
(cbrt (log1p a))
0.6b
(cbrt (log1p a))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-cube-cbrt
7×*-un-lft-identity
7×add-sqr-sqrt
4×add-log-exp
4×add-exp-log
4×add-cbrt-cube
4×pow1
3×pow1/3
Counts
4 → 40
Calls
4 calls:
Slowest
1.0ms
(cbrt (log1p a))
0.0ms
(cbrt (log1p a))
0.0ms
(cbrt (log1p a))
0.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (cbrt (log1p a))) (cbrt (log1p a))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(cbrt (log1p a))
153.0ms
(cbrt (log1p a))
136.0ms
(cbrt (log1p a))
3.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (cbrt (log1p a))) (cbrt (log1p a))))

simplify58.0ms

Counts
21 → 52
Calls
21 calls:
Slowest
5.0ms
(pow (log1p a) 1/3)
5.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))
3.0ms
(pow (log1p a) 1/3)

prune680.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 34.4b

localize34.0ms

Local error

Found 4 expressions with local error:

41.3b
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a))))) (cbrt (log1p a))))
0.6b
(cbrt (cbrt (log1p a)))
0.6b
(cbrt (cbrt (log1p a)))
0.6b
(cbrt (cbrt (log1p a)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
10×add-cube-cbrt
10×*-un-lft-identity
10×add-sqr-sqrt
4×add-log-exp
4×add-exp-log
4×add-cbrt-cube
4×pow1
3×pow1/3
Counts
4 → 49
Calls
4 calls:
Slowest
1.0ms
(cbrt (cbrt (log1p a)))
1.0ms
(cbrt (cbrt (log1p a)))
1.0ms
(cbrt (cbrt (log1p a)))
0.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a))))) (cbrt (log1p a))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(cbrt (cbrt (log1p a)))
165.0ms
(cbrt (cbrt (log1p a)))
148.0ms
(cbrt (cbrt (log1p a)))
6.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a))))) (cbrt (log1p a))))

simplify64.0ms

Counts
30 → 61
Calls
30 calls:
Slowest
4.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))
3.0ms
(cbrt (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))))
3.0ms
(cbrt (cbrt 1))

prune976.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 34.1b

localize20.0ms

Local error

Found 4 expressions with local error:

41.3b
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a))))))) (cbrt (log1p a))))
0.6b
(cbrt (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a)))))
0.6b
(cbrt (cbrt (log1p a)))
0.6b
(cbrt (cbrt (log1p a)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
19×cbrt-prod
8×add-cube-cbrt
8×*-un-lft-identity
8×add-sqr-sqrt
4×add-log-exp
4×add-exp-log
4×add-cbrt-cube
4×pow1
3×pow1/3
1×rem-cbrt-cube
1×pow3
Counts
4 → 45
Calls
4 calls:
Slowest
17.0ms
(cbrt (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a)))))
2.0ms
(cbrt (cbrt (log1p a)))
1.0ms
(cbrt (cbrt (log1p a)))
0.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a))))))) (cbrt (log1p a))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(cbrt (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a)))))
174.0ms
(cbrt (cbrt (log1p a)))
149.0ms
(cbrt (cbrt (log1p a)))
7.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (* (* (cbrt (cbrt (log1p a))) (cbrt (cbrt (log1p a)))) (cbrt (cbrt (log1p a))))))) (cbrt (log1p a))))

simplify39.0ms

Counts
26 → 57
Calls
26 calls:
Slowest
4.0ms
(fmod (cosh c) (log1p a))
4.0ms
(fmod (cosh c) (log1p a))
2.0ms
(fmod (cosh c) (log1p a))
1.0ms
(pow (log1p a) 1/9)
1.0ms
(cbrt (cbrt 1))

prune776.0ms

Pruning

43 alts after pruning (43 fresh and 0 done)

Merged error: 33.9b

regimes1.6s

Accuracy

0% (1.9b remaining)

Error of 33.7b against oracle of 31.8b and baseline of 33.7b

bsearch5.0ms

end0.0ms

sample22.0s

Algorithm
intervals
Results
16.5s7745×body10240exit
2.4s2292×body1280valid
1.3s1571×body640valid
468.0ms5059×body80nan
346.0ms154×body2560valid
319.0ms2789×body80valid
276.0ms769×body320valid
138.0ms415×body160valid
31.0ms12×body5120valid