Average Error: 34.0 → 33.6
Time: 44.7s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\left(\left(\cosh c\right) \bmod \left(\left(\sqrt[3]{\log_* (1 + a)} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}}\right)\right) \cdot e^{\log \left(\sqrt[3]{\sqrt[3]{\log_* (1 + a)} \cdot \sqrt[3]{\log_* (1 + a)}}\right)}\right)\right) \cdot \sqrt[3]{\log_* (1 + a)}\right)\right)\]

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. 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

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

  6. Applied cbrt-prod33.6

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

  8. Applied add-exp-log33.6

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

  10. Applied add-cube-cbrt33.6

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

  11. Final simplification33.6

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

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 38.2s)Debug log

sample1.1s

Algorithm
intervals

simplify8.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

8.0ms
(fmod (cosh c) (log1p a))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize27.0ms

Local error

Found 2 expressions with local error:

40.6b
(fmod (cosh c) (log1p a))
0.0b
(log1p a)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 19
Calls

2 calls. Slowest were:

1.0ms
(fmod (cosh c) (log1p a))
1.0ms
(log1p a)

series41.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

30.0ms
(log1p a)
11.0ms
(fmod (cosh c) (log1p a))

simplify934.0ms

Counts
6 → 25
Calls

6 calls. Slowest were:

369.0ms
(- (+ (/ 1 a) (log -1)) (+ (* 1/2 (/ 1 (pow a 2))) (log (/ -1 a))))
303.0ms
(- (+ a (* 1/3 (pow a 3))) (* 1/2 (pow a 2)))
246.0ms
(- (/ 1 a) (+ (* 1/2 (/ 1 (pow a 2))) (log (/ 1 a))))

prune335.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.0b

localize20.0ms

Local error

Found 4 expressions with local error:

40.7b
(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))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 48
Calls

4 calls. Slowest were:

4.0ms
(cbrt (log1p a))
1.0ms
(cbrt (log1p a))
1.0ms
(cbrt (log1p a))

series148.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

51.0ms
(cbrt (log1p a))
48.0ms
(cbrt (log1p a))
46.0ms
(cbrt (log1p a))
4.0ms
(fmod (cosh c) (* (* (cbrt (log1p a)) (cbrt (log1p a))) (cbrt (log1p a))))

simplify2.9s

Counts
21 → 60
Calls

21 calls. Slowest were:

502.0ms
(- (+ (* 1/3 (* (/ 1 a) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 2)) 1/3))) (pow (- (log -1) (log (/ -1 a))) 1/3)) (+ (* 1/6 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 2)) 1/3))) (* 1/9 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 5)) 1/3)))))
484.0ms
(- (+ (pow (- (log (/ 1 a))) 1/3) (* 1/6 (* (/ 1 (pow a 2)) (pow (/ -1 (pow (log (/ 1 a)) 2)) 1/3)))) (+ (* 1/9 (* (/ 1 (pow a 2)) (pow (/ -1 (pow (log (/ 1 a)) 5)) 1/3))) (* 1/3 (* (/ 1 a) (pow (/ -1 (pow (log (/ 1 a)) 2)) 1/3)))))
453.0ms
(- (+ (* 1/3 (* (/ 1 a) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 2)) 1/3))) (pow (- (log -1) (log (/ -1 a))) 1/3)) (+ (* 1/6 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 2)) 1/3))) (* 1/9 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 5)) 1/3)))))

prune827.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 34.1b

localize19.0ms

Local error

Found 4 expressions with local error:

40.7b
(fmod (cosh c) (* (* (* (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))) (cbrt (cbrt (log1p a)))) (cbrt (log1p a))) (cbrt (log1p a))))
0.6b
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
0.6b
(cbrt (cbrt (log1p a)))
0.6b
(cbrt (log1p a))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
4 → 49
Calls

4 calls. Slowest were:

3.0ms
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
1.0ms
(cbrt (cbrt (log1p a)))
1.0ms
(cbrt (log1p a))

series229.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

102.0ms
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
63.0ms
(cbrt (cbrt (log1p a)))
60.0ms
(cbrt (log1p a))
3.0ms
(fmod (cosh c) (* (* (* (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))) (cbrt (cbrt (log1p a)))) (cbrt (log1p a))) (cbrt (log1p a))))

simplify2.3s

Counts
22 → 61
Calls

22 calls. Slowest were:

463.0ms
(- (+ (* 1/3 (* (/ 1 a) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 2)) 1/3))) (pow (- (log -1) (log (/ -1 a))) 1/3)) (+ (* 1/6 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 2)) 1/3))) (* 1/9 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 5)) 1/3)))))
398.0ms
(- (+ (pow (pow (log (/ 1 a)) 2) 1/9) (* 1/9 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (log (/ 1 a)) 7)) 1/9)))) (+ (* 2/9 (* (/ 1 a) (pow (/ 1 (pow (log (/ 1 a)) 7)) 1/9))) (* 7/81 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (log (/ 1 a)) 16)) 1/9)))))
381.0ms
(- (+ (pow (- (log (/ 1 a))) 1/3) (* 1/6 (* (/ 1 (pow a 2)) (pow (/ -1 (pow (log (/ 1 a)) 2)) 1/3)))) (+ (* 1/9 (* (/ 1 (pow a 2)) (pow (/ -1 (pow (log (/ 1 a)) 5)) 1/3))) (* 1/3 (* (/ 1 a) (pow (/ -1 (pow (log (/ 1 a)) 2)) 1/3)))))

prune1.3s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 33.4b

localize44.0ms

Local error

Found 4 expressions with local error:

40.7b
(fmod (cosh c) (* (* (* (exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))))) (cbrt (cbrt (log1p a)))) (cbrt (log1p a))) (cbrt (log1p a))))
2.6b
(exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))))
0.6b
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
0.6b
(cbrt (cbrt (log1p a)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
4 → 55
Calls

4 calls. Slowest were:

10.0ms
(exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))))
6.0ms
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
2.0ms
(cbrt (cbrt (log1p a)))

series219.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

91.0ms
(exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))))
63.0ms
(cbrt (cbrt (log1p a)))
58.0ms
(cbrt (* (cbrt (log1p a)) (cbrt (log1p a))))
7.0ms
(fmod (cosh c) (* (* (* (exp (log (cbrt (* (cbrt (log1p a)) (cbrt (log1p a)))))) (cbrt (cbrt (log1p a)))) (cbrt (log1p a))) (cbrt (log1p a))))

simplify1.9s

Counts
29 → 67
Calls

29 calls. Slowest were:

422.0ms
(- (+ (pow (pow (log (/ 1 a)) 2) 1/9) (* 1/9 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (log (/ 1 a)) 7)) 1/9)))) (+ (* 2/9 (* (/ 1 a) (pow (/ 1 (pow (log (/ 1 a)) 7)) 1/9))) (* 7/81 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (log (/ 1 a)) 16)) 1/9)))))
386.0ms
(- (+ (pow (- (log -1) (log (/ -1 a))) 1/9) (* 1/9 (* (/ 1 a) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 8)) 1/9)))) (+ (* 4/81 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 17)) 1/9))) (* 1/18 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (- (log -1) (log (/ -1 a))) 8)) 1/9)))))
385.0ms
(- (+ (pow (pow (log (/ 1 a)) 2) 1/9) (* 1/9 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (log (/ 1 a)) 7)) 1/9)))) (+ (* 2/9 (* (/ 1 a) (pow (/ 1 (pow (log (/ 1 a)) 7)) 1/9))) (* 7/81 (* (/ 1 (pow a 2)) (pow (/ 1 (pow (log (/ 1 a)) 16)) 1/9)))))

prune1.3s

Pruning

45 alts after pruning (45 fresh and 0 done)

Merged error: 32.8b

regimes1.9s

Accuracy

0% (2.5b remaining)

Error of 33.6b against oracle of 31.1b and baseline of 33.6b

bsearch2.0ms

end0.0ms

sample22.6s

Algorithm
intervals