Details

Time bar (total: 42.4s)

sample1.6s

Algorithm
intervals
Results
904.0ms248×body10240exit
302.0ms102×body2560valid
107.0ms71×body1280valid
103.0ms509×body80nan
41.0ms44×body640valid
14.0ms20×body320valid
4.0ms10×body160valid
2.0ms9×body80valid
1.0ms1×body640nan
1.0ms1×body320nan
0.0ms1×body160nan

simplify96.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
96.0ms
(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize22.0ms

Local error

Found 3 expressions with local error:

58.6b
(fmod (cosh a) (* a a))
2.3b
(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
0.0b
(cosh a)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
1×acos-asin cosh-def
Counts
3 → 26
Calls
3 calls:
Slowest
3.0ms
(cosh a)
3.0ms
(acos (pow (fmod (cosh a) (* a a)) (log1p a)))
2.0ms
(fmod (cosh a) (* a a))

series89.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
70.0ms
(cosh a)
14.0ms
(fmod (cosh a) (* a a))
5.0ms
(acos (pow (fmod (cosh a) (* a a)) (log1p a)))

simplify469.0ms

Counts
9 → 35
Calls
9 calls:
Slowest
236.0ms
(* 1/2 (+ (exp (* -1 a)) (exp a)))
53.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
47.0ms
(+ (* 1/2 (pow a 2)) (+ (* 1/24 (pow a 4)) 1))
44.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
43.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune470.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 58.1b

localize26.0ms

Local error

Found 4 expressions with local error:

58.6b
(fmod (cosh a) (* a a))
11.5b
(log (exp (fmod (cosh a) (* a a))))
2.3b
(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0b
(cosh a)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log log-pow insert-posit16 add-log-exp
3×log-prod exp-prod
1×acos-asin cosh-def rem-log-exp
Counts
4 → 42
Calls
4 calls:
Slowest
3.0ms
(cosh a)
3.0ms
(log (exp (fmod (cosh a) (* a a))))
2.0ms
(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
0.0ms
(fmod (cosh a) (* a a))

series70.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
59.0ms
(cosh a)
5.0ms
(acos (pow (log (exp (fmod (cosh a) (* a a)))) (log1p a)))
3.0ms
(log (exp (fmod (cosh a) (* a a))))
3.0ms
(fmod (cosh a) (* a a))

simplify600.0ms

Counts
19 → 54
Calls
19 calls:
Slowest
173.0ms
(* 1/2 (+ (exp (* -1 a)) (exp a)))
64.0ms
(log (* (cbrt (exp (fmod (cosh a) (* a a)))) (cbrt (exp (fmod (cosh a) (* a a))))))
50.0ms
(log (sqrt (exp (fmod (cosh a) (* a a)))))
46.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
42.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune779.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 58.0b

localize64.0ms

Local error

Found 4 expressions with local error:

58.6b
(fmod (cosh a) (* a a))
58.6b
(fmod (cosh a) (* a a))
10.6b
(log (exp (sqrt (fmod (cosh a) (* a a)))))
2.3b
(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity log-pow add-cube-cbrt
6×exp-prod
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×log-prod sqrt-prod
1×acos-asin rem-log-exp
Counts
4 → 44
Calls
4 calls:
Slowest
6.0ms
(log (exp (sqrt (fmod (cosh a) (* a a)))))
3.0ms
(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))
1.0ms
(fmod (cosh a) (* a a))
0.0ms
(fmod (cosh a) (* a a))

series24.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
14.0ms
(log (exp (sqrt (fmod (cosh a) (* a a)))))
3.0ms
(fmod (cosh a) (* a a))
3.0ms
(fmod (cosh a) (* a a))
3.0ms
(acos (pow (* (sqrt (fmod (cosh a) (* a a))) (log (exp (sqrt (fmod (cosh a) (* a a)))))) (log1p a)))

simplify515.0ms

Counts
22 → 56
Calls
22 calls:
Slowest
57.0ms
(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
46.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))
41.0ms
(log (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a)))))))
39.0ms
(cbrt (sqrt (fmod (cosh a) (* a a))))
38.0ms
(acos (pow (fmod (cosh a) (pow a 2)) (log1p a)))

prune804.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 58.0b

localize35.0ms

Local error

Found 4 expressions with local error:

58.6b
(fmod (cosh a) (* a a))
58.6b
(fmod (cosh a) (* a a))
58.6b
(fmod (cosh a) (* a a))
10.7b
(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×log-pow
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×sqrt-pow1
6×pow1 log-prod exp-prod sqrt-prod
5×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
1×pow1/2 rem-log-exp
Counts
4 → 48
Calls
4 calls:
Slowest
4.0ms
(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
0.0ms
(fmod (cosh a) (* a a))
0.0ms
(fmod (cosh a) (* a a))
0.0ms
(fmod (cosh a) (* a a))

series174.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(log (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))
2.0ms
(fmod (cosh a) (* a a))
2.0ms
(fmod (cosh a) (* a a))
2.0ms
(fmod (cosh a) (* a a))

simplify701.0ms

Counts
26 → 60
Calls
26 calls:
Slowest
63.0ms
(log (* (cbrt (sqrt (exp (sqrt (fmod (cosh a) (* a a)))))) (cbrt (sqrt (exp (sqrt (fmod (cosh a) (* a a))))))))
54.0ms
(/ (sqrt (sqrt (fmod (cosh a) (* a a)))) 2)
53.0ms
(log (sqrt (* (cbrt (exp (sqrt (fmod (cosh a) (* a a))))) (cbrt (exp (sqrt (fmod (cosh a) (* a a))))))))
51.0ms
(/ (cbrt (sqrt (fmod (cosh a) (* a a)))) 2)
48.0ms
(/ (sqrt (cbrt (fmod (cosh a) (* a a)))) 2)

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 58.0b

regimes445.0ms

Accuracy

0% (0.2b remaining)

Error of 59.1b against oracle of 59.0b and baseline of 59.1b

bsearch6.0ms

end0.0ms

sample34.3s

Algorithm
intervals
Results
20.2s7881×body10240exit
7.2s3183×body2560valid
2.9s2550×body1280valid
2.1s16084×body80nan
881.0ms1217×body640valid
313.0ms593×body320valid
129.0ms323×body160valid
24.0ms134×body80valid
14.0ms9×body2560nan
11.0ms4×body5120nan
8.0ms10×body1280nan
6.0ms9×body640nan
4.0ms9×body320nan
2.0ms8×body160nan