Details

Time bar (total: 15.6s)

sample421.0ms

Algorithm
intervals
Results
221.0ms88×body10240exit
119.0ms73×body1280valid
43.0ms55×body640valid
14.0ms88×body80valid
8.0ms26×body320valid
3.0ms14×body160valid

simplify2.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b
(expm1 (sin (expm1 a)))
0.2b
(sin (expm1 a))
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
Counts
4 → 28
Calls
4 calls:
0.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0ms
(expm1 (sin (expm1 a)))
1.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series74.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms
(expm1 (sin (expm1 a)))
62.0ms
(sin (expm1 a))
9.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify120.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
039248
144212
254212
368212
4114212
5228212
6919212
73184212
85001212

prune161.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 32.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (expm1 a))
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
Counts
4 → 28
Calls
4 calls:
1.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series64.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sin (expm1 a))
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify100.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
023300
126256
232256
340256
468256
5142256
6643256
72176256
85001256

prune215.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
38.8b
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×add-cube-cbrt *-un-lft-identity
11×pow1
6×add-exp-log pow1/3 swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 61
Calls
4 calls:
8.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series183.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify53.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0104703
1308616
21499509
35001499

prune451.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 32.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
38.8b
(fmod (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
38.8b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod unpow-prod-down
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log
4×add-cbrt-cube add-log-exp
3×pow-unpow
2×pow-pow
1×pow-to-exp pow1/3 pow-exp sqr-pow
Counts
4 → 45
Calls
4 calls:
3.0ms
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
0.0ms
(fmod (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series199.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(pow (cbrt (cbrt (sin (expm1 a)))) 4)
3.0ms
(fmod (atan2 (expm1 (* (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (pow (cbrt (cbrt (sin (expm1 a)))) 4)) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify58.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0134647
1369562
21334555
35001555

prune311.0ms

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 31.9b

regimes511.0ms

Accuracy

0% (1.8b remaining)

Error of 33.4b against oracle of 31.6b and baseline of 33.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03058
13058

end0.0ms

sample12.5s

Algorithm
intervals
Results
6.6s2609×body10240exit
3.9s2259×body1280valid
1.2s1730×body640valid
283.0ms2815×body80valid
264.0ms783×body320valid
88.0ms410×body160valid
10.0ms2×body5120valid
2.0ms1×body2560valid