Details

Time bar (total: 15.9s)

sample369.0ms

Algorithm
intervals
Results
197.0ms72×body10240exit
100.0ms69×body1280valid
41.0ms63×body640valid
9.0ms85×body80valid
8.0ms23×body320valid
4.0ms16×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.3b

Counts
2 → 1

localize13.0ms

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))
39.3b
(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:
1.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms
(expm1 (sin (expm1 a)))
2.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series68.0ms

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))
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
039248
144212
254212
368212
4114212
5228212
6919212
73184212
85001212

prune153.0ms

Filtered
40 candidates to 28 candidates (70.0%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New271340
Fresh000
Picked101
Done000
Total281341

Merged error: 32.9b

Counts
41 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (expm1 a))
0.6b
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
1.0b
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
39.3b
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
5×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 58
Calls
4 calls:
2.0ms
(sin (expm1 a))
2.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
2.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
1.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

series100.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sin (expm1 a))
6.0ms
(cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3))
34.0ms
(pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3)) a)

simplify127.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0112584
1390527
22787521
35001521

prune209.0ms

Filtered
70 candidates to 35 candidates (50.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New64670
Fresh01212
Picked101
Done000
Total651883

Merged error: 32.7b

Counts
83 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
0.6b
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0b
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
39.3b
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
26×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
12×pow1
7×add-exp-log pow1/3
6×unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
5×add-cbrt-cube
4×add-log-exp unswap-sqr
3×pow-unpow
2×cube-mult unpow3 pow-prod-down pow-sqr pow-prod-up sqr-pow
1×pow2 pow-to-exp pow-pow pow-plus pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 91
Calls
4 calls:
2.0ms
(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
9.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
1.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series221.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3))
182.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
33.0ms
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify176.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01861576
16941424
245751224
350021224

prune375.0ms

Filtered
103 candidates to 58 candidates (56.3%)
Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New949103
Fresh21517
Picked011
Done000
Total9625121

Merged error: 32.5b

Counts
121 → 25

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
39.3b
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
39.3b
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
39.3b
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×unpow-prod-down pow-unpow cube-prod
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 44
Calls
4 calls:
2.0ms
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
1.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
1.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
1.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

series42.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)
3.0ms
(fmod (cbrt (pow (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) 3)) a)

simplify131.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (120.0ms)

IterNodesCost
01001098
1351908
22713776
35001741

prune249.0ms

Filtered
56 candidates to 39 candidates (69.6%)
Pruning

28 alts after pruning (27 fresh and 1 done)

PrunedKeptTotal
New51556
Fresh12223
Picked101
Done011
Total532881

Merged error: 32.4b

Counts
81 → 28

regimes361.0ms

Accuracy

0% (1.9b remaining)

Error of 34.0b against oracle of 32.1b and baseline of 34.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02768
12768

end0.0ms

sample13.1s

Algorithm
intervals
Results
7.1s2622×body10240exit
4.0s2345×body1280valid
1.1s1653×body640valid
285.0ms2737×body80valid
275.0ms830×body320valid
93.0ms427×body160valid
23.0ms5×body5120valid
6.0ms3×body2560valid