Details

Time bar (total: 15.7s)

sample119.0ms

Algorithm
intervals
Results
39.0ms59×body1280valid
31.0ms70×body640valid
19.0ms164×body80valid
9.0ms29×body320valid
4.0ms16×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.3b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (pow t 3.0) (sin k))
3.1b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
5.6b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
27.2b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
73×times-frac
56×add-sqr-sqrt
50×div-exp
41×add-cube-cbrt *-un-lft-identity
40×prod-exp
33×associate-*l*
30×cbrt-undiv
22×cbrt-unprod
11×div-inv
10×associate-*r*
8×associate-/l*
7×unswap-sqr
6×pow1 associate-/r*
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative sqr-pow
1×frac-times associate-*r/ pow-prod-down associate-*l/ associate-/l/
Counts
4 → 184
Calls
4 calls:
5.0ms
(* (pow t 3.0) (sin k))
9.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
8.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
17.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (pow t 3.0) (sin k))
336.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
75.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
885.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010192396
150011978

prune712.0ms

Filtered
196 candidates to 138 candidates (70.4%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New18511196
Fresh011
Picked011
Done000
Total18513198

Merged error: 26.7b

Counts
198 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (pow t 3.0) (sin k))
2.6b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
5.4b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
20.3b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
49×prod-exp
41×div-exp
33×add-sqr-sqrt
27×cbrt-unprod
25×cbrt-undiv
22×associate-*l*
21×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
8×pow1
6×unswap-sqr
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-/r* *-commutative
2×tan-quot pow-prod-down associate-/r/ sqr-pow
1×frac-times frac-2neg associate-*r/ clear-num associate-/l/ associate-/l*
Counts
4 → 150
Calls
4 calls:
6.0ms
(* (pow t 3.0) (sin k))
10.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
8.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
16.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
178.0ms
(* (pow t 3.0) (sin k))
463.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
355.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
897.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify125.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09131905
148941506
250011506

prune516.0ms

Filtered
162 candidates to 103 candidates (63.6%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1566162
Fresh7411
Picked101
Done011
Total16411175

Merged error: 26.2b

Counts
175 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.6b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
5.4b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
20.3b
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
436×add-exp-log
240×prod-exp
146×div-exp
100×add-cbrt-cube
48×pow-exp
40×cbrt-unprod
34×cbrt-undiv
33×add-sqr-sqrt
32×pow-to-exp
28×times-frac
26×add-cube-cbrt *-un-lft-identity
16×associate-*r*
15×associate-*l*
8×pow1
6×associate-/r*
5×div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*l/ unswap-sqr
2×tan-quot frac-2neg pow-prod-down clear-num associate-/r/ *-commutative
1×frac-times associate-*r/ associate-/l/
Counts
4 → 208
Calls
4 calls:
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
14.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
17.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
21.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.2s

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
512.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
605.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
978.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify58.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011653923
150013194

prune638.0ms

Filtered
220 candidates to 108 candidates (49.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2164220
Fresh279
Picked101
Done011
Total21912231

Merged error: 24.0b

Counts
231 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0))
1.9b
(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
2.6b
(/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
20.3b
(* (/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
1478×add-exp-log
766×prod-exp
565×div-exp
253×add-cbrt-cube
141×cbrt-unprod
136×pow-exp
111×cbrt-undiv
86×pow-to-exp
26×times-frac
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
17×associate-*l*
14×associate-*r*
11×pow1
8×associate-/r*
7×associate-*l/
5×div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×frac-times unpow-prod-down associate-*r/ associate-/l/ sqr-pow
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative associate-/l* unswap-sqr
Counts
4 → 392
Calls
4 calls:
8.0ms
(/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0))
17.0ms
(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
26.0ms
(/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
30.0ms
(* (/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.6s

Counts
4 → 12
Calls
4 calls:
488.0ms
(/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0))
475.0ms
(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
582.0ms
(/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
1.0s
(* (/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify110.0ms

Algorithm
egg-herbie
Counts
404 → 404
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
018389721
150018121

prune778.0ms

Filtered
404 candidates to 123 candidates (30.4%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New3995404
Fresh01010
Picked101
Done011
Total40016416

Merged error: 21.1b

Counts
416 → 16

regimes602.0ms

Accuracy

0% (2.9b remaining)

Error of 21.4b against oracle of 18.5b and baseline of 21.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03230
13230

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2066×body1280valid
789.0ms1690×body640valid
609.0ms5869×body80valid
293.0ms894×body320valid
94.0ms416×body160valid