Details

Time bar (total: 21.9s)

sample146.0ms

Algorithm
intervals
Results
58.0ms70×body1280valid
32.0ms51×body640valid
21.0ms179×body80valid
15.0ms38×body320valid
4.0ms14×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize22.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.9b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.3b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.7b
(/ (pow t 3.0) (* l l))

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×flip3-+ flip-+ add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 144
Calls
4 calls:
33.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
284.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
320.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
247.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
634.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
183.0ms
(/ (pow t 3.0) (* l l))

simplify117.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08011619
146461348
250021348

prune515.0ms

Filtered
156 candidates to 93 candidates (59.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 17.1b

localize31.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.5b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.3b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite538.0ms

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
184×prod-exp
78×add-cbrt-cube
77×div-exp
50×add-sqr-sqrt
49×times-frac
44×associate-*l/ cbrt-unprod
42×*-un-lft-identity
37×add-cube-cbrt
36×associate-*l*
34×frac-times
33×pow-exp
29×pow1
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
12×cbrt-undiv
11×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+ sqr-pow
5×associate-/l* unswap-sqr
4×add-log-exp
3×associate-/r* *-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 229
Calls
4 calls:
74.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
19.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
427.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
348.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
227.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
188.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
899.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013473795
150013312

prune979.0ms

Filtered
241 candidates to 150 candidates (62.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.3b

localize25.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.2b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.3b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1050×add-exp-log
674×times-frac
554×prod-exp
435×div-exp
404×unpow-prod-down
381×associate-*l*
343×add-sqr-sqrt
335×*-un-lft-identity
330×add-cube-cbrt
202×cbrt-prod
151×add-cbrt-cube
145×pow-to-exp pow-exp
78×cbrt-unprod
68×sqr-pow
47×associate-*l/
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r* div-inv
8×flip3-+ flip-+
5×unswap-sqr
4×*-commutative add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 710
Calls
4 calls:
120.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
162.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
17.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
771.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
280.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
357.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
237.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
723.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify139.0ms

Algorithm
egg-herbie
Counts
722 → 722
Iterations

Useful iterations: 1 (46.0ms)

IterNodesCost
0272711417
1500110598

prune3.4s

Filtered
722 candidates to 479 candidates (66.3%)
Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 10.4b

localize30.0ms

Local error

Found 4 expressions with local error:

2.8b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.6b
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
10.2b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite875.0ms

Algorithm
rewrite-expression-head
Rules
576×add-exp-log
347×prod-exp
183×div-exp
128×times-frac
103×add-cbrt-cube
80×add-sqr-sqrt
72×*-un-lft-identity
67×pow-to-exp add-cube-cbrt pow-exp
56×unpow-prod-down
53×cbrt-unprod
36×associate-*l*
34×associate-/r*
28×cbrt-prod associate-*l/
25×associate-*r/
23×cbrt-undiv
19×frac-times
14×tan-quot
13×pow1
11×associate-*r* associate-/l/
10×sqr-pow
8×flip3-+ flip-+
5×pow-prod-down unswap-sqr
4×div-inv add-log-exp
3×*-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/ associate-/l*
Counts
4 → 320
Calls
4 calls:
69.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
20.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
353.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
409.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
356.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
243.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
736.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
820.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify82.0ms

Algorithm
egg-herbie
Counts
332 → 332
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
017406179
150015668

prune1.2s

Filtered
332 candidates to 191 candidates (57.5%)
Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 7.7b

regimes834.0ms

Accuracy

60.1% (3.1b remaining)

Error of 10.2b against oracle of 7.1b and baseline of 14.9b

bsearch382.0ms

Steps
ItersRangePoint
10
6.827947625729461e-55
1.864034737252073e-41
3.0615551016496975e-53
10
-1.9927515259520666e-38
-8.070824475818105e-54
-5.029816013444314e-47

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06355
16355

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.9s2050×body1280valid
921.0ms1691×body640valid
683.0ms5907×body80valid
320.0ms834×body320valid
108.0ms412×body160valid