Details

Time bar (total: 22.3s)

sample137.0ms

Algorithm
intervals
Results
43.0ms54×body1280valid
30.0ms223×body80valid
26.0ms48×body640valid
11.0ms29×body320valid
4.0ms16×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize25.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.6b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
14.1b
(/ (pow t 3.0) (* l l))

rewrite598.0ms

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:
31.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
73.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
477.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
11.0ms
(/ (pow t 3.0) (* l l))

series1.5s

Counts
4 → 12
Calls
4 calls:
265.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
338.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
671.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
189.0ms
(/ (pow t 3.0) (* l l))

simplify120.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune497.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.1b

localize26.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
9.6b
(* (* (* (/ (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))

rewrite869.0ms

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:
134.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
28.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
681.0ms
(* (* (* (/ (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))

series1.5s

Counts
4 → 12
Calls
4 calls:
361.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
244.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
196.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
741.0ms
(* (* (* (/ (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))

simplify64.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013473795
150013312

prune989.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
3.7b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.6b
(* (* (* (/ (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))

rewrite1.5s

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:
148.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
229.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
28.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s
(* (* (* (/ (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))

series1.9s

Counts
4 → 12
Calls
4 calls:
285.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
581.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
238.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
755.0ms
(* (* (* (/ (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))

simplify135.0ms

Algorithm
egg-herbie
Counts
722 → 722
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0272711417
1500110598

prune3.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 6.2b

localize30.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0b
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
8.8b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
745×add-exp-log
479×prod-exp
210×div-exp
142×add-cbrt-cube
79×cbrt-unprod
75×pow-to-exp pow-exp
40×add-sqr-sqrt
36×associate-*l*
35×times-frac
32×*-un-lft-identity
30×cbrt-undiv
27×add-cube-cbrt
20×unpow-prod-down
18×associate-*l/
13×pow1
11×associate-*r/ associate-*r*
10×cbrt-prod
5×pow-prod-down associate-/l/ unswap-sqr
4×frac-times flip3-+ flip-+ add-log-exp sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 264
Calls
4 calls:
121.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
28.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
548.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
643.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
253.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
240.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
731.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
541.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify66.0ms

Algorithm
egg-herbie
Counts
276 → 276
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013565415
150024747

prune799.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 4.8b

regimes768.0ms

Accuracy

48% (4.2b remaining)

Error of 11.0b against oracle of 6.8b and baseline of 15.0b

bsearch394.0ms

Steps
ItersRangePoint
8
1.5975221450365432e+121
1.1260075732260117e+124
1.5486919747987578e+122
8
2.9180950556641497e-90
5.188698110549637e-86
2.797628997807244e-87
6
-1.1061742222619595e-161
-2.431471461127473e-162
-1.0912383422822797e-161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0104107
1104107

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.6s1971×body1280valid
901.0ms1757×body640valid
632.0ms5861×body80valid
318.0ms863×body320valid
109.0ms446×body160valid