Details

Time bar (total: 20.5s)

sample184.0ms

Algorithm
intervals
Results
84.0ms78×body1280valid
36.0ms210×body80valid
30.0ms43×body640valid
13.0ms25×body320valid
5.0ms13×body160valid

simplify29.0ms

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: 34.5b

localize21.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.4b
(* (/ (pow t 3.0) (* l l)) (sin k))
15.6b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.3b
(/ (pow t 3.0) (* l l))

rewrite348.0ms

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))
15.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
288.0ms
(* (* (* (/ (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:
336.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
256.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
649.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
185.0ms
(/ (pow t 3.0) (* l l))

simplify116.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08011619
146461348
250021348

prune516.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.3b

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.3b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.6b
(* (* (* (/ (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))

rewrite564.0ms

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:
77.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
447.0ms
(* (* (* (/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
368.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
238.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
202.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
755.0ms
(* (* (* (/ (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))

simplify67.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013473795
150013312

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.6b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite734.0ms

Algorithm
rewrite-expression-head
Rules
1369×add-exp-log
791×prod-exp
489×div-exp
224×pow-exp
134×pow-to-exp
115×add-cbrt-cube
63×cbrt-unprod
44×associate-*l/
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×frac-times times-frac
30×pow1 add-cube-cbrt
26×unpow-prod-down
25×cbrt-undiv
17×pow-prod-down
16×tan-quot
14×associate-*r/
13×cbrt-prod
11×associate-*r*
8×flip3-+ flip-+
5×unswap-sqr sqr-pow
4×add-log-exp
3×pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 div-inv
Counts
4 → 378
Calls
4 calls:
2.0ms
(pow (cbrt t) 3.0)
107.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
20.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
560.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (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:
307.0ms
(pow (cbrt t) 3.0)
363.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
239.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
743.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify96.0ms

Algorithm
egg-herbie
Counts
390 → 390
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
018578767
150017915

prune1.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.1b

localize34.0ms

Local error

Found 4 expressions with local error:

3.9b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.3b
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
13.0b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite886.0ms

Algorithm
rewrite-expression-head
Rules
966×add-exp-log
593×prod-exp
294×div-exp
145×pow-exp
103×add-cbrt-cube
87×pow-to-exp
83×times-frac
58×add-sqr-sqrt
53×cbrt-unprod
50×*-un-lft-identity
45×add-cube-cbrt
36×associate-*l*
28×associate-*l/
26×unpow-prod-down
25×associate-*r/
23×cbrt-undiv
19×frac-times associate-/r*
14×tan-quot
13×pow1
11×associate-*r* associate-/l/
10×cbrt-prod 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 → 343
Calls
4 calls:
69.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
350.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
414.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (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:
352.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
243.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
742.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
828.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify98.0ms

Algorithm
egg-herbie
Counts
355 → 355
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
017458071
150017433

prune1.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.0b

regimes734.0ms

Accuracy

37.7% (4.2b remaining)

Error of 12.0b against oracle of 7.8b and baseline of 14.6b

bsearch446.0ms

Steps
ItersRangePoint
10
3.426884594506339e-88
1.932681529799266e-74
2.6976781763942327e-76
8
-2.1271403311742084e-172
-3.4255614771167906e-176
-5.969066468995164e-175

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06363
16363

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.1s2077×body1280valid
1.2s1727×body640valid
1.0s6042×body80valid
434.0ms854×body320valid
147.0ms411×body160valid