Details

Time bar (total: 26.5s)

sample159.0ms

Algorithm
intervals
Results
60.0ms70×body1280valid
39.0ms62×body640valid
29.0ms167×body80valid
11.0ms26×body320valid
4.0ms13×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.9b
(* (/ (pow t 3.0) (* l l)) (sin k))
12.6b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
13.4b
(/ (pow t 3.0) (* l l))

rewrite347.0ms

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:
35.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
15.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
286.0ms
(* (* (* (/ (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:
329.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
250.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
651.0ms
(* (* (* (/ (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))

simplify120.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune515.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize32.0ms

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))
3.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
6.2b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.6b
(* (* (* (* (/ (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))

rewrite741.0ms

Algorithm
rewrite-expression-head
Rules
346×add-exp-log
203×prod-exp
97×div-exp
82×add-cbrt-cube
55×associate-*l/
46×cbrt-unprod
41×pow-exp
35×frac-times
32×pow1
28×pow-to-exp
22×*-un-lft-identity
19×pow-prod-down
17×add-sqr-sqrt add-cube-cbrt
16×tan-quot
15×times-frac associate-*r/
13×cbrt-undiv
11×associate-*r*
8×flip3-+ flip-+
5×associate-/l*
4×unpow-prod-down add-log-exp sqr-pow
3×associate-*l* associate-/r* *-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv
Counts
4 → 204
Calls
4 calls:
111.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
30.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
3.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
584.0ms
(* (* (* (* (/ (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:
379.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
303.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
203.0ms
(/ (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))

simplify65.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011793756
150013242

prune729.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
2.2b
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
3.9b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k))
12.6b
(* (* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite6.5s

Algorithm
rewrite-expression-head
Rules
2427×add-exp-log
1534×prod-exp
801×div-exp
268×pow-to-exp pow-exp
257×add-cbrt-cube
184×cbrt-unprod
151×associate-*l/
103×frac-times
63×cbrt-undiv
48×pow1
33×associate-*r/
32×tan-quot
31×pow-prod-down
16×flip3-+ flip-+
15×*-un-lft-identity
11×associate-*r*
10×add-sqr-sqrt add-cube-cbrt
6×unpow-prod-down
4×add-log-exp
3×cbrt-prod pow-unpow associate-*l* *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 sqr-pow
Counts
4 → 544
Calls
4 calls:
2.0ms
(pow (cbrt t) 3.0)
1.2s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
306.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k))
4.9s
(* (* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (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:
315.0ms
(pow (cbrt t) 3.0)
377.0ms
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
300.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k))
944.0ms
(* (* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify149.0ms

Algorithm
egg-herbie
Counts
556 → 556
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0237413114
1500212300

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.9b

localize30.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.2b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.6b
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
2898×add-exp-log
1826×prod-exp
939×div-exp
340×add-cbrt-cube
313×pow-to-exp pow-exp
246×cbrt-unprod
125×associate-*l/
103×frac-times
85×cbrt-undiv
61×pow1
41×pow-prod-down
40×add-sqr-sqrt
37×associate-*l*
34×times-frac
33×associate-*r/
32×tan-quot *-un-lft-identity
27×add-cube-cbrt
20×unpow-prod-down
16×flip3-+ flip-+
12×associate-*r*
10×cbrt-prod
5×unswap-sqr
4×*-commutative add-log-exp sqr-pow
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 684
Calls
4 calls:
93.0ms
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
356.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.5s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt 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:
303.0ms
(* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
384.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
250.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
742.0ms
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify177.0ms

Algorithm
egg-herbie
Counts
696 → 696
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0254916227
1500315241

prune1.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.0b

regimes402.0ms

Accuracy

19.6% (5.5b remaining)

Error of 16.2b against oracle of 10.7b and baseline of 17.5b

bsearch409.0ms

Steps
ItersRangePoint
10
8.64126661053094e-83
1.636465978878086e-67
2.9464035802449483e-79
8
-2.1548302214375096e-237
-2.8780882450859202e-241
-4.831398047703028e-238

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06345
16345

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s2077×body1280valid
1.0s5848×body80valid
1000.0ms1675×body640valid
361.0ms826×body320valid
136.0ms438×body160valid