Details

Time bar (total: 5.8m)

sample404.0ms

Algorithm
intervals
Results
136.0ms26×body5120valid
102.0ms56×body2560valid
86.0ms126×body1280valid
41.0ms88×body640valid
10.0ms32×body320valid
6.0ms58×body80valid
4.0ms16×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
04413
114713
285712
3500211

prune11.0ms

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: 38.6b

Counts
2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.6b
(* (pow t 3.0) (tan k))
20.0b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.2b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite437.0ms

Algorithm
rewrite-expression-head
Rules
5057×add-sqr-sqrt
2843×associate-*l*
2812×unswap-sqr
2783×times-frac
2196×associate-*r*
1235×unpow-prod-down
1036×add-cube-cbrt *-un-lft-identity
565×sqr-pow
337×add-exp-log
336×*-commutative
328×swap-sqr
220×prod-exp
81×associate-/r*
71×div-exp
65×add-cbrt-cube
51×pow-exp
34×pow-to-exp cbrt-unprod
32×div-inv
28×associate-/l*
12×pow1 cbrt-undiv
5×associate-*r/
4×pow-prod-down add-log-exp
3×tan-quot pow-unpow
1×pow-pow frac-2neg associate-*l/ clear-num associate-/r/
Counts
4 → 2589
Calls
4 calls:
5.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
98.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
21.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series907.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (/ k t) 2.0)
239.0ms
(* (pow t 3.0) (tan k))
360.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
241.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify488.0ms

Algorithm
egg-herbie
Counts
2601 → 2601
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0500153883

prune9.0s

Filtered
2601 candidates to 1663 candidates (63.9%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New2578232601
Fresh101
Picked101
Done000
Total2580232603

Merged error: 10.9b

Counts
2603 → 23

localize28.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.7b
(* (pow k 2.0) (pow t 1.0))
15.3b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite456.0ms

Algorithm
rewrite-expression-head
Rules
2158×add-sqr-sqrt
1645×add-exp-log
1373×unswap-sqr
1368×times-frac
1282×unpow-prod-down
1122×prod-exp
899×pow-exp
688×div-exp
623×sqr-pow
509×pow-to-exp
471×*-un-lft-identity
364×associate-*r*
285×unpow2
259×add-cube-cbrt
203×associate-*l*
140×rec-exp 1-exp
45×associate-/l*
44×associate-/r*
31×associate-*r/
27×*-commutative
25×add-cbrt-cube
11×pow1
7×cbrt-unprod
6×cbrt-undiv
4×clear-num div-inv add-log-exp
3×frac-2neg pow-prod-down un-div-inv
2×pow-flip
1×inv-pow
Counts
4 → 1628
Calls
4 calls:
17.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.0ms
(* (pow k 2.0) (pow t 1.0))
219.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts
4 → 12
Calls
4 calls:
333.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
324.0ms
(* (pow k 2.0) (pow t 1.0))
783.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify317.0ms

Algorithm
egg-herbie
Counts
1640 → 1640
Iterations

Useful iterations: 1 (72.0ms)

IterNodesCost
0470528157
1500126518

prune3.3s

Filtered
1640 candidates to 553 candidates (33.7%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1630101640
Fresh13922
Picked101
Done000
Total1644191663

Merged error: 3.5b

Counts
1663 → 19

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.7b
(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
6.7b
(* (pow k 2.0) (pow t 1.0))
7.0b
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
7539×add-sqr-sqrt
5740×unpow-prod-down
5696×associate-*l*
4010×times-frac
3928×associate-/l*
3881×unswap-sqr
2737×frac-times
2526×*-un-lft-identity
2212×add-exp-log
1985×add-cube-cbrt
1786×sqr-pow
1430×prod-exp
1216×associate-/r*
914×div-exp
779×pow-exp
682×associate-*r*
449×pow-to-exp
182×clear-num
181×frac-2neg
161×associate-*l/
120×rec-exp 1-exp
116×*-commutative
48×add-cbrt-cube
25×div-inv
19×cbrt-unprod
17×associate-*r/
16×pow1
12×cbrt-undiv
6×pow-prod-down
4×add-log-exp
2×pow-flip un-div-inv
1×inv-pow
Counts
4 → 4474
Calls
4 calls:
16.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
440.0ms
(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
10.0ms
(* (pow k 2.0) (pow t 1.0))
61.0ms
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)

series1.7s

Counts
4 → 12
Calls
4 calls:
335.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
663.0ms
(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
353.0ms
(* (pow k 2.0) (pow t 1.0))
384.0ms
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)

simplify1.1s

Algorithm
egg-herbie
Counts
4486 → 4486
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
06778111228

prune23.5s

Filtered
4486 candidates to 3527 candidates (78.6%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New4472144486
Fresh15318
Picked101
Done000
Total4488174505

Merged error: 1.1b

Counts
4505 → 17

localize37.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (sin k) (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l))
1.1b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.1b
(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (- (pow l 1))) (* (/ (sin k) (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)) (- (pow (sin k) 1))))
4.6b
(* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

rewrite9.5s

Algorithm
rewrite-expression-head
Rules
101588×times-frac
89469×associate-*l*
83704×add-sqr-sqrt
64377×unpow-prod-down
36577×*-un-lft-identity
35885×unswap-sqr
30560×add-cube-cbrt
15670×associate-*r*
15425×sqr-pow
4067×distribute-lft-neg-in distribute-rgt-neg-in
3724×add-exp-log
2349×prod-exp
1545×*-commutative
1513×div-exp
1234×pow-exp
856×associate-/r*
776×div-inv
581×neg-mul-1
451×pow-to-exp
271×rec-exp 1-exp
161×associate-*l/ associate-/r/
70×associate-/l*
68×add-cbrt-cube
26×cbrt-unprod
21×cbrt-undiv
12×pow1
4×frac-2neg pow-prod-down clear-num add-log-exp
2×pow-flip
1×distribute-frac-neg distribute-rgt-neg-out inv-pow
Counts
4 → 33867
Calls
4 calls:
89.0ms
(/ (sin k) (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l))
35.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.1s
(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (- (pow l 1))) (* (/ (sin k) (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)) (- (pow (sin k) 1))))
67.0ms
(* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

series1.5s

Counts
4 → 12
Calls
4 calls:
370.0ms
(/ (sin k) (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l))
332.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
380.0ms
(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (- (pow l 1))) (* (/ (sin k) (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)) (- (pow (sin k) 1))))
369.0ms
(* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

simplify14.4s

Algorithm
egg-herbie
Counts
33879 → 33879
Iterations

Useful iterations: 0 (894.0ms)

IterNodesCost
0541771471070

prune4.4m

Filtered
33879 candidates to 28912 candidates (85.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New338691033879
Fresh13316
Picked101
Done000
Total338831333896

Merged error: 0b

Counts
33896 → 13

regimes342.0ms

Accuracy

60.5% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 2.9b

bsearch984.0ms

Steps
ItersRangePoint
7
1.13933249473558e-159
3.07306015173592e-158
3.0397255266168896e-158
11
-1.4509800160483698e-90
-4.4603755505051946e-122
-1.1926451893947954e-95

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08061
110161
211361
313261
415061
515061

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.3s2235×body2560valid
4.2s1008×body5120valid
2.9s4014×body1280valid
1.2s2572×body640valid
311.0ms955×body320valid
234.0ms2081×body80valid
113.0ms454×body160valid