Details

Time bar (total: 24.0s)

sample454.0ms

Algorithm
intervals
Results
159.0ms71×body2560valid
109.0ms136×body1280valid
95.0ms34×body5120valid
43.0ms84×body640valid
11.0ms29×body320valid
11.0ms53×body80valid
5.0ms18×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111

prune12.0ms

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: 38.1b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.8b
(* (pow t 3.0) (tan k))
18.5b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.7b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
337×add-exp-log
220×prod-exp
71×div-exp
65×add-cbrt-cube
51×pow-exp
34×pow-to-exp cbrt-unprod
30×unpow-prod-down
28×add-sqr-sqrt
24×associate-*l*
23×add-cube-cbrt *-un-lft-identity
19×times-frac
12×cbrt-undiv
5×pow1 associate-*r/
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp sqr-pow
3×tan-quot pow-unpow div-inv unswap-sqr
2×*-commutative
1×pow-pow frac-2neg associate-*l/ clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 187
Calls
4 calls:
7.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
18.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
12.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series894.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(pow (/ k t) 2.0)
229.0ms
(* (pow t 3.0) (tan k))
362.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
240.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify43.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09912005
150011672

prune453.0ms

Filtered
199 candidates to 96 candidates (48.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1918199
Fresh101
Picked101
Done000
Total1938201

Merged error: 18.7b

Counts
201 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.5b
(* (pow k 2.0) (pow t 1.0))
13.5b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
1645×add-exp-log
1122×prod-exp
899×pow-exp
688×div-exp
509×pow-to-exp
140×rec-exp 1-exp
37×add-sqr-sqrt
29×unpow-prod-down
25×add-cbrt-cube
22×times-frac
20×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×associate-*l*
13×sqr-pow
12×unswap-sqr
9×associate-/r*
7×cbrt-unprod
6×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 608
Calls
4 calls:
7.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms
(* (pow k 2.0) (pow t 1.0))
23.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
342.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
328.0ms
(* (pow k 2.0) (pow t 1.0))
634.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify165.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
014397252
142967083
250037076

prune651.0ms

Filtered
620 candidates to 108 candidates (17.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New61010620
Fresh527
Picked101
Done000
Total61612628

Merged error: 14.0b

Counts
628 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.5b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite292.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1468
Calls
4 calls:
3.0ms
(pow (sin k) 2)
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
38.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
337.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
643.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify303.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune787.0ms

Filtered
1480 candidates to 95 candidates (6.4%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New147641480
Fresh2911
Picked101
Done000
Total1479131492

Merged error: 11.4b

Counts
1492 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos k) (sin k))
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.5b
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
13.5b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
3841×add-exp-log
2622×prod-exp
1370×div-exp
1330×pow-exp
679×pow-to-exp
248×rec-exp 1-exp
99×times-frac
80×add-sqr-sqrt
65×add-cbrt-cube
59×add-cube-cbrt *-un-lft-identity
45×associate-*r*
24×associate-*l*
22×cbrt-undiv cbrt-unprod
8×div-inv
7×pow1 unpow-prod-down
6×associate-/l* unswap-sqr
5×associate-*r/
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip pow-prod-down associate-/r/ inv-pow sqr-pow
Counts
4 → 939
Calls
4 calls:
4.0ms
(/ (cos k) (sin k))
13.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
22.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
33.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (cos k) (sin k))
333.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
87.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
625.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify172.0ms

Algorithm
egg-herbie
Counts
951 → 951
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0240215175
1500112337

prune719.0ms

Filtered
951 candidates to 143 candidates (15.0%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New9465951
Fresh4812
Picked011
Done000
Total95014964

Merged error: 8.9b

Counts
964 → 14

regimes385.0ms

Accuracy

42.7% (4.2b remaining)

Error of 13.4b against oracle of 9.2b and baseline of 16.5b

bsearch729.0ms

Steps
ItersRangePoint
6
7.055322399106104e-78
3.361692463022349e-77
3.330489096417523e-77
11
-2.6766715744203716e-101
-2.2769738344141557e-127
-4.0649028969036264e-114
4
-1.4501250722181258e+130
-9.551618771889815e+129
-1.4298479098591106e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06970
16970

end0.0ms

sample13.9s

Algorithm
intervals
Results
4.4s2273×body2560valid
3.8s914×body5120valid
3.2s4050×body1280valid
1.3s2518×body640valid
366.0ms988×body320valid
262.0ms2090×body80valid
103.0ms408×body160valid