Details

Time bar (total: 25.5s)

sample434.0ms

Algorithm
intervals
Results
131.0ms34×body5120valid
121.0ms71×body2560valid
91.0ms129×body1280valid
43.0ms92×body640valid
12.0ms35×body320valid
8.0ms64×body80valid
7.0ms13×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04413
114913
286912
3500111

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: 39.0b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
20.1b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.5b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite53.0ms

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:
5.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
21.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series929.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (/ k t) 2.0)
239.0ms
(* (pow t 3.0) (tan k))
373.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
252.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify44.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09912005
150011672

prune497.0ms

Filtered
199 candidates to 96 candidates (48.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1927199
Fresh011
Picked101
Done000
Total1938201

Merged error: 21.7b

Counts
201 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.6b
(* (pow k 2.0) (pow t 1.0))
16.1b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite104.0ms

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))
21.0ms
(* (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:
343.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
334.0ms
(* (pow k 2.0) (pow t 1.0))
666.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify167.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
014397252
142967083
250037076

prune687.0ms

Filtered
620 candidates to 108 candidates (17.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New60911620
Fresh347
Picked101
Done000
Total61315628

Merged error: 16.8b

Counts
628 → 15

localize25.0ms

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))))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.1b
(* (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)))

rewrite282.0ms

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))
41.0ms
(* (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:
26.0ms
(pow (sin k) 2)
344.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
669.0ms
(* (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)))

simplify308.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune838.0ms

Filtered
1480 candidates to 94 candidates (6.4%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New147281480
Fresh9514
Picked101
Done000
Total1482131495

Merged error: 13.5b

Counts
1495 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.6b
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.0b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite669.0ms

Algorithm
rewrite-expression-head
Rules
13973×add-exp-log
10155×prod-exp
8251×pow-exp
5914×div-exp
4231×pow-to-exp
920×rec-exp 1-exp
81×unpow-prod-down
64×times-frac
61×associate-*l*
49×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
21×sqrt-prod
14×cbrt-unprod
13×associate-*r*
12×sqr-pow
9×associate-/r*
8×cbrt-undiv
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 3211
Calls
4 calls:
15.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
71.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
22.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.8s

Counts
4 → 12
Calls
4 calls:
352.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
674.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
672.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify634.0ms

Algorithm
egg-herbie
Counts
3223 → 3223
Iterations

Useful iterations: 1 (54.0ms)

IterNodesCost
0344960577
1500260288

prune1.0s

Filtered
3223 candidates to 142 candidates (4.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New321763223
Fresh7512
Picked101
Done000
Total3225113236

Merged error: 13.4b

Counts
3236 → 11

regimes245.0ms

Accuracy

15.3% (4.1b remaining)

Error of 17.3b against oracle of 13.2b and baseline of 18.1b

bsearch126.0ms

Steps
ItersRangePoint
6
1.3612390649410625e-30
1.916107853091866e-29
5.772063063399388e-30

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05143
15143

end0.0ms

sample14.0s

Algorithm
intervals
Results
4.3s952×body5120valid
4.3s2264×body2560valid
3.0s4101×body1280valid
1.2s2475×body640valid
343.0ms1013×body320valid
245.0ms2086×body80valid
106.0ms432×body160valid