Details

Time bar (total: 1.1m)

sample768.0ms

Algorithm
intervals
Results
271.0ms32×body5120valid
201.0ms66×body2560valid
141.0ms119×body1280valid
87.0ms94×body640valid
18.0ms30×body320valid
13.0ms72×body80valid
6.0ms17×body160valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
01925
14425
214825
381623
4462521
done500021

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
16.2b
(/ (pow t 3.0) (* l l))
31.8b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
272×add-exp-log
153×unpow-prod-down
144×add-sqr-sqrt
137×add-cube-cbrt *-un-lft-identity
128×div-exp
103×prod-exp
59×add-cbrt-cube
58×associate-*l/
54×associate-/r/
38×tan-quot
34×pow-exp
32×div-inv
24×pow-to-exp
21×cbrt-unprod
19×cbrt-undiv frac-times associate-*r/
18×associate-/r*
17×associate-/l*
15×sqr-pow
12×associate-*l*
11×pow1
6×associate-*r*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 362
Calls
4 calls:
133.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
45.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
15.0ms
(/ (pow t 3.0) (* l l))
134.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
412.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
328.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
277.0ms
(/ (pow t 3.0) (* l l))
790.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.0s

Counts
374 → 374
Iterations

Useful iterations: done (993.0ms)

IterNodesCost
067010352
115169848
done50009342

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.9b
(* (pow k 2.0) (pow t 1.0))
17.0b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite301.0ms

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:
27.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
17.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
32.0ms
(* (pow k 2.0) (pow t 1.0))
125.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.0s

Counts
4 → 12
Calls
4 calls:
519.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
145.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
427.0ms
(* (pow k 2.0) (pow t 1.0))
876.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.8s

Counts
620 → 620
Iterations

Useful iterations: done (1.8s)

IterNodesCost
049115125
1122012973
2298412703
done500012259

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0b
(* (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)))

rewrite649.0ms

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:
8.0ms
(pow (sin k) 2)
69.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
35.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
182.0ms
(* (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)))

series1.8s

Counts
4 → 12
Calls
4 calls:
31.0ms
(pow (sin k) 2)
572.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
170.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
991.0ms
(* (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)))

simplify2.1s

Counts
1480 → 1480
Iterations

Useful iterations: done (2.1s)

IterNodesCost
060550477
1152531964
2321231674
done500130411

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.5b

localize67.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.0b
(* (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))))
5.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.5b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.2s

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:
27.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
261.0ms
(* (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))))
19.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
146.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.8s

Counts
4 → 12
Calls
4 calls:
467.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.1s
(* (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))))
149.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.0s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify3.5s

Counts
3223 → 3223
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01021126601
12425106350
24569103275
done500095088

prune1.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.2b

regimes981.0ms

Accuracy

50.3% (4.6b remaining)

Error of 13.4b against oracle of 8.8b and baseline of 18.0b

bsearch2.0s

Steps
ItersRangePoint
5
2.1675125417143413e+135
5.369016605326505e+135
5.307433067528376e+135
9
1.583357981388322e-157
1.230628501312938e-151
2.0555282651380754e-157
5
-6.148925786667236e-156
-3.026006818735111e-156
-4.884982399083622e-156
9
-2.0545059602165346e+153
-1.123814921454156e+146
-2.0150601778123175e+153

simplify23.0ms

Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
078195
199193
done99193

end0.0ms

sample31.2s

Algorithm
intervals
Results
9.5s4014×body1280valid
8.7s2225×body2560valid
7.2s898×body5120valid
3.3s2521×body640valid
831.0ms1058×body320valid
443.0ms2013×body80valid
215.0ms454×body160valid