Details

Time bar (total: 54.6s)

sample726.0ms

Algorithm
intervals
Results
211.0ms125×body1280valid
192.0ms69×body2560valid
167.0ms20×body5120valid
80.0ms83×body640valid
22.0ms32×body320valid
14.0ms63×body80valid
6.0ms17×body160valid

simplify949.0ms

Counts
1 → 1
Iterations

Useful iterations: done (949.0ms)

IterNodesCost
01925
14425
214825
384123
done500121

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (pow t 3.0) (* l l)) (sin k))
0.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.8b
(/ (pow t 3.0) (* l l))
27.3b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite364.0ms

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:
42.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
91.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.0ms
(/ (pow t 3.0) (* l l))
189.0ms
(/ (/ 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:
339.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
404.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
260.0ms
(/ (pow t 3.0) (* l l))
819.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify831.0ms

Counts
374 → 374
Iterations

Useful iterations: done (813.0ms)

IterNodesCost
067010352
117859880
done50019414

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.6b
(* (pow k 2.0) (pow t 1.0))
14.6b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite261.0ms

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:
38.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
28.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
19.0ms
(* (pow k 2.0) (pow t 1.0))
84.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.4s

Counts
4 → 12
Calls
4 calls:
613.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
144.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
603.0ms
(* (pow k 2.0) (pow t 1.0))
1.0s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify709.0ms

Counts
620 → 620
Iterations

Useful iterations: done (680.0ms)

IterNodesCost
049115125
1148113001
done500112725

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.6b
(* (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)))

rewrite612.0ms

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:
4.0ms
(pow (sin k) 2)
61.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
17.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
213.0ms
(* (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)))

series1.7s

Counts
4 → 12
Calls
4 calls:
36.0ms
(pow (sin k) 2)
489.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
147.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.0s
(* (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)))

simplify1.3s

Counts
1480 → 1480
Iterations

Useful iterations: done (1.2s)

IterNodesCost
060550477
1205133540
done500131701

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
3.7b
(* (pow (/ (* (cbrt 1) (cbrt 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))))
5.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
9.7b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
22030×add-exp-log
15939×prod-exp
12558×pow-exp
9152×div-exp
6078×pow-to-exp
1300×rec-exp 1-exp
34×unpow-prod-down
32×add-cbrt-cube
26×times-frac associate-*l*
25×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
13×associate-*r* cbrt-unprod
8×associate-/r* sqr-pow
6×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv unpow2 add-log-exp
3×pow-unpow associate-*r/ unswap-sqr
2×*-commutative
1×pow-pow frac-2neg clear-num associate-/l*
Counts
4 → 4433
Calls
4 calls:
4.0ms
(pow (sin k) 2)
287.0ms
(* (pow (/ (* (cbrt 1) (cbrt 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))))
26.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
117.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts
4 → 12
Calls
4 calls:
36.0ms
(pow (sin k) 2)
1.0s
(* (pow (/ (* (cbrt 1) (cbrt 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))))
134.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
978.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify3.3s

Counts
4445 → 4445
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01163192280
14558155498
done5000152283

prune1.4s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.9b

regimes711.0ms

Accuracy

31.7% (4.4b remaining)

Error of 16.1b against oracle of 11.7b and baseline of 18.1b

bsearch4.0ms

simplify15.0ms

Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
04782
15776
25974
36174
done6174

end0.0ms

sample28.7s

Algorithm
intervals
Results
8.2s2306×body2560valid
7.1s4121×body1280valid
6.7s923×body5120valid
3.4s2524×body640valid
1.2s982×body320valid
685.0ms2047×body80valid
561.0ms407×body160valid