Details

Time bar (total: 32.0s)

sample469.0ms

Algorithm
intervals
Results
153.0ms82×body2560valid
121.0ms141×body1280valid
104.0ms28×body5120valid
45.0ms84×body640valid
12.0ms35×body320valid
6.0ms55×body80valid
2.0ms7×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
01925
14425
214825
381623
4462521
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.8b
(* (/ (pow t 3.0) (* l l)) (sin k))
18.1b
(/ (pow t 3.0) (* l l))
26.4b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
349×times-frac
245×add-exp-log
166×unpow-prod-down
151×add-sqr-sqrt
144×add-cube-cbrt *-un-lft-identity
123×div-exp
85×prod-exp
55×associate-*l/
54×associate-/r/
45×add-cbrt-cube
36×tan-quot
34×pow-exp
33×div-inv
23×pow-to-exp
18×frac-times associate-*r/ associate-/r*
17×cbrt-undiv associate-/l*
16×sqr-pow
13×cbrt-unprod
11×associate-*l*
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×pow-unpow associate-*r*
2×frac-2neg clear-num
1×pow-pow pow-prod-down *-commutative associate-/l/
Counts
4 → 361
Calls
4 calls:
6.0ms
(pow (/ k t) 2.0)
33.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms
(/ (pow t 3.0) (* l l))
107.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow (/ k t) 2.0)
255.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
187.0ms
(/ (pow t 3.0) (* l l))
592.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify663.0ms

Counts
373 → 373
Iterations

Useful iterations: done (642.0ms)

IterNodesCost
066910050
115129562
done50009168

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.1b

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.4b
(* (pow k 2.0) (pow t 1.0))
12.8b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite187.0ms

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:
18.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0ms
(* (pow k 2.0) (pow t 1.0))
72.0ms
(* (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:
356.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
95.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
342.0ms
(* (pow k 2.0) (pow t 1.0))
674.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.2s

Counts
620 → 620
Iterations

Useful iterations: done (1.2s)

IterNodesCost
049115125
1122012973
2298412703
done500012259

prune675.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.1b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.8b
(* (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)))

rewrite427.0ms

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)
45.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
135.0ms
(* (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:
19.0ms
(pow (sin k) 2)
354.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
95.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
670.0ms
(* (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)))

simplify1.5s

Counts
1480 → 1480
Iterations

Useful iterations: done (1.5s)

IterNodesCost
060550477
1152531964
2321231674
done500130411

prune596.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.7b

localize26.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.2b
(/ (pow l 2) (fabs (sin k)))
2.2b
(* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k))))
12.8b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k)))))

rewrite395.0ms

Algorithm
rewrite-expression-head
Rules
4561×add-exp-log
3350×prod-exp
1881×pow-exp
1593×div-exp
1044×pow-to-exp
310×rec-exp 1-exp
77×add-sqr-sqrt
76×times-frac
48×add-cube-cbrt *-un-lft-identity
45×add-cbrt-cube
30×unpow-prod-down
29×associate-*r*
24×associate-*l*
16×cbrt-unprod
12×cbrt-undiv
11×associate-/l*
10×unswap-sqr sqr-pow
9×unpow2
7×pow1
5×associate-*r/ div-inv
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 inv-pow
Counts
4 → 1139
Calls
4 calls:
47.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms
(/ (pow l 2) (fabs (sin k)))
31.0ms
(* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k))))
138.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
347.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
17.0ms
(/ (pow l 2) (fabs (sin k)))
77.0ms
(* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k))))
623.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k)))))

simplify1.7s

Counts
1151 → 1151
Iterations

Useful iterations: done (1.6s)

IterNodesCost
067940729
1168827046
2377924636
done500124635

prune815.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.6b

regimes490.0ms

Accuracy

26.4% (5.4b remaining)

Error of 14.2b against oracle of 8.8b and baseline of 16.1b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04476
15576
done5576

end0.0ms

sample14.1s

Algorithm
intervals
Results
4.1s2197×body2560valid
3.9s932×body5120valid
3.4s4102×body1280valid
1.3s2477×body640valid
380.0ms1007×body320valid
252.0ms2119×body80valid
106.0ms441×body160valid