Details

Time bar (total: 49.6s)

sample648.0ms

Algorithm
intervals
Results
210.0ms36×body5120valid
173.0ms69×body2560valid
142.0ms126×body1280valid
61.0ms79×body640valid
15.0ms30×body320valid
10.0ms62×body80valid
2.0ms7×body160valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.5s)

IterNodesCost
01925
14425
214625
379823
4446721
done500021

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ (pow t 3.0) (* l l)) (sin k))
0.8b
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
16.2b
(/ (pow t 3.0) (* l l))
29.1b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite444.0ms

Algorithm
rewrite-expression-head
Rules
343×times-frac
282×add-exp-log
153×unpow-prod-down
145×add-sqr-sqrt
138×add-cube-cbrt *-un-lft-identity
137×div-exp
103×prod-exp
65×add-cbrt-cube
58×associate-*l/
57×associate-/r/
38×tan-quot
34×pow-exp
33×div-inv
24×cbrt-undiv pow-to-exp
21×cbrt-unprod
20×associate-/l*
19×frac-times associate-*r/ associate-/r*
15×sqr-pow
11×associate-*l*
6×pow1
4×add-log-exp unswap-sqr
3×frac-2neg associate-*r* clear-num
1×pow-prod-down *-commutative associate-/l/
Counts
4 → 359
Calls
4 calls:
45.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
123.0ms
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
25.0ms
(/ (pow t 3.0) (* l l))
200.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series2.1s

Counts
4 → 12
Calls
4 calls:
329.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
689.0ms
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
252.0ms
(/ (pow t 3.0) (* l l))
856.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.1s

Counts
371 → 371
Iterations

Useful iterations: done (1.0s)

IterNodesCost
065810473
114999963
done50009407

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.8b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.6b
(* (pow k 2.0) (pow t 1.0))
16.3b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite337.0ms

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×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
Calls
4 calls:
33.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
36.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
38.0ms
(* (pow k 2.0) (pow t 1.0))
135.0ms
(* (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:
508.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
139.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
509.0ms
(* (pow k 2.0) (pow t 1.0))
865.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.8s

Counts
612 → 612
Iterations

Useful iterations: 2 (843.0ms)

IterNodesCost
048315017
1109613295
2284012595
done500012595

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.0b
(/ 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))
16.3b
(* (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)))

rewrite807.0ms

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×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 → 1460
Calls
4 calls:
8.0ms
(pow (sin k) 2)
86.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
40.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
304.0ms
(* (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)))

series1.6s

Counts
4 → 12
Calls
4 calls:
23.0ms
(pow (sin k) 2)
519.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
132.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
951.0ms
(* (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)))

simplify2.5s

Counts
1472 → 1472
Iterations

Useful iterations: 2 (968.0ms)

IterNodesCost
059750343
1126233112
2294031574
done500031574

prune943.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
2.9b
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.2b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

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
27×associate-*l*
26×times-frac
25×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
13×cbrt-unprod
12×associate-*r*
8×associate-/r* sqr-pow
6×cbrt-undiv
5×pow1
4×div-inv unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×associate-*l/ *-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 4425
Calls
4 calls:
6.0ms
(pow (sin k) 2)
332.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
27.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
142.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (sin k) 2)
580.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
144.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
511.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify2.8s

Counts
4437 → 4437
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
01155192116
11878153742
23789148978
done5001148978

prune947.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.1b

regimes618.0ms

Accuracy

13.7% (5.5b remaining)

Error of 17.1b against oracle of 11.6b and baseline of 18.0b

bsearch600.0ms

Steps
ItersRangePoint
9
-4.119158304370267e+144
-1.426146707153116e+135
-4.02356273947968e+144

simplify13.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
04886
15882
done5882

end0.0ms

sample20.7s

Algorithm
intervals
Results
5.9s947×body5120valid
5.8s2169×body2560valid
5.0s4138×body1280valid
2.0s2505×body640valid
562.0ms976×body320valid
349.0ms2045×body80valid
159.0ms431×body160valid