Details

Time bar (total: 31.3s)

sample455.0ms

Algorithm
intervals
Results
144.0ms82×body2560valid
115.0ms141×body1280valid
107.0ms28×body5120valid
43.0ms84×body640valid
12.0ms35×body320valid
7.0ms55×body80valid
2.0ms7×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (975.0ms)

IterNodesCost
01925
14425
214625
379823
4446721
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.7b

localize18.0ms

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))

rewrite195.0ms

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×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 → 353
Calls
4 calls:
6.0ms
(pow (/ k t) 2.0)
35.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
12.0ms
(/ (pow t 3.0) (* l l))
119.0ms
(/ (/ 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:
68.0ms
(pow (/ k t) 2.0)
288.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
186.0ms
(/ (pow t 3.0) (* l l))
587.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify652.0ms

Counts
365 → 365
Iterations

Useful iterations: done (637.0ms)

IterNodesCost
06619956
115019468
done50009074

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.6b

localize22.0ms

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)))

rewrite195.0ms

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:
19.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms
(* (pow k 2.0) (pow t 1.0))
77.0ms
(* (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:
358.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
355.0ms
(* (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)))

simplify1.1s

Counts
612 → 612
Iterations

Useful iterations: 2 (490.0ms)

IterNodesCost
048315017
1109613295
2284012595
done500012595

prune638.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.9b

localize24.0ms

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)))

rewrite439.0ms

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:
4.0ms
(pow (sin k) 2)
49.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
148.0ms
(* (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)))

series1.3s

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (sin k) 2)
353.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
93.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
856.0ms
(* (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)))

simplify1.2s

Counts
1472 → 1472
Iterations

Useful iterations: 2 (579.0ms)

IterNodesCost
059750343
1126233112
2294031574
done500031574

prune578.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.1b

localize31.0ms

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)))))

rewrite405.0ms

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×associate-/r* add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip pow-prod-down inv-pow
Counts
4 → 1131
Calls
4 calls:
49.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
11.0ms
(/ (pow l 2) (fabs (sin k)))
34.0ms
(* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k))))
149.0ms
(* (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:
359.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
17.0ms
(/ (pow l 2) (fabs (sin k)))
74.0ms
(* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k))))
658.0ms
(* (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)))))

simplify1.5s

Counts
1143 → 1143
Iterations

Useful iterations: 2 (816.0ms)

IterNodesCost
067140577
1142627791
2352324524
done500024524

prune756.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.3b

regimes492.0ms

Accuracy

26.8% (5.3b remaining)

Error of 14.2b against oracle of 8.9b and baseline of 16.1b

bsearch4.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04272
15372
done5372

end0.0ms

sample14.1s

Algorithm
intervals
Results
4.1s2197×body2560valid
4.0s932×body5120valid
3.4s4102×body1280valid
1.3s2477×body640valid
374.0ms1007×body320valid
257.0ms2119×body80valid
116.0ms441×body160valid