Details

Time bar (total: 31.7s)

sample450.0ms

Algorithm
intervals
Results
142.0ms38×body5120valid
125.0ms71×body2560valid
95.0ms119×body1280valid
37.0ms67×body640valid
12.0ms33×body320valid
10.0ms81×body80valid
3.0ms14×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
01925
14425
214825
381623
4462521
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
0.8b
(* (/ (pow t 3.0) (* l l)) (sin k))
16.9b
(/ (pow t 3.0) (* l l))
26.9b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite245.0ms

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:
76.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
30.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms
(/ (pow t 3.0) (* l l))
106.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
342.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
261.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
191.0ms
(/ (pow t 3.0) (* l l))
606.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify672.0ms

Counts
374 → 374
Iterations

Useful iterations: done (658.0ms)

IterNodesCost
067010352
115169848
done50009342

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
5.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.1b
(* (pow k 2.0) (pow t 1.0))
12.9b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
1597×add-exp-log
1095×prod-exp
882×pow-exp
668×div-exp
492×pow-to-exp
130×rec-exp 1-exp
37×add-sqr-sqrt
32×unpow-prod-down
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
19×times-frac associate-*r*
18×associate-*l*
14×sqr-pow
12×unswap-sqr
8×associate-/r*
6×cbrt-unprod
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u unpow2 add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 575
Calls
4 calls:
3.0ms
(pow (sin k) 2)
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0ms
(* (pow k 2.0) (pow t 1.0))
69.0ms
(* (pow (/ 1 (* (pow k 2.0) (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)
92.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
349.0ms
(* (pow k 2.0) (pow t 1.0))
672.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.2s

Counts
587 → 587
Iterations

Useful iterations: done (1.2s)

IterNodesCost
044614510
1107412421
2267812181
done500011737

prune627.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cos k) (pow l 2))
0.4b
(pow (sin k) 2)
5.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.9b
(* (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)))

rewrite374.0ms

Algorithm
rewrite-expression-head
Rules
5397×add-exp-log
4347×prod-exp
2995×pow-exp
1970×div-exp
1786×pow-to-exp
403×rec-exp 1-exp
30×add-sqr-sqrt
24×unpow-prod-down
20×associate-*r* add-cbrt-cube
19×add-cube-cbrt *-un-lft-identity times-frac
14×associate-*l*
8×associate-/r* sqr-pow
7×unswap-sqr
6×cbrt-unprod unpow2
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 1380
Calls
4 calls:
14.0ms
(* (cos k) (pow l 2))
3.0ms
(pow (sin k) 2)
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
137.0ms
(* (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)))

series818.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos k) (pow l 2))
19.0ms
(pow (sin k) 2)
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
662.0ms
(* (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
1392 → 1392
Iterations

Useful iterations: done (1.1s)

IterNodesCost
056248208
1135630918
2280030660
done500029397

prune618.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.4b
(* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k))))
3.0b
(/ (pow l 2) (fabs (sin k)))
12.9b
(* (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)))))

rewrite369.0ms

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:
45.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
30.0ms
(* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k))))
8.0ms
(/ (pow l 2) (fabs (sin k)))
134.0ms
(* (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:
354.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
78.0ms
(* (/ (cos k) (fabs (sin k))) (/ (pow l 2) (fabs (sin k))))
17.0ms
(/ (pow l 2) (fabs (sin k)))
636.0ms
(* (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)))))

simplify1.6s

Counts
1151 → 1151
Iterations

Useful iterations: done (1.6s)

IterNodesCost
067940729
1168827046
2378024636
done500024635

prune825.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.4b

regimes475.0ms

Accuracy

24.1% (5.1b remaining)

Error of 14.6b against oracle of 9.5b and baseline of 16.2b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04175
15275
done5275

end0.0ms

sample14.8s

Algorithm
intervals
Results
4.5s992×body5120valid
4.2s2257×body2560valid
3.3s4014×body1280valid
1.3s2448×body640valid
382.0ms1042×body320valid
273.0ms2087×body80valid
127.0ms474×body160valid