Details

Time bar (total: 1.1m)

sample915.0ms

Algorithm
intervals
Results
286.0ms73×body2560valid
244.0ms134×body1280valid
195.0ms29×body5120valid
104.0ms79×body640valid
26.0ms35×body320valid
14.0ms64×body80valid
5.0ms10×body160valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
01925
14425
214625
379823
4446721
done500021

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.5b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
1.0b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
16.9b
(/ (pow t 3.0) (* l l))
26.1b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite319.0ms

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×pow-prod-down add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 354
Calls
4 calls:
35.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
90.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.0ms
(/ (pow t 3.0) (* l l))
146.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
435.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
498.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
307.0ms
(/ (pow t 3.0) (* l l))
914.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.1s

Counts
366 → 366
Iterations

Useful iterations: done (1.1s)

IterNodesCost
066210242
115049739
done50019233

prune2.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0b
(* (pow k 2.0) (pow t 1.0))
15.9b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite336.0ms

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:
38.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
39.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
36.0ms
(* (pow k 2.0) (pow t 1.0))
132.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.1s

Counts
4 → 12
Calls
4 calls:
478.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
102.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
532.0ms
(* (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)))

simplify1.7s

Counts
612 → 612
Iterations

Useful iterations: 2 (767.0ms)

IterNodesCost
048315017
1109613295
2284012595
done500012595

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.9b
(* (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)))

rewrite637.0ms

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)
72.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
20.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
191.0ms
(* (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)
483.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
138.0ms
(/ (* (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)))

simplify1.7s

Counts
1472 → 1472
Iterations

Useful iterations: 2 (789.0ms)

IterNodesCost
059750343
1126233112
2294031574
done500031574

prune795.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.6b
(* (pow (/ 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)))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.2b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
25023×add-exp-log
19197×prod-exp
16899×pow-exp
11140×div-exp
7959×pow-to-exp
2990×rec-exp 1-exp
51×unpow-prod-down
43×times-frac
41×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
12×associate-*r*
9×associate-/r* sqr-pow
8×cbrt-undiv
5×pow1 div-inv
4×associate-/l* add-log-exp
3×unpow2 unswap-sqr
2×frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 5762
Calls
4 calls:
23.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
304.0ms
(* (pow (/ 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)))
37.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
141.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
579.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
583.0ms
(* (pow (/ 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)))
148.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
683.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify4.0s

Counts
5774 → 5774
Iterations

Useful iterations: 2 (2.6s)

IterNodesCost
01477226017
12412201321
24559190075
done5001190075

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.9b

regimes377.0ms

Accuracy

37.1% (3.3b remaining)

Error of 13.8b against oracle of 10.5b and baseline of 15.8b

bsearch1.7s

Steps
ItersRangePoint
9
4.61796087672408e+142
4.211818690154182e+148
4.1624864010972877e+148
10
-6.354265220965125e+156
-1.7344183351890289e+146
-7.341974747858959e+153

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
059114
171114
done71114

end0.0ms

sample33.5s

Algorithm
intervals
Results
10.7s4188×body1280valid
9.3s2235×body2560valid
6.9s950×body5120valid
3.2s2468×body640valid
1.0s1065×body320valid
722.0ms489×body160valid
721.0ms2058×body80valid