Details

Time bar (total: 1.0m)

sample621.0ms

Algorithm
intervals
Results
199.0ms135×body1280valid
151.0ms58×body2560valid
145.0ms19×body5120valid
65.0ms86×body640valid
14.0ms28×body320valid
11.0ms61×body80valid
4.0ms12×body160valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.6s)

IterNodesCost
01925
14425
214625
379823
4446721
done500021

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (pow t 3.0) (* l l)) (sin k))
1.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
16.6b
(/ (pow t 3.0) (* l l))
30.2b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite406.0ms

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:
44.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
118.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.0ms
(/ (pow t 3.0) (* l l))
183.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
308.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
426.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
246.0ms
(/ (pow t 3.0) (* l l))
865.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.3s

Counts
366 → 366
Iterations

Useful iterations: done (1.3s)

IterNodesCost
066210242
115049739
done50019233

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.8b
(* (pow k 2.0) (pow t 1.0))
17.3b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite303.0ms

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)))
36.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
32.0ms
(* (pow k 2.0) (pow t 1.0))
123.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts
4 → 12
Calls
4 calls:
558.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
120.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
486.0ms
(* (pow k 2.0) (pow t 1.0))
994.0ms
(* (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 (697.0ms)

IterNodesCost
048315017
1109613295
2284012595
done500012595

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.5b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.3b
(* (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)))

rewrite574.0ms

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)
60.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
17.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
179.0ms
(* (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:
20.0ms
(pow (sin k) 2)
517.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
155.0ms
(/ (* (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)))

simplify2.0s

Counts
1472 → 1472
Iterations

Useful iterations: 2 (947.0ms)

IterNodesCost
059750343
1126233112
2294031574
done500031574

prune884.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
2.0b
(* (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)))
3.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.5b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite2.4s

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:
19.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
276.0ms
(* (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)))
34.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
154.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
516.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
592.0ms
(* (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)))
151.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
570.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify3.7s

Counts
5774 → 5774
Iterations

Useful iterations: 2 (1.9s)

IterNodesCost
01477226017
12412201321
24559190075
done5001190075

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.5b

regimes495.0ms

Accuracy

19.7% (4.8b remaining)

Error of 14.5b against oracle of 9.7b and baseline of 15.6b

bsearch689.0ms

Steps
ItersRangePoint
9
6.663579023451854e+147
2.9782181803749555e+154
1.001759920786649e+154

simplify55.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04374
15374
done5374

end0.0ms

sample32.1s

Algorithm
intervals
Results
9.8s2274×body2560valid
7.9s4079×body1280valid
7.5s956×body5120valid
3.7s2510×body640valid
1.1s2062×body80valid
910.0ms983×body320valid
241.0ms445×body160valid