Details

Time bar (total: 1.1m)

sample843.0ms

Algorithm
intervals
Results
222.0ms133×body1280valid
212.0ms36×body5120valid
195.0ms67×body2560valid
136.0ms76×body640valid
22.0ms35×body320valid
15.0ms72×body80valid
7.0ms16×body160valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.5s)

IterNodesCost
01925
14425
214825
381623
4462521
done500021

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (pow t 3.0) (* l l)) (sin k))
0.6b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.0b
(/ (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))

rewrite399.0ms

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:
46.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
95.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
20.0ms
(/ (pow t 3.0) (* l l))
213.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
357.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
496.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
208.0ms
(/ (pow t 3.0) (* l l))
651.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.2s

Counts
374 → 374
Iterations

Useful iterations: done (1.2s)

IterNodesCost
067010352
115169848
done50009342

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.5b
(* (pow k 2.0) (pow t 1.0))
15.3b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite208.0ms

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:
7.0ms
(pow (sin k) 2)
20.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms
(* (pow k 2.0) (pow t 1.0))
75.0ms
(* (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:
22.0ms
(pow (sin k) 2)
108.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
529.0ms
(* (pow k 2.0) (pow t 1.0))
835.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.5s

Counts
587 → 587
Iterations

Useful iterations: done (1.5s)

IterNodesCost
044614510
1107412421
2267812181
done500011737

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.3b

localize47.0ms

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))))
0.4b
(pow (sin k) 2)
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.3b
(* (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)))

rewrite673.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 1468
Calls
4 calls:
58.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms
(pow (sin k) 2)
34.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
232.0ms
(* (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:
524.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
21.0ms
(pow (sin k) 2)
124.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
986.0ms
(* (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)))

simplify2.2s

Counts
1480 → 1480
Iterations

Useful iterations: done (2.1s)

IterNodesCost
060550477
1152531964
2321531674
done500030411

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 7.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.9b
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
9.8b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite2.5s

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
40×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r* sqr-pow
8×cbrt-undiv
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 5770
Calls
4 calls:
29.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
269.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
113.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.8s

Counts
4 → 12
Calls
4 calls:
644.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
156.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.0s
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
1.0s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify3.3s

Counts
5782 → 5782
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01484226187
13385190742
done5000190248

prune1.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 7.3b

regimes831.0ms

Accuracy

48% (4.9b remaining)

Error of 13.6b against oracle of 8.7b and baseline of 18.1b

bsearch2.3s

Steps
ItersRangePoint
9
2.5488352682387853e+146
1.9386293038794674e+155
1.2831542385858316e+154
10
2.378213114367462e-220
6.669886766093751e-209
6.579520119656326e-209
6
-6.655609047880391e-133
-8.638556380710241e-134
-2.954141845484123e-133
7
-1.42823748890123e+142
-1.2907434956747758e+140
-1.3957682818437775e+142

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
065184
182184
done82184

end0.0ms

sample32.6s

Algorithm
intervals
Results
10.6s961×body5120valid
7.9s2247×body2560valid
7.8s3994×body1280valid
3.4s2502×body640valid
1.0s1008×body320valid
552.0ms2040×body80valid
299.0ms441×body160valid