Details

Time bar (total: 18.2s)

sample141.0ms

Algorithm
intervals
Results
49.0ms61×body1280valid
37.0ms63×body640valid
21.0ms189×body80valid
11.0ms30×body320valid
3.0ms12×body160valid

simplify31.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
04813
116113
294413
3500212
done500212

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.6b

localize21.0ms

Local error

Found 4 expressions with local error:

2.6b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
2.9b
(* (pow t 3.0) (sin k))
4.0b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
29.7b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
73×times-frac
56×add-sqr-sqrt
50×div-exp
41×add-cube-cbrt *-un-lft-identity
40×prod-exp
33×associate-*l*
30×cbrt-undiv
22×cbrt-unprod
11×div-inv
10×associate-*r*
8×associate-/l*
7×unswap-sqr
6×pow1 associate-/r*
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative sqr-pow
1×frac-times associate-*r/ pow-prod-down associate-*l/ associate-/l/
Counts
4 → 184
Calls
4 calls:
20.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
14.0ms
(* (pow t 3.0) (sin k))
11.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
63.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
334.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
174.0ms
(* (pow t 3.0) (sin k))
78.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
896.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify47.0ms

Counts
196 → 196
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010192396
150011978
done50011978

prune720.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 28.4b

localize22.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (pow t 3.0) (sin k))
4.5b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
5.0b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
20.2b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
49×prod-exp
41×div-exp
33×add-sqr-sqrt
27×cbrt-unprod
25×cbrt-undiv
22×associate-*l*
21×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
8×pow1
6×unswap-sqr
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-/r* *-commutative
2×tan-quot pow-prod-down associate-/r/ sqr-pow
1×frac-times frac-2neg associate-*r/ clear-num associate-/l/ associate-/l*
Counts
4 → 150
Calls
4 calls:
14.0ms
(* (pow t 3.0) (sin k))
26.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
31.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
90.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (pow t 3.0) (sin k))
463.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
357.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
901.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify113.0ms

Counts
162 → 162
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09131905
148941506
250011506
done50011506

prune563.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.9b

localize27.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))
4.5b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
5.0b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
20.2b
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite466.0ms

Algorithm
rewrite-expression-head
Rules
474×add-exp-log
272×prod-exp
145×div-exp
103×add-cbrt-cube
60×pow-exp
43×cbrt-unprod
40×pow-to-exp
33×cbrt-undiv
26×add-sqr-sqrt
20×associate-*l*
19×add-cube-cbrt *-un-lft-identity times-frac
17×associate-*r*
8×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-/r* *-commutative unswap-sqr
2×tan-quot pow-prod-down associate-/r/
1×frac-times unpow-prod-down frac-2neg associate-*r/ clear-num associate-/l/ associate-/l* sqr-pow
Counts
4 → 213
Calls
4 calls:
34.0ms
(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))
69.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
97.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
251.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.3s

Counts
4 → 12
Calls
4 calls:
203.0ms
(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))
713.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
401.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
969.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify54.0ms

Counts
225 → 225
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011964087
150013315
done50013315

prune655.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.7b

localize30.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)
1.7b
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
4.5b
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
20.2b
(* (/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite579.0ms

Algorithm
rewrite-expression-head
Rules
770×add-exp-log
376×prod-exp
305×div-exp
203×add-cbrt-cube
88×cbrt-unprod
71×cbrt-undiv
69×pow-exp
52×times-frac associate-*l*
45×pow-to-exp
43×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity
18×sqrt-prod
17×associate-*r*
13×pow1
8×associate-*l/
6×unpow-prod-down sqr-pow
5×pow-prod-down div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times associate-*r/ associate-/r* *-commutative associate-/l/ unswap-sqr
2×tan-quot associate-/r/
1×frac-2neg clear-num associate-/l*
Counts
4 → 306
Calls
4 calls:
38.0ms
(* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)
99.0ms
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
93.0ms
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
323.0ms
(* (/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.7s

Counts
4 → 12
Calls
4 calls:
440.0ms
(* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)
534.0ms
(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l))
637.0ms
(/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
1.1s
(* (/ (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify73.0ms

Counts
318 → 318
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
016266820
150025449
done50025449

prune883.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.7b

regimes598.0ms

Accuracy

32.7% (1.8b remaining)

Error of 21.7b against oracle of 19.9b and baseline of 22.6b

bsearch369.0ms

Steps
ItersRangePoint
9
2.526624684472541e-05
51.26549425761527
7.198698039624432
9
5.888921208787221e-155
1.4278337163799014e-147
8.791943776431501e-155

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05756
15756
done5756

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2074×body1280valid
937.0ms1732×body640valid
677.0ms5979×body80valid
315.0ms842×body320valid
106.0ms411×body160valid