Details

Time bar (total: 55.9s)

sample805.0ms

Algorithm
intervals
Results
243.0ms126×body1280valid
221.0ms73×body2560valid
193.0ms35×body5120valid
66.0ms73×body640valid
19.0ms33×body320valid
13.0ms62×body80valid
6.0ms13×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01925
14425
214725
383223
done500121

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k)))
1.5b
(* (/ (pow t 3.0) (* l l)) (sin k))
16.6b
(/ (pow t 3.0) (* l l))
28.9b
(/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (* (tan k) (pow (/ k t) 2.0)))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
150×div-exp
109×prod-exp
77×add-cbrt-cube
34×times-frac pow-exp
32×cbrt-undiv
25×add-sqr-sqrt pow-to-exp
22×cbrt-unprod
18×*-un-lft-identity add-cube-cbrt associate-/l*
11×associate-*l*
10×unpow-prod-down
6×pow1 div-inv
5×associate-*l/
4×associate-/r/ add-log-exp unswap-sqr sqr-pow
3×clear-num associate-/r* frac-2neg associate-*r*
1×pow-prod-down tan-quot *-commutative associate-/l/
Counts
4 → 185
Calls
4 calls:
37.0ms
(/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k)))
57.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
13.0ms
(/ (pow t 3.0) (* l l))
41.0ms
(/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (* (tan k) (pow (/ k t) 2.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
441.0ms
(/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k)))
363.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
238.0ms
(/ (pow t 3.0) (* l l))
826.0ms
(/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (* (tan k) (pow (/ k t) 2.0)))

simplify505.0ms

Counts
197 → 197
Iterations

Useful iterations: done (498.0ms)

IterNodesCost
02944203
18813918
done50003276

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow t 1.0) (pow k 2.0)))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.4b
(* (pow t 1.0) (pow k 2.0))
16.2b
(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite248.0ms

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×*-un-lft-identity add-cube-cbrt
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×clear-num frac-2neg *-commutative
1×associate-*r/ pow-flip inv-pow
Counts
4 → 600
Calls
4 calls:
28.0ms
(/ 1 (* (pow t 1.0) (pow k 2.0)))
26.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.0ms
(* (pow t 1.0) (pow k 2.0))
81.0ms
(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.0s

Counts
4 → 12
Calls
4 calls:
498.0ms
(/ 1 (* (pow t 1.0) (pow k 2.0)))
95.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
398.0ms
(* (pow t 1.0) (pow k 2.0))
1.0s
(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify507.0ms

Counts
612 → 612
Iterations

Useful iterations: done (474.0ms)

IterNodesCost
043715017
1121713309
done500013047

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.2b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.5b
(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.2b
(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite516.0ms

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×*-un-lft-identity add-cube-cbrt
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×clear-num frac-2neg
1×pow-pow associate-*r/ *-commutative pow-flip inv-pow
Counts
4 → 1460
Calls
4 calls:
6.0ms
(pow (sin k) 2)
47.0ms
(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
20.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
191.0ms
(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
38.0ms
(pow (sin k) 2)
440.0ms
(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
110.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
966.0ms
(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify816.0ms

Counts
1472 → 1472
Iterations

Useful iterations: done (709.0ms)

IterNodesCost
057450335
1174134666
done500032857

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (* (cbrt 1) (cbrt 1)) (* (pow t 1.0) (pow k (/ 2.0 2))))
5.3b
(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2))
7.7b
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2)))
8.2b
(* (pow (/ (* (cbrt 1) (cbrt 1)) (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
19559×add-exp-log
13708×prod-exp
10744×pow-exp
8260×div-exp
5156×pow-to-exp
876×rec-exp 1-exp
49×unpow-prod-down
40×add-cbrt-cube
39×times-frac
38×associate-*l*
33×add-sqr-sqrt
28×*-un-lft-identity add-cube-cbrt
17×cbrt-unprod
13×associate-*r*
10×cbrt-undiv
9×associate-/r* sqr-pow
5×div-inv
4×pow1 add-log-exp
3×unpow2 unswap-sqr
2×clear-num frac-2neg *-commutative associate-/l*
1×associate-*r/
Counts
4 → 3743
Calls
4 calls:
28.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (pow t 1.0) (pow k (/ 2.0 2))))
71.0ms
(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2))
94.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2)))
190.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2)))

series2.4s

Counts
4 → 12
Calls
4 calls:
498.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (pow t 1.0) (pow k (/ 2.0 2))))
472.0ms
(/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2))
419.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2)))
963.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (/ (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2)))

simplify2.2s

Counts
3755 → 3755
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01044165074
13470137177
done5000130094

prune1.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.8b

regimes1.1s

Accuracy

34.1% (4.1b remaining)

Error of 16.5b against oracle of 12.4b and baseline of 18.7b

bsearch1.8s

Steps
ItersRangePoint
10
1.0340362933942865e+150
1.8480168599026896e+163
1.3396743901283733e+154
10
-1.3048497031372084e+178
-2.3820198978012742e+162
-2.4279636162567888e+162

simplify16.0ms

Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
051110
163108
264106
done64106

end0.0ms

sample31.3s

Algorithm
intervals
Results
9.7s4144×body1280valid
8.9s2198×body2560valid
7.1s950×body5120valid
3.1s2565×body640valid
864.0ms948×body320valid
461.0ms1978×body80valid
248.0ms471×body160valid