Details

Time bar (total: 26.2s)

sample468.0ms

Algorithm
intervals
Results
150.0ms82×body2560valid
118.0ms28×body5120valid
109.0ms127×body1280valid
43.0ms86×body640valid
12.0ms36×body320valid
6.0ms50×body80valid
3.0ms11×body160valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114713
285712
3500211
done500211

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.6b
(* (pow t 3.0) (tan k))
20.4b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.9b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
337×add-exp-log
220×prod-exp
71×div-exp
65×add-cbrt-cube
51×pow-exp
34×pow-to-exp cbrt-unprod
30×unpow-prod-down
28×add-sqr-sqrt
24×associate-*l*
23×add-cube-cbrt *-un-lft-identity
19×times-frac
12×cbrt-undiv
5×pow1 associate-*r/
4×associate-*r* add-log-exp sqr-pow
3×tan-quot pow-unpow div-inv unswap-sqr
2×*-commutative
1×pow-pow frac-2neg associate-*l/ clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 179
Calls
4 calls:
7.0ms
(pow (/ k t) 2.0)
14.0ms
(* (pow t 3.0) (tan k))
89.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
44.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series982.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ k t) 2.0)
255.0ms
(* (pow t 3.0) (tan k))
402.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
262.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify139.0ms

Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09741954
149951620
250011620
done50011620

prune455.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.7b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.9b
(* (pow k 2.0) (pow t 1.0))
17.1b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite187.0ms

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:
17.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0ms
(* (pow k 2.0) (pow t 1.0))
71.0ms
(* (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:
365.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
98.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
349.0ms
(* (pow k 2.0) (pow t 1.0))
693.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify143.0ms

Counts
612 → 612
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
013167194
141627025
250027018
done50027018

prune627.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.1b

localize29.0ms

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))))
3.7b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.1b
(* (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)))

rewrite432.0ms

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:
3.0ms
(pow (sin k) 2)
45.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
133.0ms
(* (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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
20.0ms
(pow (sin k) 2)
358.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
94.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
701.0ms
(* (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)))

simplify269.0ms

Counts
1472 → 1472
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
0174223543
1457419111
2500217858
done500217858

prune570.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.4b
(* (pow (/ (sqrt 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))))
3.7b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
13973×add-exp-log
10155×prod-exp
8251×pow-exp
5914×div-exp
4231×pow-to-exp
920×rec-exp 1-exp
81×unpow-prod-down
64×times-frac
61×associate-*l*
49×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
21×sqrt-prod
14×cbrt-unprod
13×associate-*r*
12×sqr-pow
9×associate-/r*
8×cbrt-undiv
5×pow1 div-inv
4×associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 3203
Calls
4 calls:
18.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
174.0ms
(* (pow (/ (sqrt 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))))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
76.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.8s

Counts
4 → 12
Calls
4 calls:
351.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
675.0ms
(* (pow (/ (sqrt 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))))
94.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
687.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify559.0ms

Counts
3215 → 3215
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0296560483
1500160194
done500160194

prune958.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.5b

regimes235.0ms

Accuracy

0% (4.6b remaining)

Error of 18.5b against oracle of 13.9b and baseline of 18.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03321
13321
done3321

end0.0ms

sample14.2s

Algorithm
intervals
Results
4.2s2217×body2560valid
4.1s935×body5120valid
3.3s4107×body1280valid
1.3s2524×body640valid
373.0ms1039×body320valid
249.0ms2045×body80valid
107.0ms400×body160valid