Details

Time bar (total: 58.6s)

sample917.0ms

Algorithm
intervals
Results
325.0ms81×body2560valid
223.0ms32×body5120valid
205.0ms121×body1280valid
76.0ms86×body640valid
25.0ms32×body320valid
15.0ms71×body80valid
7.0ms15×body160valid

simplify954.0ms

Counts
1 → 1
Iterations

Useful iterations: done (954.0ms)

IterNodesCost
01925
14425
214825
384123
done500121

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.5b
(* (/ (pow t 3.0) (* l l)) (sin k))
14.8b
(/ (pow t 3.0) (* l l))
27.8b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite411.0ms

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:
114.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
57.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
12.0ms
(/ (pow t 3.0) (* l l))
195.0ms
(/ (/ 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:
517.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
313.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
213.0ms
(/ (pow t 3.0) (* l l))
662.0ms
(/ (/ 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 (1.1s)

IterNodesCost
067010352
117859880
done50009414

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.3b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.7b
(* (pow k 2.0) (pow t 1.0))
16.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite300.0ms

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×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 608
Calls
4 calls:
28.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
30.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
21.0ms
(* (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:
547.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
123.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
520.0ms
(* (pow k 2.0) (pow t 1.0))
980.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify797.0ms

Counts
620 → 620
Iterations

Useful iterations: done (776.0ms)

IterNodesCost
049115125
1148113001
done500112725

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.8b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
0.4b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.3b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.4b
(* (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)))

rewrite669.0ms

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:
6.0ms
(pow (sin k) 2)
63.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
265.0ms
(* (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)))

series1.8s

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (sin k) 2)
523.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
130.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.1s
(* (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)))

simplify1.1s

Counts
1480 → 1480
Iterations

Useful iterations: done (1.0s)

IterNodesCost
060550477
1205133540
done500131701

prune1.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
2.5b
(* (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))))
4.3b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.0b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite2.1s

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:
37.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
294.0ms
(* (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))))
28.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
173.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series3.1s

Counts
4 → 12
Calls
4 calls:
475.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
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))))
146.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.5s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.8s

Counts
5782 → 5782
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01484226187
done5000203113

prune3.1s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.6b

regimes870.0ms

Accuracy

27.4% (5.7b remaining)

Error of 15.6b against oracle of 9.8b and baseline of 17.7b

bsearch3.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04478
15474
25574
done5574

end0.0ms

sample29.8s

Algorithm
intervals
Results
8.5s2179×body2560valid
8.1s4081×body1280valid
6.7s903×body5120valid
3.0s2498×body640valid
1.2s1027×body320valid
962.0ms2058×body80valid
288.0ms405×body160valid