Details

sample36.0ms

Algorithm

intervals

Results

11.0ms

281×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	20	11
2	33	11
3	54	11
4	86	11
5	128	11
6	158	11
7	176	11
8	202	11
9	249	11
10	324	11
11	431	11
12	605	11
13	795	11
14	1040	11
15	1217	11
16	1403	11
17	1606	11
18	1783	11
19	1969	11
20	2172	11
21	2347	11
22	2533	11
23	2734	11
24	2909	11
25	3093	11
26	3294	11
27	3469	11
28	3652	11
29	3852	11
30	4027	11
31	4210	11
32	4410	11
33	4585	11
34	4768	11
35	4968	11
done	5000	11

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.8b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- a t))))
0.0b	(/ (- z t) (- a t))
2.5b	(* y (/ (- z t) (- a t)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 113

Calls

3 calls:

3.0ms	(+ x (* y (/ (- z t) (- a t))))
9.0ms	(/ (- z t) (- a t))
15.0ms	(* y (/ (- z t) (- a t)))

series63.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ x (* y (/ (- z t) (- a t))))
10.0ms	(/ (- z t) (- a t))
18.0ms	(* y (/ (- z t) (- a t)))

simplify904.0ms

Counts

122 → 122

Iterations

Useful iterations: done (901.0ms)

Iter	Nodes	Cost
0	162	1555
1	424	1454
2	1278	1368
3	4226	1368
done	5001	1366

prune152.0ms

Filtered

85 candidates to 122 candidates (-43.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Merged error: 0b

Counts

123 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (* (- z t) (/ 1 (- a t)))))
0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
2.5b	(* y (* (- z t) (/ 1 (- a t))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-r/` `associate-l*` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`flip3--` `div-exp` `flip--` `add-log-exp`
5×	`associate-/r*`
4×	`frac-times` `pow-prod-down` `associate-*l/` `associate-/r/`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 130

Calls

4 calls:

4.0ms	(+ x (* y (* (- z t) (/ 1 (- a t)))))
6.0ms	(/ 1 (- a t))
18.0ms	(* (- z t) (/ 1 (- a t)))
14.0ms	(* y (* (- z t) (/ 1 (- a t))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ x (* y (* (- z t) (/ 1 (- a t)))))
5.0ms	(/ 1 (- a t))
10.0ms	(* (- z t) (/ 1 (- a t)))
18.0ms	(* y (* (- z t) (/ 1 (- a t))))

simplify508.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (139.0ms)

Iter	Nodes	Cost
0	182	1728
1	459	1436
2	1707	1228
done	5000	1228

prune127.0ms

Filtered

85 candidates to 142 candidates (-67.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	142	6	148

Merged error: 0b

Counts

148 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
3.7b	(cbrt (/ (- z t) (- a t)))
3.7b	(cbrt (/ (- z t) (- a t)))
3.7b	(cbrt (/ (- z t) (- a t)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

333×	`*-un-lft-identity`
277×	`cbrt-prod`
273×	`add-sqr-sqrt`
229×	`times-frac`
106×	`distribute-lft-out--`
93×	`add-cube-cbrt`
78×	`difference-of-squares`
58×	`swap-sqr`
34×	`associate-r` `associate-l`
14×	`associate-/r/`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `flip3--` `flip--` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 276

Calls

4 calls:

41.0ms	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
8.0ms	(cbrt (/ (- z t) (- a t)))
8.0ms	(cbrt (/ (- z t) (- a t)))
8.0ms	(cbrt (/ (- z t) (- a t)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
66.0ms	(cbrt (/ (- z t) (- a t)))
69.0ms	(cbrt (/ (- z t) (- a t)))
72.0ms	(cbrt (/ (- z t) (- a t)))

simplify863.0ms

Counts

288 → 288

Iterations

Useful iterations: done (851.0ms)

Iter	Nodes	Cost
0	296	6474
1	554	6111
2	1634	5934
3	4855	5621
done	5000	5619

prune257.0ms

Filtered

176 candidates to 288 candidates (-63.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	288	6	294

Merged error: 0b

Counts

294 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (pow (* (- z t) (/ y (- a t))) 1))
0.0b	(/ y (- a t))
10.0b	(* (- z t) (/ y (- a t)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-l` `associate-/r*` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `distribute-lft-out`

Counts

3 → 95

Calls

3 calls:

4.0ms	(+ x (pow (* (- z t) (/ y (- a t))) 1))
6.0ms	(/ y (- a t))
14.0ms	(* (- z t) (/ y (- a t)))

series58.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ x (pow (* (- z t) (/ y (- a t))) 1))
8.0ms	(/ y (- a t))
17.0ms	(* (- z t) (/ y (- a t)))

simplify462.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	157	1262
1	377	1141
2	1438	1063
done	5000	1063

prune111.0ms

Filtered

77 candidates to 104 candidates (-35.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	104	6	110

Merged error: 0b

Counts

110 → 6

regimes474.0ms

Accuracy

43.9% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 1.5b

bsearch18.0ms

Steps

Iters	Range		Point
2	5.691295351696058e-12	6.447125064489246e-12	6.1636889221918e-12
5	-2.0905344850362395e-22	-6.092576105087712e-23	-2.060365571784887e-22

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	45
1	34	43
done	34	43

end0.0ms

sample873.0ms

Algorithm

intervals

Results

339.0ms	8728×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid

Details

sample36.0ms

simplify2.1s

prune4.0ms

localize8.0ms

rewrite33.0ms

series63.0ms

simplify904.0ms

prune152.0ms

localize13.0ms

rewrite47.0ms

series67.0ms

simplify508.0ms

prune127.0ms

localize12.0ms

rewrite88.0ms

series299.0ms

simplify863.0ms

prune257.0ms

localize10.0ms

rewrite29.0ms

series58.0ms

simplify462.0ms

prune111.0ms

regimes474.0ms

bsearch18.0ms

simplify3.0ms

end0.0ms

sample873.0ms

Profiling