Details

sample30.0ms

Algorithm

intervals

Results

10.0ms

280×

body

valid

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	21	11
2	34	11
3	55	11
4	87	11
5	127	11
6	169	11
7	188	11
8	214	11
9	249	11
10	315	11
11	421	11
12	549	11
13	785	11
14	1021	11
15	1318	11
16	1656	11
17	2079	11
18	2538	11
19	3072	11
20	3671	11
21	4324	11
22	4991	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: 1.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- z a))
2.2b	(* y (/ (- z t) (- z a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 102

Calls

2 calls:

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

series37.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(/ (- z t) (- z a))
27.0ms	(* y (/ (- z t) (- z a)))

simplify867.0ms

Counts

108 → 108

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	138	1319
1	354	1257
2	1049	1173
3	3571	1167
done	5001	1165

prune116.0ms

Filtered

72 candidates to 108 candidates (-50.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Merged error: 0b

Counts

109 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(* y (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))))
3.5b	(cbrt (/ (- z t) (- z a)))
3.5b	(cbrt (/ (- z t) (- z a)))
3.5b	(cbrt (/ (- z t) (- z a)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
38×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1` `add-exp-log`
7×	`cbrt-div` `add-cbrt-cube`
6×	`associate-/r/`
4×	`associate-*r/` `add-log-exp`
3×	`flip3--` `pow1/3` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `div-inv`
1×	`frac-times` `associate-r` `associate-l/` `-commutative` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

23.0ms	(* y (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))))
8.0ms	(cbrt (/ (- z t) (- z a)))
8.0ms	(cbrt (/ (- z t) (- z a)))
8.0ms	(cbrt (/ (- z t) (- z a)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* y (* (cbrt (/ (- z t) (- z a))) (cbrt (/ (- z t) (- z a)))))
33.0ms	(cbrt (/ (- z t) (- z a)))
33.0ms	(cbrt (/ (- z t) (- z a)))
41.0ms	(cbrt (/ (- z t) (- z a)))

simplify1.1s

Counts

154 → 154

Iterations

Useful iterations: 4 (529.0ms)

Iter	Nodes	Cost
0	160	2642
1	315	2524
2	655	2390
3	1477	2361
4	3816	2345
done	5000	2345

prune152.0ms

Filtered

106 candidates to 154 candidates (-45.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	154	4	158

Merged error: 0b

Counts

158 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (- z a))
12.0b	(* (* (- z t) y) (/ 1 (- z a)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
28×	`add-exp-log`
21×	`add-cube-cbrt` `associate-r`
16×	`add-cbrt-cube`
12×	`prod-exp`
8×	`pow1`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`div-exp` `associate-*l/` `cbrt-unprod`
5×	`associate-/r*`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-/l*`
2×	`frac-times` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `associate-l` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 91

Calls

2 calls:

6.0ms	(/ 1 (- z a))
15.0ms	(* (* (- z t) y) (/ 1 (- z a)))

series22.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ 1 (- z a))
17.0ms	(* (* (- z t) y) (/ 1 (- z a)))

simplify1.1s

Counts

97 → 97

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	137	1154
1	383	1001
2	1561	832
done	5000	812

prune81.0ms

Filtered

50 candidates to 97 candidates (-94.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	97	4	101

Merged error: 0b

Counts

101 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt y) (sqrt (/ (- z t) (- z a))))
0.1b	(* (* (sqrt y) (sqrt (/ (- z t) (- z a)))) (* (sqrt y) (sqrt (/ (- z t) (- z a)))))
2.9b	(sqrt (/ (- z t) (- z a)))
2.9b	(sqrt (/ (- z t) (- z a)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
103×	`sqrt-prod`
100×	`*-un-lft-identity`
79×	`times-frac`
65×	`pow1`
40×	`add-cube-cbrt`
38×	`pow-prod-down`
35×	`associate-r`
30×	`distribute-lft-out--` `difference-of-squares`
20×	`sqrt-pow1` `pow1/2`
18×	`add-exp-log` `add-cbrt-cube`
9×	`prod-exp` `cbrt-unprod`
8×	`pow-prod-up`
7×	`sqrt-div` `associate-l`
6×	`sqrt-unprod` `associate-*r/` `associate-/r/` `pow-sqr` `unswap-sqr`
4×	`rem-sqrt-square` `add-log-exp`
3×	`flip3--` `flip--` `div-inv`
2×	`pow-plus` `*-commutative`
1×	`pow2` `frac-times` `swap-sqr` `associate-*l/` `rem-square-sqrt`

Counts

4 → 194

Calls

4 calls:

18.0ms	(* (sqrt y) (sqrt (/ (- z t) (- z a))))
27.0ms	(* (* (sqrt y) (sqrt (/ (- z t) (- z a)))) (* (sqrt y) (sqrt (/ (- z t) (- z a)))))
9.0ms	(sqrt (/ (- z t) (- z a)))
9.0ms	(sqrt (/ (- z t) (- z a)))

series133.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt y) (sqrt (/ (- z t) (- z a))))
35.0ms	(* (* (sqrt y) (sqrt (/ (- z t) (- z a)))) (* (sqrt y) (sqrt (/ (- z t) (- z a)))))
30.0ms	(sqrt (/ (- z t) (- z a)))
30.0ms	(sqrt (/ (- z t) (- z a)))

simplify548.0ms

Counts

206 → 206

Iterations

Useful iterations: done (542.0ms)

Iter	Nodes	Cost
0	215	3308
1	451	2737
2	1368	2485
done	5001	2439

prune152.0ms

Filtered

124 candidates to 206 candidates (-66.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	206	4	210

Merged error: 0b

Counts

210 → 4

regimes527.0ms

Accuracy

42.3% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 1.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	25	36
done	25	36

end0.0ms

sample884.0ms

Algorithm

intervals

Results

326.0ms	8754×	body	80	valid
0.0ms	2×	body	1280	valid

Details

sample30.0ms

simplify5.0s

prune4.0ms

localize8.0ms

rewrite28.0ms

series37.0ms

simplify867.0ms

prune116.0ms

localize12.0ms

rewrite54.0ms

series157.0ms

simplify1.1s

prune152.0ms

localize9.0ms

rewrite24.0ms

series22.0ms

simplify1.1s

prune81.0ms

localize12.0ms

rewrite82.0ms

series133.0ms

simplify548.0ms

prune152.0ms

regimes527.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample884.0ms

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