Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
5.0ms	284×	pre	80	false
5.0ms	256×	pre	80	true

simplify783.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	98	11
4	201	11
5	450	11
6	746	11
7	3030	11
done	5000	11

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 13.8b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
0.0b	(- (* a a) (* b b))
13.4b	(/ (- (* a a) (* b b)) (* a a))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`sqrt-prod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 52

Calls

3 calls:

1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
4.0ms	(- (* a a) (* b b))
9.0ms	(/ (- (* a a) (* b b)) (* a a))

series27.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
6.0ms	(- (* a a) (* b b))
9.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify869.0ms

Counts

61 → 61

Iterations

Useful iterations: done (867.0ms)

Iter	Nodes	Cost
0	90	893
1	226	771
2	820	676
3	3652	668
done	5000	667

prune97.0ms

Filtered

43 candidates to 61 candidates (-41.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	2	63

Merged error: 0b

Counts

63 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ a (- a (* (/ b a) b)))
0.0b	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
0.0b	(/ 1 (/ a (- a (* (/ b a) b))))
0.1b	(* (/ b a) b)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
71×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
18×	`associate-/r*`
16×	`add-cbrt-cube`
13×	`associate-l`
11×	`associate-/r/`
9×	`div-exp`
8×	`pow1`
7×	`div-inv`
6×	`associate-/l*`
5×	`cbrt-undiv` `flip3--` `flip--`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
2×	`rec-exp` `frac-2neg` `1-exp` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 158

Calls

4 calls:

5.0ms	(/ a (- a (* (/ b a) b)))
1.0ms	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
8.0ms	(/ 1 (/ a (- a (* (/ b a) b))))
7.0ms	(* (/ b a) b)

series31.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ a (- a (* (/ b a) b)))
9.0ms	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
10.0ms	(/ 1 (/ a (- a (* (/ b a) b))))
4.0ms	(* (/ b a) b)

simplify458.0ms

Counts

170 → 170

Iterations

Useful iterations: done (444.0ms)

Iter	Nodes	Cost
0	244	2848
1	556	2597
2	1946	2283
done	5000	2275

prune190.0ms

Filtered

104 candidates to 170 candidates (-63.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	170	2	172

Merged error: 0b

Counts

172 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (/ (* b b) a))
0.0b	(sqrt (fabs (* (/ 1 a) (- a (/ (* b b) a)))))
0.2b	(* (/ 1 a) (- a (/ (* b b) a)))
13.0b	(/ (* b b) a)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-exp-log`
16×	`times-frac`
15×	`add-cube-cbrt`
14×	`add-cbrt-cube`
13×	`associate-l`
7×	`pow1`
6×	`associate-r` `add-log-exp`
5×	`prod-exp`
4×	`div-exp` `difference-of-squares`
3×	`cbrt-undiv` `sub-neg` `flip3--` `associate-/r*` `sqrt-prod` `flip--` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `div-inv` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l*`

Counts

4 → 95

Calls

4 calls:

5.0ms	(- a (/ (* b b) a))
1.0ms	(sqrt (fabs (* (/ 1 a) (- a (/ (* b b) a)))))
12.0ms	(* (/ 1 a) (- a (/ (* b b) a)))
8.0ms	(/ (* b b) a)

series29.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- a (/ (* b b) a))
9.0ms	(sqrt (fabs (* (/ 1 a) (- a (/ (* b b) a)))))
11.0ms	(* (/ 1 a) (- a (/ (* b b) a)))
4.0ms	(/ (* b b) a)

simplify441.0ms

Counts

107 → 107

Iterations

Useful iterations: done (439.0ms)

Iter	Nodes	Cost
0	156	1415
1	385	1231
2	1375	1086
done	5001	1074

prune143.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	107	2	109

Merged error: 0b

Counts

109 → 2

regimes97.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	13	13
done	13	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

310.0ms	8000×	body	80	valid
148.0ms	8000×	pre	80	true
147.0ms	7875×	pre	80	false

Details

sample38.0ms

simplify783.0ms

prune10.0ms

localize8.0ms

rewrite16.0ms

series27.0ms

simplify869.0ms

prune97.0ms

localize9.0ms

rewrite28.0ms

series31.0ms

simplify458.0ms

prune190.0ms

localize9.0ms

rewrite29.0ms

series29.0ms

simplify441.0ms

prune143.0ms

regimes97.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

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