Details

sample51.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
6.0ms	262×	pre	80	false
5.0ms	256×	pre	80	true

simplify4.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	98	11
4	187	11
5	332	11
6	498	11
7	1408	11
done	5001	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
31.6b	(/ (* b b) (* a a))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-undiv` `add-sqr-sqrt` `div-exp` `prod-exp` `cbrt-unprod`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-log-exp`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

2 → 34

Calls

2 calls:

2.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
15.0ms	(/ (* b b) (* a a))

series55.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
37.0ms	(/ (* b b) (* a a))

simplify9.6s

Counts

40 → 40

Iterations

Useful iterations: 4 (8.4s)

Iter	Nodes	Cost
0	65	498
1	145	462
2	488	370
3	1836	355
4	4570	345
done	5001	345

prune133.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
0.1b	(* b (/ b a))
14.8b	(/ (* b (/ b a)) a)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`times-frac` `associate-r`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-l` `associate-/r*` `sqrt-prod` `add-log-exp`
2×	`associate-*r/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

3 → 69

Calls

3 calls:

1.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
19.0ms	(* b (/ b a))
15.0ms	(/ (* b (/ b a)) a)

series85.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
33.0ms	(* b (/ b a))
34.0ms	(/ (* b (/ b a)) a)

simplify3.7s

Counts

78 → 78

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	113	789
1	258	734
2	747	623
3	2567	599
done	5000	599

prune260.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (pow (/ (pow b 2) a) 1) a))))
14.8b	(/ (pow (/ (pow b 2) a) 1) a)
15.8b	(/ (pow b 2) a)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

216×	`times-frac`
160×	`unpow-prod-down`
119×	`add-sqr-sqrt`
118×	`add-cube-cbrt` `*-un-lft-identity`
40×	`associate-/l*`
21×	`add-exp-log`
20×	`sqr-pow`
16×	`unpow2`
12×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-exp` `associate-/r*` `div-inv`
4×	`pow1`
3×	`pow-to-exp` `sqrt-prod` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

3 → 210

Calls

3 calls:

7.0ms	(sqrt (fabs (- 1 (/ (pow (/ (pow b 2) a) 1) a))))
46.0ms	(/ (pow (/ (pow b 2) a) 1) a)
9.0ms	(/ (pow b 2) a)

series107.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (fabs (- 1 (/ (pow (/ (pow b 2) a) 1) a))))
45.0ms	(/ (pow (/ (pow b 2) a) 1) a)
33.0ms	(/ (pow b 2) a)

simplify1.6s

Counts

219 → 219

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	378	3671
1	563	2811
2	1580	2530
done	5000	2330

prune706.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
14.6b	(/ (- (* a a) (* b b)) (* a a))

rewrite35.0ms

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:

8.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
24.0ms	(/ (- (* a a) (* b b)) (* a a))

series155.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(- (* a a) (* b b))
32.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
90.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify2.3s

Counts

61 → 61

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	90	893
1	218	771
2	639	676
3	3171	668
done	5001	668

prune215.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes184.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	12	11
done	12	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

300.0ms	8000×	body	80	valid
149.0ms	8000×	pre	80	true
148.0ms	8104×	pre	80	false