Details

sample282.0ms

Algorithm

intervals

Results

8.0ms	194×	body	80	valid
8.0ms	40×	body	2560	valid
5.0ms	28×	body	1280	valid
2.0ms	76×	body	80	nan
1.0ms	10×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 118

Calls

4 calls:

40.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
22.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
38.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify545.0ms

Counts

130 → 130

Iterations

Useful iterations: done (540.0ms)

Iter	Nodes	Cost
0	195	2408
1	446	2113
2	1382	1856
done	5000	1855

prune326.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
0.4b	(- (* b_2 b_2) (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify685.0ms

Counts

78 → 78

Iterations

Useful iterations: done (684.0ms)

Iter	Nodes	Cost
0	67	930
1	156	850
2	468	768
3	1488	766
done	5000	762

prune264.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
20.4b	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 60

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
0.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify708.0ms

Counts

72 → 72

Iterations

Useful iterations: done (706.0ms)

Iter	Nodes	Cost
0	84	1019
1	181	815
2	530	737
3	1729	734
done	5000	731

prune251.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify685.0ms

Counts

79 → 79

Iterations

Useful iterations: done (683.0ms)

Iter	Nodes	Cost
0	67	979
1	156	877
2	468	802
3	1488	799
done	5000	795

prune260.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.7b

regimes216.0ms

Accuracy

86% (4.0b remaining)

Error of 9.8b against oracle of 5.8b and baseline of 34.5b

bsearch100.0ms

Steps

Iters	Range		Point
8	1.225968609186083e-71	5.862533224041234e-67	5.083748087944341e-70
11	-1.829086240692416e+154	-2.187052964502477e+134	-1.0524969308880696e+141

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	46
1	28	46
done	28	46

end0.0ms

sample1.1s

Algorithm

intervals

Results

228.0ms	1107×	body	2560	valid
200.0ms	5865×	body	80	valid
153.0ms	908×	body	1280	valid
96.0ms	2861×	body	80	nan
53.0ms	422×	body	640	valid
24.0ms	97×	body	5120	valid
23.0ms	216×	body	320	valid
8.0ms	117×	body	160	valid