Details

sample230.0ms

Algorithm

intervals

Results

22.0ms	192×	body	80	valid
19.0ms	31×	body	2560	valid
13.0ms	25×	body	1280	valid
9.0ms	99×	body	80	nan
5.0ms	5×	body	5120	valid
4.0ms	12×	body	640	valid
2.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify79.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	29
5	29
4	27
3	25
2	22
1	14
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

83.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
51.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
103.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
48.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

100 → 100

Iterations

Iter	Nodes
3	2948
2	997
1	377
0	158

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`sqrt-prod`
2×	`flip3--` `pow1/3` `sqrt-div` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 53

Calls

4 calls:

2.0ms	(cbrt a)
1.0ms	(cbrt a)
15.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(cbrt a)
249.0ms	(cbrt a)
40.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

65 → 65

Iterations

Iter	Nodes
4	3861
3	1394
2	494
1	187
0	83

prune834.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 61

Calls

4 calls:

11.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(sqrt (- (* b_2 b_2) (* a c)))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

73 → 73

Iterations

Iter	Nodes
4	3437
3	1222
2	407
1	146
0	60

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
9.5b	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
24.5b	(sqrt (- (* b_2 b_2) (* a c)))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`
1×	`difference-of-squares`

Counts

4 → 59

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts

71 → 71

Iterations

Iter	Nodes
4	6497
3	1974
2	628
1	222
0	93

prune681.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.9b

regimes417.0ms

Accuracy

82.9% (4.8b remaining)

Error of 10.5b against oracle of 5.7b and baseline of 33.7b

bsearch141.0ms

Steps

Iters	Range		Point
6	3.7222086374392734e-21	4.963951531010332e-20	7.189328114522003e-21
8	-3.585760457965514e+97	-4.884785332531034e+94	-1.3735480881409494e+97

simplify15.0ms

Iterations

Iter	Nodes
2	37
1	37
0	31

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	5858×	body	80	valid
814.0ms	1029×	body	2560	valid
611.0ms	890×	body	1280	valid
455.0ms	2857×	body	80	nan
285.0ms	469×	body	640	valid
126.0ms	107×	body	5120	valid
111.0ms	201×	body	320	valid
31.0ms	140×	body	160	valid