Details

sample235.0ms

Algorithm

intervals

Results

32.0ms	199×	body	80	valid
26.0ms	30×	body	2560	valid
22.0ms	30×	body	1280	valid
12.0ms	90×	body	80	nan
6.0ms	10×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	7×	body	320	valid
1.0ms	2×	body	160	valid

simplify106.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	61
5	61
4	57
3	51
2	44
1	34
0	10

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite203.0ms

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:

118.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
29.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
41.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

100 → 100

Iterations

Iter	Nodes
3	2918
2	1363
1	660
0	158

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.6b	(sqrt (- (* b_2 b_2) (* a c)))
19.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

41.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
35.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
4	2944
3	1561
2	709
1	331
0	80

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
10.3b	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
19.6b	(sqrt (- (* b_2 b_2) (* a c)))
19.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite105.0ms

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:

14.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b_2 b_2) (* a c))
99.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
3	2027
2	838
1	385
0	93

prune1.0s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.6b	(sqrt (- (* b_2 b_2) (* a c)))
19.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

42.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
34.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
80.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
4	2944
3	1561
2	709
1	331
0	80

prune1.1s

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 5.3b

regimes380.0ms

Accuracy

85.3% (4.1b remaining)

Error of 9.3b against oracle of 5.2b and baseline of 33.1b

bsearch198.0ms

Steps

Iters	Range		Point
9	9.392283277667625e-73	1.0297697901410487e-64	1.1310477508076152e-72
9	-2.1289244816744743e+133	-2.3153117107728934e+126	-1.1783617127509567e+133

simplify29.0ms

Iterations

Iter	Nodes
2	28
1	28
0	24

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	5794×	body	80	valid
812.0ms	1065×	body	2560	valid
663.0ms	924×	body	1280	valid
363.0ms	2872×	body	80	nan
217.0ms	423×	body	640	valid
190.0ms	112×	body	5120	valid
111.0ms	242×	body	320	valid
23.0ms	99×	body	160	valid