Details

sample345.0ms

Algorithm

intervals

Results

122.0ms	29×	body	2560	valid
73.0ms	24×	body	1280	valid
31.0ms	186×	body	80	valid
14.0ms	88×	body	80	nan
10.0ms	17×	body	640	valid
5.0ms	10×	body	320	valid
3.0ms	3×	body	5120	valid

simplify37.0ms

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: 33.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite406.0ms

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:

129.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
218.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
38.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
44.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify906.0ms

Counts

100 → 100

Iterations

Iter	Nodes
3	2929
2	997
1	379
0	158

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite175.0ms

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:

81.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
64.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
108.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
54.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

100 → 100

Iterations

Iter	Nodes
3	2929
2	997
1	379
0	158

prune948.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize30.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
1.6b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `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`

Counts

4 → 58

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

70 → 70

Iterations

Iter	Nodes
4	3514
3	1222
2	409
1	148
0	60

prune947.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize90.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
25.2b	(cbrt (- (* b_2 b_2) (* a c)))
25.2b	(cbrt (- (* b_2 b_2) (* a c)))
25.2b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 93

Calls

4 calls:

118.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
11.0ms	(cbrt (- (* b_2 b_2) (* a c)))
11.0ms	(cbrt (- (* b_2 b_2) (* a c)))
10.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series846.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
109.0ms	(cbrt (- (* b_2 b_2) (* a c)))
479.0ms	(cbrt (- (* b_2 b_2) (* a c)))
151.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

105 → 105

Iterations

Iter	Nodes
4	3648
3	1482
2	661
1	340
0	184

prune1.9s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

regimes412.0ms

Accuracy

84.2% (4.4b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.0b

bsearch186.0ms

Steps

Iters	Range		Point
9	2.5177836961106285e-119	1.1213560046341023e-113	7.296044290893796e-114
7	-4.611849920572465e+95	-3.3021145473587595e+93	-3.177289780863109e+94

simplify4.0ms

Iterations

Iter	Nodes
2	28
1	28
0	24

end0.0ms

sample3.7s

Algorithm

intervals

Results

835.0ms	5835×	body	80	valid
802.0ms	1092×	body	2560	valid
695.0ms	2905×	body	80	nan
550.0ms	914×	body	1280	valid
253.0ms	458×	body	640	valid
93.0ms	126×	body	5120	valid
65.0ms	228×	body	320	valid
44.0ms	100×	body	160	valid