Details

sample134.0ms

Algorithm

intervals

Results

9.0ms	186×	body	80	valid
9.0ms	30×	body	2560	valid
7.0ms	102×	body	80	nan
5.0ms	23×	body	1280	valid
2.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize29.0ms

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))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite241.0ms

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--` `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 → 84

Calls

4 calls:

125.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
26.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
58.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
131.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify856.0ms

Counts

96 → 96

Iterations

Useful iterations: done (852.0ms)

Iter	Nodes	Cost
0	154	1624
1	384	1534
2	1459	1426
done	5001	1420

prune569.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 162

Calls

4 calls:

68.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
6.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
53.0ms	(- (* b_2 b_2) (* a c))
120.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

174 → 174

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	258	3976
1	640	3493
2	3009	3359
done	5001	3142

prune720.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.6b	(- (* b_2 b_2) (* a c))
5.5b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`times-frac`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--` `distribute-lft-out--`
3×	`associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-exp` `frac-sub` `sub-div`

Counts

4 → 93

Calls

4 calls:

26.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
12.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
38.0ms	(- (* b_2 b_2) (* a c))
134.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify732.0ms

Counts

105 → 105

Iterations

Useful iterations: done (728.0ms)

Iter	Nodes	Cost
0	175	1826
1	404	1686
2	1329	1596
done	5001	1594

prune644.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize24.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
23.8b	(cbrt (- (* b_2 b_2) (* a c)))
23.8b	(cbrt (- (* b_2 b_2) (* a c)))
23.8b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite137.0ms

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` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

115.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
7.0ms	(cbrt (- (* b_2 b_2) (* a c)))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))
5.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
123.0ms	(cbrt (- (* b_2 b_2) (* a c)))
120.0ms	(cbrt (- (* b_2 b_2) (* a c)))
139.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

101 → 101

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	182	3107
1	357	2783
2	817	2200
3	3016	2149
done	5000	2069

prune615.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

regimes432.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 34.1b

bsearch175.0ms

Steps

Iters	Range		Point
9	7.013128997607284e-77	5.714800893424793e-72	4.425266767149826e-76
8	-9.061058506829192e+105	-7.154008779742083e+102	-5.062954969806706e+105

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	40
1	26	40
done	26	40

end0.0ms

sample3.0s

Algorithm

intervals

Results

941.0ms	5961×	body	80	valid
637.0ms	1055×	body	2560	valid
377.0ms	880×	body	1280	valid
266.0ms	2944×	body	80	nan
115.0ms	451×	body	640	valid
48.0ms	97×	body	5120	valid
42.0ms	218×	body	320	valid
13.0ms	109×	body	160	valid