Details

sample333.0ms

Algorithm

intervals

Results

39.0ms	92×	body	80	nan
19.0ms	181×	body	80	valid
17.0ms	33×	body	2560	valid
10.0ms	27×	body	1280	valid
4.0ms	14×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	8×	body	320	valid
2.0ms	6×	body	160	valid

simplify86.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (51.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize56.0ms

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))
1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite257.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

91.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
11.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
40.0ms	(- (* b_2 b_2) (* a c))
84.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify897.0ms

Counts

96 → 96

Iterations

Useful iterations: done (893.0ms)

Iter	Nodes	Cost
0	154	1624
1	384	1534
2	1453	1428
done	5001	1420

prune409.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize26.0ms

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))
1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite205.0ms

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×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

80.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
17.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
46.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

174 → 174

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	258	3976
1	640	3493
2	3061	3359
done	5000	3142

prune490.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cbrt 1) (cbrt 1)) (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
54×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`associate-/r*`
16×	`add-exp-log`
14×	`difference-of-squares`
12×	`add-cbrt-cube`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
3×	`div-inv`
2×	`sub-neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 110

Calls

4 calls:

70.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
53.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
50.0ms	(- (* b_2 b_2) (* a c))
114.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

122 → 122

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	213	2550
1	576	2147
2	2325	1936
done	5000	1829

prune448.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize14.0ms

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))
1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite215.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

110.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
53.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify904.0ms

Counts

96 → 96

Iterations

Useful iterations: done (900.0ms)

Iter	Nodes	Cost
0	154	1624
1	384	1534
2	1453	1428
done	5001	1420

prune344.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

regimes341.0ms

Accuracy

84.9% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 33.9b

bsearch120.0ms

Steps

Iters	Range		Point
7	1.2976235572645919e-73	6.718394677208045e-72	4.089744618622775e-73
7	-4.1637922183371475e+115	-1.3908068482385633e+114	-1.2857618218282695e+115

simplify14.0ms

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	29	48
1	37	40
2	41	36
done	41	36

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	5894×	body	80	valid
601.0ms	1093×	body	2560	valid
321.0ms	850×	body	1280	valid
317.0ms	3045×	body	80	nan
119.0ms	461×	body	640	valid
75.0ms	96×	body	5120	valid
44.0ms	239×	body	320	valid
13.0ms	101×	body	160	valid