Details

sample281.0ms

Algorithm

intervals

Results

7.0ms	187×	body	80	valid
7.0ms	40×	body	2560	valid
3.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify22.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite74.0ms

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:

34.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
2.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

96 → 96

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	154	1624
1	362	1526
2	950	1426
3	2685	1418
done	5001	1416

prune255.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 85

Calls

4 calls:

60.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
2.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
36.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

97 → 97

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	174	1603
1	423	1403
2	1201	1255
3	3911	1247
done	5000	1246

prune215.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite62.0ms

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:

36.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
2.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
35.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

96 → 96

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	154	1624
1	362	1526
2	950	1426
3	2685	1418
done	5001	1416

prune203.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
21.9b	(cbrt (- (* b_2 b_2) (* a c)))
21.9b	(cbrt (- (* b_2 b_2) (* a c)))
21.9b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

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` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

33.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
2.0ms	(cbrt (- (* b_2 b_2) (* a c)))
2.0ms	(cbrt (- (* b_2 b_2) (* a c)))
2.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
86.0ms	(cbrt (- (* b_2 b_2) (* a c)))
85.0ms	(cbrt (- (* b_2 b_2) (* a c)))
90.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

101 → 101

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	182	3107
1	327	2783
2	652	2200
3	1527	2149
4	4540	2068
done	5001	2068

prune254.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

regimes163.0ms

Accuracy

83.6% (4.6b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 33.7b

bsearch72.0ms

Steps

Iters	Range		Point
8	1.3679096689958957e-81	5.608239720335765e-77	3.84613441880261e-81
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	36
1	28	36
done	28	36

end0.0ms

sample951.0ms

Algorithm

intervals

Results

195.0ms	1075×	body	2560	valid
185.0ms	5844×	body	80	valid
139.0ms	911×	body	1280	valid
89.0ms	2888×	body	80	nan
51.0ms	451×	body	640	valid
23.0ms	102×	body	5120	valid
20.0ms	231×	body	320	valid
7.0ms	119×	body	160	valid