Details

sample287.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
8.0ms	187×	body	80	valid
4.0ms	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

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize18.0ms

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)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 118

Calls

4 calls:

42.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
3.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify625.0ms

Counts

130 → 130

Iterations

Useful iterations: done (621.0ms)

Iter	Nodes	Cost
0	195	2408
1	466	2113
2	1585	1856
done	5000	1855

prune335.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize9.0ms

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)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `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 → 119

Calls

4 calls:

62.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
5.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify909.0ms

Counts

131 → 131

Iterations

Useful iterations: done (906.0ms)

Iter	Nodes	Cost
0	215	2391
1	532	2008
2	2039	1683
done	5001	1682

prune297.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

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)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 118

Calls

4 calls:

44.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
3.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(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)))

simplify605.0ms

Counts

130 → 130

Iterations

Useful iterations: done (600.0ms)

Iter	Nodes	Cost
0	195	2408
1	466	2113
2	1585	1856
done	5000	1855

prune318.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

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)))
23.0b	(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

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)))
0.0ms	(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))

series348.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt (- (* b_2 b_2) (* a c)))
84.0ms	(cbrt (- (* b_2 b_2) (* a c)))
84.0ms	(cbrt (- (* b_2 b_2) (* a c)))
96.0ms	(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))

simplify748.0ms

Counts

67 → 67

Iterations

Useful iterations: done (746.0ms)

Iter	Nodes	Cost
0	82	1212
1	193	1060
2	543	943
3	1741	921
done	5000	894

prune268.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes180.0ms

Accuracy

83.4% (4.7b remaining)

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

bsearch78.0ms

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: 1 (1.0ms)

Iter	Nodes	Cost
0	25	36
1	30	30
done	30	30

end0.0ms

sample1.0s

Algorithm

intervals

Results

206.0ms	1075×	body	2560	valid
195.0ms	5844×	body	80	valid
147.0ms	911×	body	1280	valid
90.0ms	2888×	body	80	nan
58.0ms	451×	body	640	valid
28.0ms	102×	body	5120	valid
21.0ms	231×	body	320	valid
7.0ms	119×	body	160	valid