Details

sample283.0ms

Algorithm

intervals

Results

7.0ms	37×	body	2560	valid
6.0ms	195×	body	80	valid
5.0ms	21×	body	1280	valid
2.0ms	81×	body	80	nan
2.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

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:

43.0ms	(/ (- (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)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
34.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

130 → 130

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	195	2408
1	452	2113
2	1143	1874
3	3880	1795
done	5001	1792

prune328.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 196

Calls

4 calls:

30.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
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)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
37.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts

208 → 208

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	299	4764
1	655	4148
2	1750	3649
3	4960	3500
done	5000	3500

prune353.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)))
0.5b	(fma b_2 b_2 (- (* c a)))
1.2b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
20.6b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
18×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
7×	`div-exp`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `fma-udef` `inv-pow`

Counts

4 → 188

Calls

4 calls:

14.0ms	(/ 1 (/ a (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)))
0.0ms	(fma b_2 b_2 (- (* c a)))
6.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
1.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ 1 (/ a (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)))
45.0ms	(fma b_2 b_2 (- (* c a)))
85.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
70.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.8s

Counts

200 → 200

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	278	4616
1	588	4021
2	1491	3542
3	4109	3388
done	5000	3388

prune340.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
0.4b	(- (pow b_2 2) (* a c))
1.2b	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
20.6b	(sqrt (- (pow b_2 2) (* a c)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
62×	`prod-diff`
60×	`*-un-lft-identity`
55×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
14×	`fma-neg`
13×	`add-exp-log` `associate-l`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`unpow-prod-down` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sqrt-div` `diff-log` `associate-*r/` `div-exp` `cbrt-unprod` `distribute-lft-out--` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 172

Calls

4 calls:

101.0ms	(* (/ 1 a) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
9.0ms	(- (pow b_2 2) (* a c))
50.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
10.0ms	(sqrt (- (pow b_2 2) (* a c)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (/ 1 a) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
34.0ms	(- (pow b_2 2) (* a c))
75.0ms	(- (sqrt (- (pow b_2 2) (* a c))) b_2)
65.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify1.7s

Counts

184 → 184

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	254	4225
1	621	3436
2	1667	2707
done	5000	2479

prune333.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes168.0ms

Accuracy

83.4% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch104.0ms

Steps

Iters	Range		Point
10	3.056596725548563e-78	7.076105677608322e-63	3.446447862996811e-75
10	-1.852183237050365e+100	-1.9127319211193897e+86	-4.123103533644211e+95

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	37
1	34	37
2	36	37
done	36	37

end0.0ms

sample1.0s

Algorithm

intervals

Results

211.0ms	1099×	body	2560	valid
198.0ms	5881×	body	80	valid
138.0ms	851×	body	1280	valid
97.0ms	2944×	body	80	nan
57.0ms	470×	body	640	valid
26.0ms	109×	body	5120	valid
20.0ms	219×	body	320	valid
6.0ms	98×	body	160	valid