Details

sample281.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
5.0ms	36×	body	1280	valid
5.0ms	165×	body	80	valid
3.0ms	86×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	4×	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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.6b	(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:

39.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
3.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- (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)))

simplify553.0ms

Counts

130 → 130

Iterations

Useful iterations: done (549.0ms)

Iter	Nodes	Cost
0	195	2408
1	446	2113
2	1384	1856
done	5000	1855

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.0b	(- (* b_2 b_2) (* a c))
8.3b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

481×	`times-frac`
378×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
358×	`add-cube-cbrt`
287×	`prod-diff`
143×	`sqrt-prod`
39×	`div-inv`
23×	`fma-neg`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 411

Calls

4 calls:

7.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms	(- (* b_2 b_2) (* a c))
50.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
37.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify891.0ms

Counts

423 → 423

Iterations

Useful iterations: done (874.0ms)

Iter	Nodes	Cost
0	497	18768
1	1053	16536
2	2586	13156
done	5000	13111

prune711.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
17.5b	(- (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (/ b_2 a))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

10335×	`times-frac`
7608×	`sqrt-prod`
6023×	`add-sqr-sqrt`
5920×	`*-un-lft-identity`
5914×	`add-cube-cbrt`
3927×	`prod-diff`
508×	`sqrt-div`
442×	`div-inv`
303×	`fma-neg`
266×	`associate-/r/`
130×	`flip3--` `flip--`
26×	`difference-of-squares`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`
1×	`frac-sub`

Counts

4 → 4321

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
411.0ms	(- (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (/ b_2 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b_2 b_2) (* a c))
86.0ms	(- (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (/ b_2 a))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

4333 → 4333

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	3060	331544
done	5000	295958

prune14.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))
23.3b	(fma (/ (sqrt 1) a) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (- (/ b_2 a)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 60

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
0.0ms	(fma (/ (sqrt 1) a) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (- (/ b_2 a)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))
104.0ms	(fma (/ (sqrt 1) a) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 (sqrt (sqrt (- (* b_2 b_2) (* a c)))))) (- (/ b_2 a)))

simplify746.0ms

Counts

72 → 72

Iterations

Useful iterations: done (744.0ms)

Iter	Nodes	Cost
0	88	1141
1	193	1055
2	561	917
3	1801	772
done	5000	769

prune289.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.4b

regimes225.0ms

Accuracy

81.9% (5.1b remaining)

Error of 10.8b against oracle of 5.7b and baseline of 33.9b

bsearch78.0ms

Steps

Iters	Range		Point
9	2.365685850767504e-168	1.2053288471691685e-161	1.1860189201379418e-161
6	-2.0136180636941443e+142	-1.4127342237564056e+141	-2.61268387266151e+141

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample988.0ms

Algorithm

intervals

Results

196.0ms	5914×	body	80	valid
195.0ms	1026×	body	2560	valid
141.0ms	897×	body	1280	valid
91.0ms	2995×	body	80	nan
53.0ms	444×	body	640	valid
25.0ms	107×	body	5120	valid
21.0ms	208×	body	320	valid
11.0ms	104×	body	160	valid