Details

sample210.0ms

Algorithm

intervals

Results

61.0ms	102×	body	80	nan
16.0ms	30×	body	2560	valid
16.0ms	186×	body	80	valid
10.0ms	23×	body	1280	valid
4.0ms	14×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `sum-log` `flip3-+` `flip3--` `sqrt-div` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `div-inv`

Counts

4 → 100

Calls

4 calls:

71.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
60.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
118.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	164	1638
1	405	1539
2	1655	1357
done	5001	1344

prune708.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.4b	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.9b	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
21×	`distribute-lft-neg-in`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r*` `fma-neg` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 284

Calls

4 calls:

35.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
63.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series739.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
259.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
270.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify486.0ms

Counts

296 → 296

Iterations

Useful iterations: done (469.0ms)

Iter	Nodes	Cost
0	390	10604
1	974	8179
done	5000	7437

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize50.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.4b	(/ (/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))) a)
10.9b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

337×	`times-frac`
220×	`add-sqr-sqrt`
219×	`*-un-lft-identity`
159×	`add-cube-cbrt`
60×	`prod-diff`
48×	`sqrt-prod`
45×	`associate-/l*`
41×	`add-exp-log`
36×	`distribute-rgt-neg-in`
30×	`distribute-lft-out--` `difference-of-squares`
24×	`div-exp`
23×	`add-cbrt-cube`
21×	`distribute-lft-neg-in`
18×	`div-inv`
11×	`cbrt-undiv`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `diff-log` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log`

Counts

4 → 323

Calls

4 calls:

26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
129.0ms	(/ (/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))) a)
125.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
158.0ms	(/ (/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))) a)
144.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))
113.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify748.0ms

Counts

335 → 335

Iterations

Useful iterations: done (730.0ms)

Iter	Nodes	Cost
0	525	11427
1	1441	9216
done	5000	8322

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
0.6b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
569×	`add-sqr-sqrt`
568×	`*-un-lft-identity`
396×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
76×	`sqrt-prod`
64×	`distribute-rgt-neg-in`
61×	`prod-diff`
44×	`add-exp-log`
43×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/l*`
21×	`distribute-lft-neg-in`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 548

Calls

4 calls:

123.0ms	(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
13.0ms	(- (* b_2 b_2) (* a c))
48.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
70.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

560 → 560

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	690	20575
1	2192	15944
done	5001	14680

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

regimes444.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 30.0b

bsearch264.0ms

Steps

Iters	Range	Point
7	1.9371672431899034e+133	5.16149553175908e+134	1.183295134100389e+134
9	1.657231371314425e-305	1.760208242016082e-296	1.6905899892511143e-305
8	-9.061058506829192e+105	-7.154008779742083e+102	-5.062954969806706e+105

Iters

Range

Point

1.9371672431899034e+133

5.16149553175908e+134

1.183295134100389e+134

1.657231371314425e-305

1.760208242016082e-296

1.6905899892511143e-305

-9.061058506829192e+105

-7.154008779742083e+102

-5.062954969806706e+105

simplify11.0ms

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	38	62
1	49	58
2	52	56
done	52	56

end0.0ms

sample2.9s

Algorithm

intervals

Results

677.0ms	1055×	body	2560	valid
491.0ms	5961×	body	80	valid
425.0ms	218×	body	320	valid
340.0ms	880×	body	1280	valid
225.0ms	2944×	body	80	nan
105.0ms	451×	body	640	valid
45.0ms	97×	body	5120	valid
13.0ms	109×	body	160	valid