Details

sample138.0ms

Algorithm

intervals

Results

11.0ms	185×	body	80	valid
10.0ms	37×	body	2560	valid
7.0ms	33×	body	1280	valid
5.0ms	81×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
113.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
108.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1414	3549
done	5000	3001

prune552.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
3.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
9.9b	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
24.4b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`flip3--` `fma-neg` `flip--` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 217

Calls

4 calls:

18.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
65.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
50.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series675.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
214.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
257.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
101.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.4s

Counts

229 → 229

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	329	6395
1	757	5450
2	2207	5130
done	5002	5015

prune936.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma b_2 b_2 (- (* c a)))
0.1b	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
0.4b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
24.4b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-exp-log` `fma-neg` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 109

Calls

4 calls:

1.0ms	(fma b_2 b_2 (- (* c a)))
41.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
22.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
4.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma b_2 b_2 (- (* c a)))
317.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
92.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
102.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.5s

Counts

121 → 121

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	167	2224
1	334	1950
2	705	1731
3	1975	1653
done	5000	1598

prune462.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c)
0.2b	(/ (/ 1 1) (* (/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c) 1))
0.4b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
24.4b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
70×	`div-exp`
65×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
49×	`times-frac`
44×	`add-cube-cbrt`
39×	`1-exp`
28×	`prod-exp`
27×	`add-cbrt-cube`
20×	`sqrt-prod`
19×	`associate-/l*`
18×	`prod-diff`
12×	`cbrt-undiv`
10×	`rec-exp` `difference-of-squares`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-*l/` `associate-/r/`

Counts

4 → 182

Calls

4 calls:

33.0ms	(/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c)
25.0ms	(/ (/ 1 1) (* (/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c) 1))
26.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c)
170.0ms	(/ (/ 1 1) (* (/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c) 1))
109.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
121.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify3.7s

Counts

194 → 194

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	316	4124
1	653	3308
2	1325	2856
3	3627	2679
done	5000	2667

prune507.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

regimes314.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.3b

bsearch149.0ms

Steps

Iters	Range		Point
8	1.538525478595148e+72	6.402915924844171e+74	4.19865099347443e+74
5	1.3461159678365104e-246	2.760780588216915e-246	1.3645292833571162e-246
6	-3.779251410483496e+105	-5.080294099506613e+104	-3.7277239731487426e+105

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	37	58
1	47	54
2	49	54
done	49	54

end0.0ms

sample2.8s

Algorithm

intervals

Results

885.0ms	5846×	body	80	valid
664.0ms	1058×	body	2560	valid
259.0ms	921×	body	1280	valid
160.0ms	2929×	body	80	nan
141.0ms	503×	body	640	valid
78.0ms	210×	body	320	valid
55.0ms	109×	body	5120	valid
11.0ms	109×	body	160	valid