Details

sample74.0ms

Algorithm

intervals

Results

21.0ms	185×	body	80	valid
12.0ms	37×	body	2560	valid
9.0ms	33×	body	1280	valid
4.0ms	81×	body	80	nan
4.0ms	20×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize24.0ms

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)))

rewrite241.0ms

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:

15.0ms	(- (* b_2 b_2) (* a c))
112.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
83.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b_2 b_2) (* a c))
141.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
101.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
100.0ms	(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

prune515.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize32.0ms

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))))

rewrite141.0ms

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:

12.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
62.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
52.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
3.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series828.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
266.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
315.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
129.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.3s

Counts

229 → 229

Iterations

Useful iterations: done (2.3s)

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

prune896.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize13.0ms

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))))

rewrite49.0ms

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)))
26.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
13.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series1.0s

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma b_2 b_2 (- (* c a)))
726.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
130.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
112.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.3s

Counts

121 → 121

Iterations

Useful iterations: done (2.3s)

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

prune398.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
156×	`times-frac`
127×	`*-un-lft-identity`
93×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
25×	`associate-/r*`
18×	`prod-diff`
17×	`add-exp-log` `distribute-lft-out--`
11×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp`
6×	`pow1` `fma-neg` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-/r/` `inv-pow`

Counts

4 → 214

Calls

4 calls:

32.0ms	(/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c)
32.0ms	(/ 1 (/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c))
12.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c)
174.0ms	(/ 1 (/ (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2) c))
130.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
133.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify3.2s

Counts

226 → 226

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	299	5151
1	684	4543
2	1394	4082
3	3618	3965
done	5002	3953

prune757.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

regimes359.0ms

Accuracy

94.9% (1.2b remaining)

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

bsearch204.0ms

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

simplify17.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	39	62
1	50	54
2	52	54
done	52	54

end0.0ms

sample2.7s

Algorithm

intervals

Results

902.0ms	1058×	body	2560	valid
448.0ms	5846×	body	80	valid
321.0ms	921×	body	1280	valid
220.0ms	2929×	body	80	nan
178.0ms	503×	body	640	valid
47.0ms	109×	body	5120	valid
34.0ms	210×	body	320	valid
13.0ms	109×	body	160	valid