Details

sample129.0ms

Algorithm

intervals

Results

12.0ms	39×	body	2560	valid
8.0ms	166×	body	80	valid
7.0ms	36×	body	1280	valid
4.0ms	89×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify35.0ms

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: 36.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite158.0ms

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:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
82.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

183 → 183

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	242	5993
1	578	4337
2	2145	3551
done	5003	3006

prune624.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
4.4b	(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
9.8b	(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
22.6b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite159.0ms

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 (- c) a (* b_2 b_2))) b_2)
78.0ms	(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
55.0ms	(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
3.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
328.0ms	(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
279.0ms	(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
130.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.2s

Counts

229 → 229

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	313	6352
1	752	5415
2	3627	5099
done	5001	5039

prune908.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
4.4b	(/ (/ (+ 0 (* c a)) (+ (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) (+ b_2 (- b_2)))) a)
9.8b	(/ (+ 0 (* c a)) (+ (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) (+ b_2 (- b_2))))
22.6b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite501.0ms

Algorithm

rewrite-expression-head

Rules

429×	`*-un-lft-identity`
246×	`times-frac`
160×	`distribute-lft-out`
128×	`add-sqr-sqrt`
123×	`add-cube-cbrt`
49×	`distribute-lft-out--`
40×	`associate-/l*`
32×	`distribute-rgt-neg-in`
30×	`associate-/r/`
20×	`frac-add`
18×	`prod-diff`
16×	`flip3-+` `sqrt-prod` `flip-+`
12×	`associate-/r*`
11×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
6×	`fma-neg` `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` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 285

Calls

4 calls:

22.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
289.0ms	(/ (/ (+ 0 (* c a)) (+ (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) (+ b_2 (- b_2)))) a)
151.0ms	(/ (+ 0 (* c a)) (+ (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) (+ b_2 (- b_2))))
13.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series748.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
274.0ms	(/ (/ (+ 0 (* c a)) (+ (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) (+ b_2 (- b_2)))) a)
249.0ms	(/ (+ 0 (* c a)) (+ (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) (+ b_2 (- b_2))))
91.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify667.0ms

Counts

297 → 297

Iterations

Useful iterations: done (646.0ms)

Iter	Nodes	Cost
0	358	10283
1	969	8393
done	5000	7374

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0))
2.1b	(/ c (/ (- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0)) a))
4.4b	(/ (* 1 (/ c (/ (- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0)) a))) a)
22.6b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
166×	`add-sqr-sqrt`
162×	`times-frac`
101×	`add-cube-cbrt`
45×	`distribute-lft-out--`
39×	`prod-diff`
34×	`sqrt-prod`
32×	`add-exp-log` `difference-of-squares`
28×	`associate-/r*`
23×	`add-cbrt-cube`
16×	`div-exp`
11×	`associate--r+`
10×	`cbrt-undiv`
9×	`add-log-exp`
6×	`fma-neg` `prod-exp` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`diff-log` `1-exp` `cbrt-unprod`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-*r/` `associate-/r/` `flip--` `associate-/l/` `associate--r-`

Counts

4 → 233

Calls

4 calls:

37.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0))
55.0ms	(/ c (/ (- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0)) a))
58.0ms	(/ (* 1 (/ c (/ (- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0)) a))) a)
4.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series818.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0))
287.0ms	(/ c (/ (- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0)) a))
305.0ms	(/ (* 1 (/ c (/ (- (sqrt (fma (- c) a (* b_2 b_2))) (- b_2 0)) a))) a)
97.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify742.0ms

Counts

245 → 245

Iterations

Useful iterations: done (726.0ms)

Iter	Nodes	Cost
0	371	6648
1	998	5294
done	5000	4637

prune895.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

regimes347.0ms

Accuracy

90.8% (2.3b remaining)

Error of 8.0b against oracle of 5.7b and baseline of 30.9b

bsearch359.0ms

Steps

Iters	Range		Point
11	8.182113676652236e-12	2116652649.122401	2098867031.9345784
11	9.132164512921457e-291	8.018752023592085e-262	1.7395064399479094e-284
9	-7.992092370788522e+101	-1.0157407143165378e+93	-1.9512547643887412e+95

simplify13.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	37	60
1	44	58
2	45	58
done	45	58

end0.0ms

sample3.0s

Algorithm

intervals

Results

935.0ms	5936×	body	80	valid
606.0ms	1015×	body	2560	valid
385.0ms	912×	body	1280	valid
192.0ms	2930×	body	80	nan
149.0ms	100×	body	5120	valid
144.0ms	438×	body	640	valid
43.0ms	232×	body	320	valid
15.0ms	123×	body	160	valid