Details

sample197.0ms

Algorithm

intervals

Results

19.0ms	196×	body	80	valid
16.0ms	34×	body	2560	valid
9.0ms	20×	body	1280	valid
6.0ms	78×	body	80	nan
5.0ms	15×	body	640	valid
4.0ms	6×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify92.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite441.0ms

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:

216.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
181.0ms	(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	2130	3551
done	5000	3006

prune523.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

10.0ms	(- (* b_2 b_2) (* a c))
135.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
87.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.5s

Counts

181 → 181

Iterations

Useful iterations: done (4.5s)

Iter	Nodes	Cost
0	261	5917
1	648	4200
2	3691	3317
done	5000	3316

prune506.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (pow b_2 2) (* c a))
0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
0.4b	(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
22.4b	(sqrt (- (pow b_2 2) (* c a)))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

175×	`add-sqr-sqrt`
174×	`*-un-lft-identity`
165×	`times-frac`
122×	`add-cube-cbrt`
68×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`fma-neg`
15×	`add-exp-log`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1` `unpow-prod-down`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp` `unpow2` `sqr-pow`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 271

Calls

4 calls:

37.0ms	(- (pow b_2 2) (* c a))
133.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
54.0ms	(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
18.0ms	(sqrt (- (pow b_2 2) (* c a)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (pow b_2 2) (* c a))
152.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
108.0ms	(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
112.0ms	(sqrt (- (pow b_2 2) (* c a)))

simplify2.5s

Counts

283 → 283

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	366	8832
1	901	6686
2	4222	6256
done	5000	6255

prune808.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
2.2b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
10.2b	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
22.4b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite151.0ms

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:

22.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
70.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
45.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
3.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
196.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
302.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
142.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.2s

Counts

229 → 229

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	313	6352
1	752	5415
2	3626	5099
done	5000	5039

prune841.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.4b

regimes316.0ms

Accuracy

85.9% (4.0b remaining)

Error of 9.8b against oracle of 5.8b and baseline of 34.4b

bsearch157.0ms

Steps

Iters	Range		Point
8	3932480935863.943	2020002846347102.2	1920982614230223.5
9	-7.152300718152866e-253	-1.7963911490351415e-262	-1.2951718304590299e-256
6	-2.350179250111568e+55	-1.828939172749339e+54	-7.359940312872037e+54

simplify9.0ms

Iterations

Useful iterations: done (8.0ms)

Iter	Nodes	Cost
0	40	60
1	44	60
done	44	58

end0.0ms

sample3.2s

Algorithm

intervals

Results

831.0ms	5763×	body	80	valid
654.0ms	2859×	body	80	nan
492.0ms	1057×	body	2560	valid
396.0ms	933×	body	1280	valid
105.0ms	445×	body	640	valid
56.0ms	116×	body	5120	valid
42.0ms	234×	body	320	valid
14.0ms	119×	body	160	valid