Details

sample185.0ms

Algorithm

intervals

Results

64.0ms	178×	body	80	valid
15.0ms	41×	body	2560	valid
9.0ms	26×	body	1280	valid
5.0ms	75×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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: 34.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite338.0ms

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:

128.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
59.0ms	(- (* b_2 b_2) (* a c))
116.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
136.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

183 → 183

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1408	3549
done	5000	3001

prune459.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma b_2 b_2 (- (* c a)))
3.2b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
10.9b	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
24.6b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`div-inv`
5×	`pow1` `flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef`

Counts

4 → 186

Calls

4 calls:

0.0ms	(fma b_2 b_2 (- (* c a)))
59.0ms	(/ (/ (+ 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))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma b_2 b_2 (- (* c a)))
219.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
250.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
128.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.2s

Counts

198 → 198

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	295	5516
1	678	4787
2	2110	4608
done	5000	4543

prune810.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
0.6b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
1.0b	(fma b_2 b_2 (- (* c a)))
24.6b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite71.0ms

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:

31.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
28.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
1.0ms	(fma b_2 b_2 (- (* c a)))
4.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
128.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
64.0ms	(fma b_2 b_2 (- (* c a)))
95.0ms	(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	702	1731
3	1968	1653
done	5000	1598

prune380.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma b_2 b_2 (- (* c a)))
15.9b	(fma (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (- b_2))
24.6b	(sqrt (fma b_2 b_2 (- (* c a))))
24.6b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma b_2 b_2 (- (* c a)))
0.0ms	(fma (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (- b_2))
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))
2.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma b_2 b_2 (- (* c a)))
128.0ms	(fma (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (sqrt (sqrt (fma b_2 b_2 (- (* c a))))) (- b_2))
101.0ms	(sqrt (fma b_2 b_2 (- (* c a))))
97.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.5s

Counts

62 → 62

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	62	811
1	108	632
2	257	570
3	833	567
4	2795	565
done	5001	565

prune267.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.3b

regimes248.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.5b

bsearch234.0ms

Steps

Iters	Range	Point
9	5.30600492772346e+88	5.894388948599132e+93	3.3616367997262596e+93
10	1.8932238735467414e-306	6.8449465898973125e-295	3.657998399682532e-302
8	-5.7211821970331905e+156	-1.4082798590396656e+153	-1.0772396285489054e+154

Iters

Range

Point

5.30600492772346e+88

5.894388948599132e+93

3.3616367997262596e+93

1.8932238735467414e-306

6.8449465898973125e-295

3.657998399682532e-302

-5.7211821970331905e+156

-1.4082798590396656e+153

-1.0772396285489054e+154

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	37	57
1	45	49
2	47	49
done	47	49

end0.0ms

sample1.7s

Algorithm

intervals

Results

317.0ms	1061×	body	2560	valid
296.0ms	5876×	body	80	valid
201.0ms	854×	body	1280	valid
148.0ms	2976×	body	80	nan
86.0ms	471×	body	640	valid
43.0ms	113×	body	5120	valid
34.0ms	242×	body	320	valid
12.0ms	125×	body	160	valid