Details

sample273.0ms

Algorithm

intervals

Results

7.0ms	39×	body	2560	valid
7.0ms	183×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	84×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	45	13
4	47	13
done	47	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

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))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

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:

42.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify594.0ms

Counts

183 → 183

Iterations

Useful iterations: done (588.0ms)

Iter	Nodes	Cost
0	242	5993
1	536	4313
2	1422	3549
done	5001	3540

prune379.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

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:

53.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
35.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify714.0ms

Counts

181 → 181

Iterations

Useful iterations: done (709.0ms)

Iter	Nodes	Cost
0	261	5917
1	595	4127
2	1603	3313
done	5000	3300

prune355.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.7b	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) a)
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
10×	`fma-def` `add-log-exp`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) a)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(/ (+ (* b_2 (- b_2 b_2)) (* a c)) a)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

103 → 103

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	158	1360
1	384	1137
2	1143	943
3	3455	887
done	5000	886

prune300.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 99

Calls

4 calls:

24.0ms	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
36.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

111 → 111

Iterations

Useful iterations: 3 (479.0ms)

Iter	Nodes	Cost
0	154	1589
1	351	1476
2	946	1301
3	2810	1283
done	5000	1283

prune254.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

regimes173.0ms

Accuracy

92.7% (1.8b remaining)

Error of 7.1b against oracle of 5.3b and baseline of 29.4b

bsearch108.0ms

Steps

Iters	Range		Point
9	1.790439840991813e+53	4.6520850645607246e+61	4.581932003920303e+61
6	1.9974031211523764e-132	9.034365154863063e-132	2.021456790140741e-132
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.286134886319968e+57

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	50
1	36	50
done	36	50

end0.0ms

sample999.0ms

Algorithm

intervals

Results

216.0ms	1071×	body	2560	valid
196.0ms	5863×	body	80	valid
133.0ms	830×	body	1280	valid
89.0ms	2880×	body	80	nan
62.0ms	477×	body	640	valid
27.0ms	110×	body	5120	valid
23.0ms	244×	body	320	valid
7.0ms	116×	body	160	valid