Details

sample287.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
5.0ms	36×	body	1280	valid
5.0ms	165×	body	80	valid
3.0ms	86×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

38.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
3.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
34.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

96 → 96

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	154	1624
1	362	1526
2	950	1426
3	2675	1422
done	5001	1420

prune262.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.0b	(- (* b_2 b_2) (* a c))
8.3b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`times-frac`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--` `distribute-lft-out--`
3×	`associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 93

Calls

4 calls:

9.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
38.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

105 → 105

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	173	1824
1	381	1686
2	927	1598
3	2580	1594
done	5001	1591

prune264.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c)))))
1.0b	(- (* b_2 b_2) (* a c))
11.7b	(- (/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

312×	`times-frac`
221×	`add-sqr-sqrt`
159×	`sqrt-prod`
158×	`*-un-lft-identity`
146×	`add-cube-cbrt`
24×	`associate-/r*`
20×	`difference-of-squares`
16×	`sqrt-div`
15×	`associate-/r/`
10×	`flip3--` `flip--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `add-log-exp`
6×	`associate-/l*`
5×	`pow1`
3×	`cbrt-undiv` `div-exp`
2×	`sub-neg` `diff-log` `distribute-lft-out--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `frac-sub`

Counts

4 → 251

Calls

4 calls:

14.0ms	(/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
169.0ms	(- (/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c)))))
39.0ms	(- (* b_2 b_2) (* a c))
99.0ms	(- (/ (sqrt 1) (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

263 → 263

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	350	7145
1	768	5815
2	1422	5217
3	3458	5111
done	5001	5110

prune327.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
14.1b	(- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c)))) (/ b_2 a))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`add-exp-log` `times-frac` `associate-l`
10×	`sqrt-div`
9×	`sqrt-prod` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `flip3--` `flip--`
6×	`associate-r` `unswap-sqr`
5×	`frac-sub`
4×	`frac-times` `associate-*r/` `prod-exp`
3×	`associate-*l/`
2×	`sub-neg` `diff-log` `div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `*-commutative` `div-inv` `sub-div`

Counts

4 → 90

Calls

4 calls:

18.0ms	(* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c)))) (/ b_2 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c)))) (/ b_2 a))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

102 → 102

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	170	1837
1	413	1580
2	1074	1406
3	2920	1398
done	5000	1397

prune248.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

regimes200.0ms

Accuracy

82% (5.2b remaining)

Error of 10.9b against oracle of 5.7b and baseline of 34.3b

bsearch82.0ms

Steps

Iters	Range		Point
9	2.365685850767504e-168	1.2053288471691685e-161	1.1860189201379418e-161
6	-2.0136180636941443e+142	-1.4127342237564056e+141	-2.4317863954914854e+141

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	42
1	31	42
done	31	42

end0.0ms

sample994.0ms

Algorithm

intervals

Results

193.0ms	1026×	body	2560	valid
191.0ms	5914×	body	80	valid
137.0ms	897×	body	1280	valid
94.0ms	2995×	body	80	nan
61.0ms	444×	body	640	valid
25.0ms	107×	body	5120	valid
19.0ms	208×	body	320	valid
8.0ms	104×	body	160	valid