Details

sample218.0ms

Algorithm

intervals

Results

17.0ms	184×	body	80	valid
15.0ms	31×	body	2560	valid
15.0ms	33×	body	1280	valid
7.0ms	90×	body	80	nan
4.0ms	12×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify98.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize35.0ms

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))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

143.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
70.0ms	(- (* b_2 b_2) (* a c))
145.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
129.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

92 → 92

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	151	1534
1	378	1440
2	1557	1268
done	5001	1260

prune627.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize40.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.5b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.4b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

42.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
175.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
130.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series860.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
279.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
332.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
121.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts

218 → 218

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	307	6418
1	777	5561
2	4237	5359
done	5000	5359

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.3b	(/ (+ 0 (* a c)) (* a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`flip3--` `sqrt-prod` `flip--`
3×	`times-frac` `diff-log` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `associate-*r/` `div-exp` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
48.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms	(/ (+ 0 (* a c)) (* a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b_2 b_2) (* a c))
128.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
256.0ms	(/ (+ 0 (* a c)) (* a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

82 → 82

Iterations

Useful iterations: 2 (645.0ms)

Iter	Nodes	Cost
0	159	1468
1	424	1303
2	2846	1149
done	5001	1149

prune627.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

localize33.0ms

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))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`prod-exp` `distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

156.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
23.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
73.0ms	(- (* b_2 b_2) (* a c))
146.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
130.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.9s

Counts

96 → 96

Iterations

Useful iterations: done (5.9s)

Iter	Nodes	Cost
0	175	1643
1	476	1488
2	3145	1228
done	5001	1210

prune678.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

regimes541.0ms

Accuracy

83.2% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 32.7b

bsearch503.0ms

Steps

Iters	Range		Point
8	4.049254448328916e+76	2.3057443967677173e+80	4.7587535552882655e+78
8	7.120367950694928e-51	1.9906506898914158e-47	1.1310446734884525e-47
6	4.02886392125618e-70	3.9850540170413814e-69	4.40565710546396e-70
8	7.520261887413394e-140	8.544177483477188e-136	2.4581158795060287e-136
10	-6.623625638726693e+82	-6.4709084601913214e+72	-1.6581383089037873e+81

simplify16.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	43	94
1	52	90
2	53	90
done	53	90

end0.0ms

sample3.7s

Algorithm

intervals

Results

977.0ms	907×	body	1280	valid
679.0ms	5796×	body	80	valid
678.0ms	1066×	body	2560	valid
318.0ms	2977×	body	80	nan
181.0ms	451×	body	640	valid
73.0ms	124×	body	5120	valid
52.0ms	231×	body	320	valid
21.0ms	135×	body	160	valid