Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	39×	body	2560	valid
6.0ms	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

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	40	13
4	42	13
done	42	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize9.0ms

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)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
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 → 91

Calls

4 calls:

35.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

103 → 103

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	156	1821
1	368	1727
2	997	1611
3	3181	1595
done	5000	1594

prune253.0ms

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)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `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 → 89

Calls

4 calls:

53.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
34.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

101 → 101

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	175	1741
1	427	1541
2	1237	1375
3	4392	1349
done	5000	1348

prune241.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize12.0ms

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	(/ (+ 0 (* a c)) a)
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`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-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 71

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(/ (+ 0 (* a c)) a)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(/ (+ 0 (* a c)) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

83 → 83

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	144	1084
1	341	915
2	1080	825
3	4301	785
done	5000	785

prune228.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1 (/ c 1)) (+ (- 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)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

26.0ms	(/ (* 1 (/ c 1)) (+ (- 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))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (* 1 (/ c 1)) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
34.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

88 → 88

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	161	1530
1	436	1274
2	1127	1060
3	3694	1044
done	5000	1043

prune199.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

regimes367.0ms

Accuracy

92.7% (1.8b remaining)

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

bsearch118.0ms

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: 1 (2.0ms)

Iter	Nodes	Cost
0	31	54
1	39	50
done	39	50

end0.0ms

sample1.0s

Algorithm

intervals

Results

216.0ms	1071×	body	2560	valid
206.0ms	5863×	body	80	valid
139.0ms	830×	body	1280	valid
91.0ms	2880×	body	80	nan
66.0ms	477×	body	640	valid
27.0ms	110×	body	5120	valid
24.0ms	244×	body	320	valid
10.0ms	116×	body	160	valid