Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
8.0ms	194×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	76×	body	80	nan
1.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

18.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
6.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.0ms	(* (* 4.0 a) c)
49.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (879.0ms)

Iter	Nodes	Cost
0	120	1001
1	279	903
2	991	825
3	3822	821
done	5000	821

prune214.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.6b

localize18.0ms

Local error

Found 4 expressions with local error:

24.7b	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

34.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
101.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
103.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

101 → 101

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	189	3740
1	339	3330
2	733	2673
3	2181	2622
done	5001	2621

prune341.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.6b

localize16.0ms

Local error

Found 4 expressions with local error:

12.0b	(- (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

56.0ms	(- (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

69 → 69

Iterations

Useful iterations: 3 (313.0ms)

Iter	Nodes	Cost
0	81	1576
1	203	1462
2	640	914
3	2286	871
done	5000	871

prune267.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
3.6b	(exp (log (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1`
10×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
6×	`log-prod` `exp-sum` `add-log-exp`
4×	`exp-prod` `sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`log-div` `exp-diff` `sqrt-div` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `log-pow` `*-commutative` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 65

Calls

4 calls:

6.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(exp (log (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 4.0 a) c)
52.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(exp (log (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

77 → 77

Iterations

Useful iterations: 3 (972.0ms)

Iter	Nodes	Cost
0	148	1164
1	315	1013
2	1033	915
3	3919	911
done	5000	911

prune214.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.6b

regimes188.0ms

Accuracy

86.1% (3.1b remaining)

Error of 15.1b against oracle of 12.0b and baseline of 34.2b

bsearch150.0ms

Steps

Iters	Range		Point
8	1.9230140876291547e+24	5.884487837986356e+26	1.9426371746037666e+24
11	-1.829086240692416e+154	-2.187052964502477e+134	-1.3358786167585806e+154

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	50
1	37	50
done	37	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

255.0ms	1104×	body	2560	valid
240.0ms	5868×	body	80	valid
171.0ms	910×	body	1280	valid
109.0ms	2861×	body	80	nan
61.0ms	422×	body	640	valid
29.0ms	96×	body	5120	valid
24.0ms	212×	body	320	valid
9.0ms	120×	body	160	valid