Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	28×	body	1280	valid
7.0ms	194×	body	80	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

simplify47.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize10.0ms

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)))

rewrite31.0ms

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:

17.0ms	(- (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)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(* (* 4.0 a) c)
65.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (767.0ms)

Iter	Nodes	Cost
0	120	1001
1	279	903
2	998	825
3	4312	821
done	5000	821

prune189.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.6b

localize17.0ms

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)))

rewrite44.0ms

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:

33.0ms	(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)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

101 → 101

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	189	3740
1	339	3330
2	835	2673
3	3474	2622
done	5000	2621

prune280.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.6b

localize15.0ms

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)))

rewrite66.0ms

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:

51.0ms	(- (* (* (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)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (* (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)
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

69 → 69

Iterations

Useful iterations: 3 (281.0ms)

Iter	Nodes	Cost
0	81	1576
1	203	1462
2	641	914
3	2324	871
done	5001	871

prune235.0ms

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)))

rewrite27.0ms

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)
2.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(exp (log (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 4.0 a) c)
47.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(exp (log (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

77 → 77

Iterations

Useful iterations: 3 (811.0ms)

Iter	Nodes	Cost
0	148	1164
1	315	1013
2	1044	915
3	4432	911
done	5000	911

prune190.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.6b

regimes170.0ms

Accuracy

86.1% (3.1b remaining)

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

bsearch130.0ms

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

256.0ms	1104×	body	2560	valid
226.0ms	5868×	body	80	valid
166.0ms	910×	body	1280	valid
104.0ms	2861×	body	80	nan
62.0ms	422×	body	640	valid
26.0ms	96×	body	5120	valid
23.0ms	212×	body	320	valid
9.0ms	120×	body	160	valid