Details

sample57.0ms

Algorithm

intervals

Results

13.0ms	43×	body	2560	valid
8.0ms	155×	body	80	valid
7.0ms	26×	body	1280	valid
5.0ms	94×	body	80	nan
4.0ms	19×	body	640	valid
2.0ms	12×	body	320	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	160	valid

simplify87.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	104
5	104
4	96
3	76
2	41
1	21
0	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.6b	(- (* b b) (* (* 3.0 a) c))
1.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
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:

14.0ms	(* (* 3.0 a) c)
12.0ms	(- (* b b) (* (* 3.0 a) c))
38.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 3.0 a) c)
64.0ms	(- (* b b) (* (* 3.0 a) c))
134.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
113.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1593
1	302
0	120

prune474.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.4b

localize89.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (* (* 3.0 a) c))
16.3b	(cbrt (* (* 3.0 a) c))
16.3b	(cbrt (* (* 3.0 a) c))
21.4b	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 42

Calls

4 calls:

12.0ms	(cbrt (* (* 3.0 a) c))
10.0ms	(cbrt (* (* 3.0 a) c))
10.0ms	(cbrt (* (* 3.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (* (* 3.0 a) c))
138.0ms	(cbrt (* (* 3.0 a) c))
132.0ms	(cbrt (* (* 3.0 a) c))
196.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

simplify2.2s

Counts

54 → 54

Iterations

Iter	Nodes
done	5002
3	3204
2	628
1	213
0	88

prune555.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.3b

localize50.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (* c a))
16.3b	(cbrt (* (* 3.0 a) c))
16.3b	(cbrt (* (* 3.0 a) c))
21.4b	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (* (cbrt (* c a)) (cbrt 3.0)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 42

Calls

4 calls:

3.0ms	(cbrt (* c a))
10.0ms	(cbrt (* (* 3.0 a) c))
20.0ms	(cbrt (* (* 3.0 a) c))
12.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (* (cbrt (* c a)) (cbrt 3.0)))))

series562.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (* c a))
133.0ms	(cbrt (* (* 3.0 a) c))
154.0ms	(cbrt (* (* 3.0 a) c))
181.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (* (cbrt (* c a)) (cbrt 3.0)))))

simplify3.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	4330
2	764
1	232
0	100

prune550.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.3b

localize50.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (* c a))
16.3b	(cbrt (* (* 3.0 a) c))
16.3b	(cbrt (* (* 3.0 a) c))
21.4b	(sqrt (- (* b b) (* (* (* (cbrt (* c a)) (cbrt 3.0)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 42

Calls

4 calls:

3.0ms	(cbrt (* c a))
10.0ms	(cbrt (* (* 3.0 a) c))
10.0ms	(cbrt (* (* 3.0 a) c))
12.0ms	(sqrt (- (* b b) (* (* (* (cbrt (* c a)) (cbrt 3.0)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

series562.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (* c a))
135.0ms	(cbrt (* (* 3.0 a) c))
145.0ms	(cbrt (* (* 3.0 a) c))
192.0ms	(sqrt (- (* b b) (* (* (* (cbrt (* c a)) (cbrt 3.0)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

simplify2.9s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	4114
2	741
1	232
0	101

prune412.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.3b

regimes790.0ms

Accuracy

86.1% (3.1b remaining)

Error of 15.5b against oracle of 12.4b and baseline of 34.7b

bsearch185.0ms

Steps

Iters	Range		Point
9	5.75915985305395e-78	3.6929333590207295e-72	3.564941316298826e-72
8	-4.757707542143071e+61	-1.7219225168681383e+58	-4.700064339395893e+61

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1103×	body	2560	valid
556.0ms	5735×	body	80	valid
431.0ms	956×	body	1280	valid
251.0ms	2942×	body	80	nan
214.0ms	461×	body	640	valid
55.0ms	106×	body	5120	valid
45.0ms	227×	body	320	valid
16.0ms	119×	body	160	valid