Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	37×	body	2560	valid
7.0ms	195×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	81×	body	80	nan
2.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify55.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	100	16
5	108	16
done	108	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 94

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
42.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts

106 → 106

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	161	1863
1	362	1562
2	1193	1333
done	5000	1246

prune258.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
1.1b	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
20.6b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
6×	`cbrt-prod` `fma-neg` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/3` `sqrt-div` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

0.0ms	(cbrt c)
0.0ms	(cbrt c)
22.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
4.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt c)
177.0ms	(cbrt c)
94.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
85.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify2.3s

Counts

96 → 96

Iterations

Useful iterations: 3 (849.0ms)

Iter	Nodes	Cost
0	138	2172
1	305	1828
2	898	1090
3	4205	1003
done	5000	1003

prune282.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt c))
0.6b	(cbrt (cbrt c))
1.1b	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))) b)
20.6b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`cbrt-prod` `prod-diff`
16×	`sqrt-prod`
6×	`fma-neg` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/3` `sqrt-div` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

1.0ms	(cbrt (cbrt c))
1.0ms	(cbrt (cbrt c))
22.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))) b)
5.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

series692.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(cbrt (cbrt c))
257.0ms	(cbrt (cbrt c))
100.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))) b)
89.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

simplify1.2s

Counts

102 → 102

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	148	3036
1	323	2609
2	980	1874
done	5000	1091

prune311.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 11.4b

localize12.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.1b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

22.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
25.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
81.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts

128 → 128

Iterations

Useful iterations: 3 (641.0ms)

Iter	Nodes	Cost
0	113	2856
1	262	2310
2	756	1948
3	2877	1774
done	5001	1774

prune347.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 11.4b

regimes384.0ms

Accuracy

84.9% (3.4b remaining)

Error of 15.5b against oracle of 12.2b and baseline of 34.4b

bsearch112.0ms

Steps

Iters	Range		Point
10	3.056596725548563e-78	7.076105677608322e-63	3.127343185313157e-68
7	-1.9127319211193897e+86	-3.881068201361415e+84	-1.885822949172535e+86

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	62
1	34	62
done	34	62

end0.0ms

sample1.1s

Algorithm

intervals

Results

241.0ms	1097×	body	2560	valid
219.0ms	5881×	body	80	valid
151.0ms	853×	body	1280	valid
108.0ms	2944×	body	80	nan
66.0ms	470×	body	640	valid
31.0ms	108×	body	5120	valid
22.0ms	213×	body	320	valid
7.0ms	104×	body	160	valid