Details

sample76.0ms

Algorithm

intervals

Results

16.0ms	43×	body	2560	valid
12.0ms	175×	body	80	valid
10.0ms	31×	body	1280	valid
6.0ms	106×	body	80	nan
5.0ms	18×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify138.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite129.0ms

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:

18.0ms	(* (* 3.0 a) c)
18.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
19.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (* 3.0 a) c)
51.0ms	(- (* b b) (* (* 3.0 a) c))
105.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
131.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.2s

Counts

106 → 106

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	161	1863
1	367	1562
2	1128	1333
3	4517	1245
done	5000	1245

prune359.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.4b

localize35.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite270.0ms

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:

109.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
106.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
105.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
96.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
96.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.3s

Counts

128 → 128

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	113	2856
1	268	2310
2	718	1948
3	2711	1774
done	5001	1674

prune508.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.4b

localize34.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

66.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
124.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
131.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
119.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.1s

Counts

104 → 104

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	113	2042
1	268	1675
2	718	1476
3	2711	1387
done	5001	1337

prune532.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.4b

localize19.0ms

Local error

Found 4 expressions with local error:

25.5b	(cbrt (- (* b b) (* (* 3.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 3.0 a) c)))
25.5b	(cbrt (- (* b b) (* (* 3.0 a) c)))
25.9b	(fma (sqrt (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

13.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
0.0ms	(fma (sqrt (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

series623.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
161.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
143.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
191.0ms	(fma (sqrt (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (- b))

simplify2.8s

Counts

67 → 67

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	88	1442
1	199	1258
2	559	1121
3	2005	1103
done	5001	1076

prune455.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.1b

regimes515.0ms

Accuracy

85.7% (3.3b remaining)

Error of 14.6b against oracle of 11.3b and baseline of 34.5b

bsearch230.0ms

Steps

Iters	Range		Point
8	6.197633265120061e-63	2.959335775732887e-60	2.915997880138567e-60
11	-2.936095699822542e+100	-2.175955675887007e+75	-1.7188907543362147e+100

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	57
1	32	57
done	32	57

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	5872×	body	80	valid
638.0ms	1076×	body	2560	valid
408.0ms	3010×	body	80	nan
383.0ms	885×	body	1280	valid
199.0ms	491×	body	640	valid
89.0ms	218×	body	320	valid
62.0ms	105×	body	5120	valid
15.0ms	95×	body	160	valid