Details

sample39.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify47.0ms

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: 34.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

42.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
43.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify584.0ms

Counts

118 → 118

Iterations

Useful iterations: done (581.0ms)

Iter	Nodes	Cost
0	195	2476
1	471	2171
2	1480	1863
done	5000	1839

prune460.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
0.8b	(- (* b b) (* 3.0 (* a c)))
1.3b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

73.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
3.0ms	(- (* b b) (* 3.0 (* a c)))
21.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
42.0ms	(- (* b b) (* 3.0 (* a c)))
75.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
68.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify595.0ms

Counts

118 → 118

Iterations

Useful iterations: done (591.0ms)

Iter	Nodes	Cost
0	194	2476
1	472	2171
2	1456	1863
done	5000	1839

prune254.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
1.3b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 3.0 (* a c))))
21.1b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite53.0ms

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:

20.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
21.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
76.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
69.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))
67.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.4s

Counts

128 → 128

Iterations

Useful iterations: 3 (527.0ms)

Iter	Nodes	Cost
0	112	2856
1	261	2310
2	756	1948
3	2891	1774
done	5000	1774

prune332.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b	(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:

8.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
46.0ms	(- (* b b) (* (* 3.0 a) c))
87.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
100.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify994.0ms

Counts

106 → 106

Iterations

Useful iterations: done (991.0ms)

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

prune216.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

regimes306.0ms

Accuracy

83% (4.9b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 34.1b

bsearch92.0ms

Steps

Iters	Range		Point
8	1.3679096689958957e-81	5.608239720335765e-77	3.84613441880261e-81
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	55
1	35	55
done	35	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

240.0ms	1075×	body	2560	valid
220.0ms	5843×	body	80	valid
159.0ms	906×	body	1280	valid
104.0ms	2890×	body	80	nan
63.0ms	453×	body	640	valid
29.0ms	101×	body	5120	valid
27.0ms	234×	body	320	valid
8.0ms	119×	body	160	valid