Details

sample45.0ms

Algorithm

intervals

Results

8.0ms	206×	body	80	valid
6.0ms	28×	body	2560	valid
5.0ms	28×	body	1280	valid
4.0ms	107×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	6×	body	160	valid
0.0ms	4×	body	320	valid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite162.0ms

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:

88.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
48.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
87.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify973.0ms

Counts

118 → 118

Iterations

Useful iterations: done (969.0ms)

Iter	Nodes	Cost
0	195	2476
1	480	2169
2	1441	1861
done	5000	1789

prune329.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

57.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
50.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
49.0ms	(- (* b b) (* (* 4.0 a) c))
91.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

164 → 164

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	261	4025
1	587	3484
2	1656	3082
done	5001	2938

prune335.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)
1.0b	(- (pow b 2) (* 4.0 (* a c)))
1.2b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.3b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
34×	`add-cube-cbrt`
26×	`prod-diff`
20×	`sqrt-prod`
18×	`times-frac`
14×	`fma-neg`
10×	`difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `unpow-prod-down` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 132

Calls

4 calls:

133.0ms	(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)
18.0ms	(- (pow b 2) (* 4.0 (* a c)))
79.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
17.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) a)
51.0ms	(- (pow b 2) (* 4.0 (* a c)))
82.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
78.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify951.0ms

Counts

144 → 144

Iterations

Useful iterations: done (946.0ms)

Iter	Nodes	Cost
0	212	2996
1	500	2658
2	1260	2358
done	5000	2278

prune401.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
1.0b	(- (pow b 2) (* 4.0 (* a c)))
1.2b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.3b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
141×	`add-sqr-sqrt`
114×	`*-un-lft-identity`
88×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`prod-diff` `difference-of-squares`
24×	`associate-/r*`
15×	`add-exp-log`
14×	`fma-neg`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1` `unpow-prod-down`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 210

Calls

4 calls:

72.0ms	(/ 1 (/ a (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
17.0ms	(- (pow b 2) (* 4.0 (* a c)))
77.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
20.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1 (/ a (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
54.0ms	(- (pow b 2) (* 4.0 (* a c)))
88.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
72.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify951.0ms

Counts

222 → 222

Iterations

Useful iterations: done (943.0ms)

Iter	Nodes	Cost
0	316	5606
1	686	4861
2	1578	4371
done	5000	4221

prune458.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

regimes206.0ms

Accuracy

78% (6.2b remaining)

Error of 11.6b against oracle of 5.4b and baseline of 33.4b

bsearch240.0ms

Steps

Iters	Range		Point
8	0.0001820196720056695	0.3848154462067827	0.00018465375781150442
6	3.6410892437809104e-110	3.0960233903298005e-109	4.731827132847258e-110
8	1.0691773024250323e-170	5.5548132533506025e-168	2.175674080408203e-169
9	-1.4924982923623064e+60	-5.817343306680769e+54	-1.4784065354805617e+60

simplify9.0ms

Iterations

Useful iterations: done (9.0ms)

Iter	Nodes	Cost
0	37	84
1	49	76
2	52	59
3	55	59
done	55	58

end0.0ms

sample1.2s

Algorithm

intervals

Results

247.0ms	5926×	body	80	valid
239.0ms	1042×	body	2560	valid
169.0ms	905×	body	1280	valid
106.0ms	2856×	body	80	nan
66.0ms	463×	body	640	valid
28.0ms	102×	body	5120	valid
24.0ms	225×	body	320	valid
7.0ms	95×	body	160	valid