Details

sample119.0ms

Algorithm

intervals

Results

25.0ms	176×	body	80	valid
24.0ms	43×	body	2560	valid
15.0ms	31×	body	1280	valid
10.0ms	106×	body	80	nan
6.0ms	18×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify148.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite264.0ms

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:

147.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
12.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
59.0ms	(- (* b b) (* (* 4.0 a) c))
128.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
134.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: done (1.4s)

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

prune496.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune27.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite221.0ms

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:

84.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
17.0ms	(- (* b b) (* (* 4.0 a) c))
88.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
66.0ms	(- (* b b) (* (* 4.0 a) c))
106.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

164 → 164

Iterations

Useful iterations: done (1.3s)

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

prune424.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (/ c b) (/ b a))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

249×	`times-frac`
202×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
190×	`add-cube-cbrt`
169×	`prod-diff`
27×	`div-inv`
13×	`fma-neg`
4×	`difference-of-squares`
3×	`add-log-exp`
2×	`distribute-lft-out--`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 203

Calls

1 calls:

53.0ms

(- (/ c b) (/ b a))

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

(- (/ c b) (/ b a))

simplify3.9s

Counts

206 → 206

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	310	7860
1	681	6866
2	1473	4941
3	4664	3536
done	5000	3536

prune223.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.2b

regimes379.0ms

Accuracy

82.2% (6.0b remaining)

Error of 11.9b against oracle of 5.9b and baseline of 39.8b

bsearch163.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
7	-1.8340745317516165e+50	-1.0728429653156412e+49	-1.5476666036365373e+50

simplify9.0ms

Iterations

Useful iterations: done (9.0ms)

Iter	Nodes	Cost
0	34	49
1	41	49
done	41	47

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	5876×	body	80	valid
688.0ms	1074×	body	2560	valid
498.0ms	885×	body	1280	valid
468.0ms	107×	body	5120	valid
229.0ms	3010×	body	80	nan
197.0ms	492×	body	640	valid
49.0ms	218×	body	320	valid
13.0ms	92×	body	160	valid