Details

sample154.0ms

Algorithm

intervals

Results

18.0ms	36×	body	2560	valid
18.0ms	187×	body	80	valid
11.0ms	26×	body	1280	valid
6.0ms	84×	body	80	nan
4.0ms	12×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
5	34
4	32
3	30
2	23
1	15
0	10

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 122

Calls

4 calls:

91.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series780.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
193.0ms	(- (* b_2 b_2) (* a c))
275.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
110.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

134 → 134

Iterations

Iter	Nodes
done	2006
2	1393
1	494
0	199

prune567.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 200

Calls

4 calls:

57.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
12.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
62.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify653.0ms

Counts

212 → 212

Iterations

Iter	Nodes
done	2000
1	742
0	303

prune745.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
507×	`add-sqr-sqrt`
420×	`*-un-lft-identity`
334×	`add-cube-cbrt`
86×	`difference-of-squares`
58×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/r*`
19×	`prod-diff`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 461

Calls

4 calls:

65.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
41.0ms	(- (* b_2 b_2) (* a c))
83.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify958.0ms

Counts

473 → 473

Iterations

Iter	Nodes
done	2000
1	1843
0	632

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

localize56.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b	(sqrt (- (* b_2 b_2) (* a c)))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

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×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `diff-log` `distribute-lft-out--`

Counts

4 → 96

Calls

4 calls:

66.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify638.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2003
2	878
1	287
0	112

prune642.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes369.0ms

Accuracy

84.5% (4.4b remaining)

Error of 9.7b against oracle of 5.2b and baseline of 33.9b

bsearch414.0ms

Steps

Iters	Range		Point
8	2.469533614662255e-16	6.384179586440732e-13	5.297236684235463e-16
9	2.201345904528094e-30	9.673336284784144e-25	1.8656332031849816e-25
10	5.0092461758030895e-88	5.0325836698121444e-76	1.739098950628615e-79
9	-7.806260788625035e+148	-1.2289413495061505e+143	-1.4758305599808076e+144

simplify25.0ms

Iterations

Iter	Nodes
done	44
1	44
0	35

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.3s	1104×	body	2560	valid
1.2s	5760×	body	80	valid
602.0ms	957×	body	1280	valid
378.0ms	2976×	body	80	nan
193.0ms	482×	body	640	valid
120.0ms	116×	body	5120	valid
68.0ms	226×	body	320	valid
24.0ms	121×	body	160	valid