Details

sample82.0ms

Algorithm

intervals

Results

26.0ms	31×	body	1280	valid
16.0ms	190×	body	80	valid
14.0ms	31×	body	2560	valid
6.0ms	84×	body	80	nan
4.0ms	13×	body	640	valid
2.0ms	4×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite541.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

97.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
394.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(- (* b_2 b_2) (* a c))
92.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify756.0ms

Counts

187 → 187

Iterations

Iter	Nodes
done	2004
2	1521
1	578
0	248

prune750.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 261

Calls

4 calls:

64.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
65.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify779.0ms

Counts

273 → 273

Iterations

Iter	Nodes
done	2001
1	837
0	355

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
569×	`add-sqr-sqrt`
568×	`*-un-lft-identity`
396×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
76×	`sqrt-prod`
64×	`distribute-rgt-neg-in`
61×	`prod-diff`
44×	`add-exp-log`
43×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/r*`
21×	`distribute-lft-neg-in`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 552

Calls

4 calls:

34.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
54.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify726.0ms

Counts

564 → 564

Iterations

Iter	Nodes
done	2000
0	685

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
52×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-prod` `flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `neg-log`

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt a)
15.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(cbrt a)
70.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify765.0ms

Counts

152 → 152

Iterations

Iter	Nodes
done	2000
2	1145
1	453
0	204

prune594.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.1b

regimes642.0ms

Accuracy

83.9% (4.5b remaining)

Error of 9.8b against oracle of 5.3b and baseline of 33.3b

bsearch210.0ms

Steps

Iters	Range		Point
7	1.9723660647371773e+81	3.4101289177416236e+83	1.7665622931893247e+83
7	-8.865960730997555e-39	-3.628908962658003e-41	-5.7874989996849275e-40

simplify8.0ms

Iterations

Iter	Nodes
done	31
1	31
0	27

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	5925×	body	80	valid
994.0ms	1054×	body	2560	valid
594.0ms	921×	body	1280	valid
367.0ms	2980×	body	80	nan
200.0ms	420×	body	640	valid
163.0ms	116×	body	5120	valid
97.0ms	222×	body	320	valid
60.0ms	123×	body	160	valid