Details

sample59.0ms

Algorithm

intervals

Results

12.0ms	193×	body	80	valid
11.0ms	31×	body	2560	valid
6.0ms	97×	body	80	nan
5.0ms	18×	body	1280	valid
4.0ms	18×	body	640	valid
3.0ms	6×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite190.0ms

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:

111.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
48.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
50.0ms	(- (* b_2 b_2) (* a c))
121.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
113.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	1521
1	578
0	248

prune691.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite175.0ms

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:

85.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
17.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
62.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

273 → 273

Iterations

Iter	Nodes
done	5023
2	2295
1	837
0	355

prune808.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite183.0ms

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:

95.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
15.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
37.0ms	(- (* b_2 b_2) (* a c))
113.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

273 → 273

Iterations

Iter	Nodes
done	5023
2	2295
1	837
0	355

prune916.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite210.0ms

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:

95.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
14.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
43.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.0s

Counts

564 → 564

Iterations

Iter	Nodes
done	5007
2	4328
1	2004
0	685

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.3b

regimes582.0ms

Accuracy

82.5% (4.8b remaining)

Error of 10.4b against oracle of 5.5b and baseline of 33.1b

bsearch140.0ms

Steps

Iters	Range		Point
8	2.5230591910300896e+45	6.095379443414697e+48	5.6488521390017767e+48
8	-1.0278134165845925e-62	-2.127595877901746e-66	-1.1962309819144974e-65

simplify9.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample2.5s

Algorithm

intervals

Results

848.0ms	5847×	body	80	valid
519.0ms	1069×	body	2560	valid
329.0ms	903×	body	1280	valid
172.0ms	465×	body	640	valid
172.0ms	3066×	body	80	nan
113.0ms	122×	body	5120	valid
37.0ms	215×	body	320	valid
13.0ms	115×	body	160	valid