Details

sample164.0ms

Algorithm

intervals

Results

54.0ms	196×	body	80	valid
15.0ms	26×	body	2560	valid
12.0ms	26×	body	1280	valid
9.0ms	96×	body	80	nan
7.0ms	16×	body	640	valid
5.0ms	6×	body	5120	valid
2.0ms	4×	body	160	valid
1.0ms	5×	body	320	valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite130.0ms

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--` `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 → 171

Calls

4 calls:

76.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
60.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
130.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

183 → 183

Iterations

Iter	Nodes
3	3980
2	1411
1	572
0	244

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.2b	(- (* b_2 b_2) (* a c))
6.4b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

1339×	`times-frac`
946×	`add-sqr-sqrt`
940×	`*-un-lft-identity`
926×	`add-cube-cbrt`
749×	`prod-diff`
323×	`sqrt-prod`
210×	`distribute-rgt-neg-in`
207×	`distribute-lft-neg-in`
69×	`neg-mul-1`
60×	`div-inv`
35×	`fma-neg`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `div-exp` `frac-sub` `sub-div`

Counts

4 → 889

Calls

4 calls:

13.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
44.0ms	(- (* b_2 b_2) (* a c))
133.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
116.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

901 → 901

Iterations

Iter	Nodes
2	4268
1	1998
0	903

prune12.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.2b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
146×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
130×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
13×	`associate-l` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sqrt-div` `div-exp` `associate-*r/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 292

Calls

4 calls:

69.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
59.0ms	(- (* b_2 b_2) (* a c))
122.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

304 → 304

Iterations

Iter	Nodes
2	2029
1	994
0	356

prune3.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize46.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
13.9b	(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
48×	`add-sqr-sqrt`
46×	`*-un-lft-identity` `add-cube-cbrt`
35×	`fma-neg` `prod-diff`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`sqrt-div`
8×	`add-log-exp`
6×	`pow1` `neg-mul-1` `flip3--` `sqrt-prod` `flip--`
5×	`frac-sub`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l/` `associate-r/` `div-inv`
1×	`associate--l-` `neg-sub0` `div-sub` `sub-div`

Counts

4 → 139

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
47.0ms	(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b_2 b_2) (* a c))
146.0ms	(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

151 → 151

Iterations

Iter	Nodes
3	5023
2	1651
1	592
0	242

prune1.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

regimes612.0ms

Accuracy

84.8% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 33.4b

bsearch179.0ms

Steps

Iters	Range		Point
9	1.5347927881719531e+137	5.414027326126016e+143	7.803671648955123e+137
7	-3.433369562555282e-53	-1.9970851824949347e-54	-2.852138444177435e-54

simplify8.0ms

Iterations

Iter	Nodes
3	35
2	35
1	31
0	24

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	1057×	body	2560	valid
709.0ms	5844×	body	80	valid
616.0ms	957×	body	1280	valid
350.0ms	2883×	body	80	nan
245.0ms	462×	body	640	valid
87.0ms	198×	body	320	valid
83.0ms	109×	body	5120	valid
22.0ms	110×	body	160	valid