Details

sample108.0ms

Algorithm

intervals

Results

38.0ms	39×	body	2560	valid
17.0ms	173×	body	80	valid
13.0ms	30×	body	1280	valid
8.0ms	89×	body	80	nan
7.0ms	16×	body	640	valid
4.0ms	5×	body	5120	valid
3.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid

simplify138.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.0b

localize51.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.4b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
26.8b	(sqrt (fma (* -4 a) c (* b b)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 156

Calls

3 calls:

24.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
21.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series340.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
101.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
107.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.4s

Counts

165 → 165

Iterations

Iter	Nodes
3	2842
2	1111
1	477
0	211

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize12.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
1	0
0	0

prune54.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.6b

localize34.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
1.4b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
26.8b	(sqrt (fma (* -4 a) c (* b b)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`prod-diff`
53×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
12×	`add-exp-log`
11×	`times-frac`
10×	`fma-neg`
8×	`add-cbrt-cube`
7×	`neg-mul-1` `associate-l` `add-log-exp`
6×	`pow1`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `unswap-sqr`
2×	`frac-times` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

3 → 154

Calls

3 calls:

37.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
19.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series323.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
93.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
97.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.2s

Counts

163 → 163

Iterations

Iter	Nodes
3	3112
2	1319
1	538
0	230

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.6b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.4b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
26.8b	(sqrt (fma (* -4 a) c (* b b)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 156

Calls

3 calls:

46.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
20.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series331.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
116.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
93.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.4s

Counts

165 → 165

Iterations

Iter	Nodes
3	2842
2	1111
1	477
0	211

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.6b

regimes433.0ms

Accuracy

86.7% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 39.3b

bsearch221.0ms

Steps

Iters	Range		Point
9	2.662790715355376e+61	3.00977400694497e+66	2.9822108876570007e+66
9	-6.352668374011919e-47	-5.750941040768736e-55	-7.406397712303184e-53

simplify4.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.3s	1064×	body	2560	valid
917.0ms	5799×	body	80	valid
731.0ms	916×	body	1280	valid
709.0ms	444×	body	640	valid
476.0ms	2970×	body	80	nan
147.0ms	120×	body	5120	valid
133.0ms	243×	body	320	valid
32.0ms	125×	body	160	valid