Details

sample138.0ms

Algorithm

intervals

Results

30.0ms	37×	body	2560	valid
27.0ms	194×	body	80	valid
25.0ms	18×	body	640	valid
19.0ms	28×	body	1280	valid
11.0ms	86×	body	80	nan
5.0ms	5×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify132.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.8b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
25.0b	(sqrt (fma (* -4 a) c (* b b)))

rewrite38.0ms

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:

22.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
12.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
77.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
81.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify932.0ms

Counts

165 → 165

Iterations

Iter	Nodes
done	2000
3	2000
2	1124
1	479
0	211

prune586.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize41.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
25.0b	(sqrt (fma (* -4 a) c (* b b)))

rewrite82.0ms

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:

55.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
23.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series271.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
93.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
80.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.1s

Counts

163 → 163

Iterations

Iter	Nodes
done	2000
3	2000
2	1322
1	541
0	230

prune686.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
0.2b	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
25.0b	(sqrt (fma (* -4 a) c (* b b)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
10×	`fma-neg`
8×	`div-exp` `add-log-exp`
7×	`neg-mul-1`
6×	`pow1` `flip3--` `div-inv` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `diff-log` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 290

Calls

4 calls:

24.0ms	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
24.0ms	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
101.0ms	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
75.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
82.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify984.0ms

Counts

302 → 302

Iterations

Iter	Nodes
done	2006
3	2006
2	1985
1	801
0	340

prune897.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a))
0.2b	(/ 1 (/ 1 (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)))
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
25.0b	(sqrt (fma (* -4 a) c (* b b)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
630×	`add-sqr-sqrt`
629×	`*-un-lft-identity`
433×	`add-cube-cbrt`
105×	`associate-/r*`
98×	`distribute-lft-out--` `difference-of-squares`
82×	`sqrt-prod`
70×	`distribute-rgt-neg-in`
60×	`prod-diff`
58×	`add-exp-log`
42×	`div-exp`
22×	`div-inv`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube`
15×	`rec-exp` `1-exp`
10×	`fma-neg`
9×	`cbrt-undiv`
8×	`pow1` `add-log-exp`
7×	`neg-mul-1`
6×	`associate-/r/` `associate-/l*`
5×	`pow-flip`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`inv-pow`
2×	`clear-num` `frac-2neg` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `flip--` `remove-double-div`

Counts

4 → 600

Calls

4 calls:

26.0ms	(/ 1 (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a))
25.0ms	(/ 1 (/ 1 (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)))
10.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ 1 (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a))
139.0ms	(/ 1 (/ 1 (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)))
117.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
87.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.6s

Counts

612 → 612

Iterations

Iter	Nodes
done	2003
2	2003
1	1725
0	649

prune2.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

regimes415.0ms

Accuracy

83.4% (4.6b remaining)

Error of 9.9b against oracle of 5.2b and baseline of 33.3b

bsearch259.0ms

Steps

Iters	Range		Point
9	1.1500868835104234e+100	1.1016243770318365e+105	2.5703497435733685e+102
10	-1.094129558870314e-56	-1.2317994276347943e-74	-1.8774910265390396e-73

simplify14.0ms

Iterations

Iter	Nodes
done	35
1	35
0	30

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.4s	5820×	body	80	valid
1.1s	1095×	body	2560	valid
867.0ms	948×	body	1280	valid
487.0ms	2996×	body	80	nan
316.0ms	445×	body	640	valid
156.0ms	225×	body	320	valid
142.0ms	98×	body	5120	valid
33.0ms	116×	body	160	valid