Details

sample133.0ms

Algorithm

intervals

Results

33.0ms	39×	body	2560	valid
27.0ms	188×	body	80	valid
22.0ms	31×	body	1280	valid
12.0ms	87×	body	80	nan
11.0ms	13×	body	640	valid
4.0ms	3×	body	5120	valid
3.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify89.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	113
5	113
4	105
3	81
2	43
1	22
0	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* -3 a) c (* b b))
0.2b	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
0.4b	(- (sqrt (fma (* -3 a) c (* b b))) b)
23.1b	(sqrt (fma (* -3 a) c (* b b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `fma-neg` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma (* -3 a) c (* b b))
24.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
8.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
1.0ms	(sqrt (fma (* -3 a) c (* b b)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma (* -3 a) c (* b b))
224.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
116.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
102.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.5s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1069
1	348
0	152

prune754.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3)
0.2b	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
0.4b	(- (sqrt (fma (* -3 a) c (* b b))) b)
23.1b	(sqrt (fma (* -3 a) c (* b b)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
156×	`times-frac`
127×	`*-un-lft-identity`
93×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
28×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 213

Calls

4 calls:

23.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3)
31.0ms	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
8.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
2.0ms	(sqrt (fma (* -3 a) c (* b b)))

series1.0s

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3)
242.0ms	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
569.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
94.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.9s

Counts

225 → 225

Iterations

Iter	Nodes
done	5001
2	1838
1	638
0	282

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.5b

localize39.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (fma (* -3 a) c (* b b))) b)
4.5b	(/ (/ (/ (fma c (* -3 a) 0) (+ (sqrt (fma (* -3 a) c (* b b))) b)) 3) a)
11.1b	(/ (fma c (* -3 a) 0) (+ (sqrt (fma (* -3 a) c (* b b))) b))
23.1b	(sqrt (fma (* -3 a) c (* b b)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

546×	`times-frac`
329×	`*-un-lft-identity`
248×	`add-sqr-sqrt`
247×	`add-cube-cbrt`
61×	`associate-/l*`
41×	`distribute-lft-out`
26×	`associate-/r/`
18×	`div-inv`
15×	`add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `flip-+`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`fma-def` `sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 328

Calls

4 calls:

12.0ms	(+ (sqrt (fma (* -3 a) c (* b b))) b)
35.0ms	(/ (/ (/ (fma c (* -3 a) 0) (+ (sqrt (fma (* -3 a) c (* b b))) b)) 3) a)
12.0ms	(/ (fma c (* -3 a) 0) (+ (sqrt (fma (* -3 a) c (* b b))) b))
2.0ms	(sqrt (fma (* -3 a) c (* b b)))

series965.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(+ (sqrt (fma (* -3 a) c (* b b))) b)
312.0ms	(/ (/ (/ (fma c (* -3 a) 0) (+ (sqrt (fma (* -3 a) c (* b b))) b)) 3) a)
343.0ms	(/ (fma c (* -3 a) 0) (+ (sqrt (fma (* -3 a) c (* b b))) b))
156.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify2.4s

Counts

340 → 340

Iterations

Iter	Nodes
done	5017
2	4170
1	1285
0	573

prune2.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 16.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma b b (* (* -3 a) c))
1.1b	(+ (sqrt (fma b b (* (* -3 a) c))) b)
14.4b	(/ a (* (* -3 a) c))
23.1b	(sqrt (fma b b (* (* -3 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
6×	`fma-def` `sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma b b (* (* -3 a) c))
7.0ms	(+ (sqrt (fma b b (* (* -3 a) c))) b)
33.0ms	(/ a (* (* -3 a) c))
3.0ms	(sqrt (fma b b (* (* -3 a) c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(fma b b (* (* -3 a) c))
134.0ms	(+ (sqrt (fma b b (* (* -3 a) c))) b)
14.0ms	(/ a (* (* -3 a) c))
152.0ms	(sqrt (fma b b (* (* -3 a) c)))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1107
1	310
0	130

prune533.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 10.0b

regimes695.0ms

Accuracy

97.5% (0.5b remaining)

Error of 10.4b against oracle of 9.9b and baseline of 29.9b

bsearch533.0ms

Steps

Iters	Range	Point
9	2.186481029015607e+142	3.2832683303982924e+151	1.5879900645620077e+150
9	1.1434221264748056e-201	3.385720996279136e-192	1.1685637944370405e-201
9	-5.599802959155633e+154	-4.186518194588193e+147	-1.3282248930815427e+154

Iters

Range

Point

2.186481029015607e+142

3.2832683303982924e+151

1.5879900645620077e+150

1.1434221264748056e-201

3.385720996279136e-192

1.1685637944370405e-201

-5.599802959155633e+154

-4.186518194588193e+147

-1.3282248930815427e+154

simplify16.0ms

Iterations

Iter	Nodes
done	61
1	61
0	47

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	5889×	body	80	valid
1.1s	1064×	body	2560	valid
576.0ms	903×	body	1280	valid
484.0ms	2854×	body	80	nan
274.0ms	446×	body	640	valid
95.0ms	95×	body	5120	valid
75.0ms	206×	body	320	valid
32.0ms	133×	body	160	valid