Details

sample128.0ms

Algorithm

intervals

Results

42.0ms	31×	body	2560	valid
21.0ms	35×	body	1280	valid
21.0ms	173×	body	80	valid
9.0ms	20×	body	640	valid
9.0ms	82×	body	80	nan
5.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	126
5	126
4	118
3	87
2	43
1	22
0	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

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))
0.9b	(- (sqrt (fma (* -3 a) c (* b b))) b)
22.2b	(sqrt (fma (* -3 a) c (* b b)))

rewrite41.0ms

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))
29.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
7.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
1.0ms	(sqrt (fma (* -3 a) c (* b b)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma (* -3 a) c (* b b))
152.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
125.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
119.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.5s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1279
1	350
0	152

prune580.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 28.3b

localize28.0ms

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)
0.9b	(- (sqrt (fma (* -3 a) c (* b b))) b)
22.2b	(sqrt (fma (* -3 a) c (* b b)))

rewrite59.0ms

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:

20.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3)
20.0ms	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
13.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
1.0ms	(sqrt (fma (* -3 a) c (* b b)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3)
152.0ms	(/ (/ (- (sqrt (fma (* -3 a) c (* b b))) b) 3) a)
105.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
89.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.6s

Counts

225 → 225

Iterations

Iter	Nodes
done	5001
2	2514
1	666
0	282

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 28.3b

localize51.0ms

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) (* a 3))
0.9b	(- (sqrt (fma (* -3 a) c (* b b))) b)
22.2b	(sqrt (fma (* -3 a) c (* b b)))

rewrite59.0ms

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))
38.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* a 3))
15.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
2.0ms	(sqrt (fma (* -3 a) c (* b b)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (* -3 a) c (* b b))
165.0ms	(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* a 3))
107.0ms	(- (sqrt (fma (* -3 a) c (* b b))) b)
128.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1290
1	350
0	152

prune684.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 28.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (fma (* -3 a) c (* b b))) 3)
0.2b	(/ (- (/ (sqrt (fma (* -3 a) c (* b b))) 3) (/ b 3)) a)
0.9b	(- (/ (sqrt (fma (* -3 a) c (* b b))) 3) (/ b 3))
22.2b	(sqrt (fma (* -3 a) c (* b b)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

575×	`times-frac`
481×	`add-sqr-sqrt`
425×	`*-un-lft-identity`
385×	`add-cube-cbrt`
286×	`prod-diff`
151×	`sqrt-prod`
48×	`div-inv`
30×	`difference-of-squares`
22×	`fma-neg`
20×	`associate-/l*` `distribute-lft-out--`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `add-log-exp`
5×	`pow1` `distribute-rgt-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `frac-sub` `flip--` `sub-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 473

Calls

4 calls:

9.0ms	(/ (sqrt (fma (* -3 a) c (* b b))) 3)
46.0ms	(/ (- (/ (sqrt (fma (* -3 a) c (* b b))) 3) (/ b 3)) a)
32.0ms	(- (/ (sqrt (fma (* -3 a) c (* b b))) 3) (/ b 3))
2.0ms	(sqrt (fma (* -3 a) c (* b b)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (sqrt (fma (* -3 a) c (* b b))) 3)
179.0ms	(/ (- (/ (sqrt (fma (* -3 a) c (* b b))) 3) (/ b 3)) a)
134.0ms	(- (/ (sqrt (fma (* -3 a) c (* b b))) 3) (/ b 3))
116.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify2.5s

Counts

485 → 485

Iterations

Iter	Nodes
done	5000
2	4000
1	1240
0	548

prune2.7s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 28.1b

regimes1.0s

Accuracy

89.2% (0.6b remaining)

Error of 29.2b against oracle of 28.7b and baseline of 33.9b

bsearch164.0ms

Steps

Iters	Range		Point
10	3.302865865338161e+140	2.8302951796802603e+150	5.03307751825146e+142

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.3s	1055×	body	2560	valid
921.0ms	5742×	body	80	valid
769.0ms	978×	body	1280	valid
511.0ms	2913×	body	80	nan
292.0ms	455×	body	640	valid
203.0ms	138×	body	5120	valid
94.0ms	257×	body	320	valid
31.0ms	118×	body	160	valid