Details

sample73.0ms

Algorithm

intervals

Results

34.0ms	279×	body	80	valid
9.0ms	84×	body	80	nan

simplify204.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	170
7	170
6	168
5	164
4	157
3	132
2	76
1	39
0	20

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize110.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.0b	(- (sqrt (fma c (* a -4) (* b b))) b)
20.7b	(sqrt (fma c (* a -4) (* b b)))
20.7b	(sqrt (fma c (* a -4) (* b b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

20.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
9.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
1.0ms	(sqrt (fma c (* a -4) (* b b)))
1.0ms	(sqrt (fma c (* a -4) (* b b)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
96.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
114.0ms	(sqrt (fma c (* a -4) (* b b)))
141.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify2.5s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
3	3147
2	965
1	427
0	194

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.7b

localize169.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma c (* a -4) (* b b)))
21.5b	(cbrt (fma c (* a -4) (* b b)))
21.5b	(cbrt (fma c (* a -4) (* b b)))
21.5b	(cbrt (fma c (* a -4) (* b b)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

2.0ms	(sqrt (fma c (* a -4) (* b b)))
1.0ms	(cbrt (fma c (* a -4) (* b b)))
1.0ms	(cbrt (fma c (* a -4) (* b b)))
2.0ms	(cbrt (fma c (* a -4) (* b b)))

series933.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (fma c (* a -4) (* b b)))
237.0ms	(cbrt (fma c (* a -4) (* b b)))
283.0ms	(cbrt (fma c (* a -4) (* b b)))
293.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify2.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	5019
4	3363
3	861
2	279
1	124
0	68

prune697.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.7b

localize203.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma c (* a -4) (* b b)))
20.7b	(sqrt (fma c (* a -4) (* b b)))
21.5b	(cbrt (fma c (* a -4) (* b b)))
21.5b	(cbrt (fma c (* a -4) (* b b)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 60

Calls

4 calls:

2.0ms	(sqrt (fma c (* a -4) (* b b)))
3.0ms	(sqrt (fma c (* a -4) (* b b)))
1.0ms	(cbrt (fma c (* a -4) (* b b)))
13.0ms	(cbrt (fma c (* a -4) (* b b)))

series701.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (fma c (* a -4) (* b b)))
100.0ms	(sqrt (fma c (* a -4) (* b b)))
226.0ms	(cbrt (fma c (* a -4) (* b b)))
264.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify2.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5019
4	3363
3	861
2	279
1	124
0	68

prune825.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.7b

localize170.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma c (* a -4) (* b b)))
21.5b	(cbrt (fma c (* a -4) (* b b)))
21.5b	(cbrt (fma c (* a -4) (* b b)))
21.5b	(cbrt (fma c (* a -4) (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

1.0ms	(sqrt (fma c (* a -4) (* b b)))
1.0ms	(cbrt (fma c (* a -4) (* b b)))
1.0ms	(cbrt (fma c (* a -4) (* b b)))
1.0ms	(cbrt (fma c (* a -4) (* b b)))

series805.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (fma c (* a -4) (* b b)))
219.0ms	(cbrt (fma c (* a -4) (* b b)))
241.0ms	(cbrt (fma c (* a -4) (* b b)))
235.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify2.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5019
4	3363
3	861
2	279
1	124
0	68

prune753.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.7b

regimes404.0ms

Accuracy

88.2% (0.8b remaining)

Error of 13.1b against oracle of 12.3b and baseline of 19.0b

bsearch162.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	9.19242293018462e+63

simplify12.0ms

Iterations

Iter	Nodes
done	33
1	33
0	30

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.2s	8746×	body	80	valid
604.0ms	3007×	body	80	nan