Details

sample133.0ms

Algorithm

intervals

Results

85.0ms	277×	body	80	valid
20.0ms	86×	body	80	nan

simplify142.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	160
7	160
6	159
5	152
4	140
3	108
2	63
1	36
0	20

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize141.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (fma -4 (* c a) (* b b))) b)
1.2b	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
23.5b	(sqrt (fma -4 (* c a) (* b b)))
23.5b	(sqrt (fma -4 (* c a) (* b b)))

rewrite49.0ms

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:

15.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
21.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
5.0ms	(sqrt (fma -4 (* c a) (* b b)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (sqrt (fma -4 (* c a) (* b b))) b)
103.0ms	(- (- b) (sqrt (fma -4 (* c a) (* b b))))
118.0ms	(sqrt (fma -4 (* c a) (* b b)))
146.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify1.0s

Counts

177 → 177

Iterations

Iter	Nodes
3	2261
2	875
1	415
0	194

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize168.0ms

Local error

Found 4 expressions with local error:

21.3b	(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))
23.5b	(sqrt (fma -4 (* c a) (* b b)))
23.5b	(sqrt (fma -4 (* c a) (* b b)))
23.5b	(sqrt (fma -4 (* c a) (* b b)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
2.0ms	(sqrt (fma -4 (* c a) (* b b)))
3.0ms	(sqrt (fma -4 (* c a) (* b b)))

series728.0ms

Counts

4 → 12

Calls

4 calls:

406.0ms	(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))
109.0ms	(sqrt (fma -4 (* c a) (* b b)))
84.0ms	(sqrt (fma -4 (* c a) (* b b)))
130.0ms	(sqrt (fma -4 (* c a) (* b b)))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
4	2376
3	684
2	236
1	111
0	65

prune652.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.7b

localize191.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (fma -4 (* c a) (* b b)))
24.2b	(cbrt (fma -4 (* c a) (* b b)))
24.2b	(cbrt (fma -4 (* c a) (* b b)))
24.2b	(cbrt (fma -4 (* c a) (* 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 -4 (* c a) (* b b)))
2.0ms	(cbrt (fma -4 (* c a) (* b b)))
1.0ms	(cbrt (fma -4 (* c a) (* b b)))
2.0ms	(cbrt (fma -4 (* c a) (* b b)))

series914.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt (fma -4 (* c a) (* b b)))
254.0ms	(cbrt (fma -4 (* c a) (* b b)))
254.0ms	(cbrt (fma -4 (* c a) (* b b)))
302.0ms	(cbrt (fma -4 (* c a) (* b b)))

simplify2.9s

Counts

70 → 70

Iterations

Iter	Nodes
5	6385
4	1989
3	676
2	257
1	121
0	68

prune837.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.7b

localize201.0ms

Local error

Found 4 expressions with local error:

24.2b	(cbrt (fma -4 (* c a) (* b b)))
24.2b	(cbrt (fma -4 (* c a) (* b b)))
24.2b	(cbrt (fma -4 (* c a) (* b b)))
24.2b	(cbrt (fma -4 (* c a) (* b b)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (fma -4 (* c a) (* b b)))
306.0ms	(cbrt (fma -4 (* c a) (* b b)))
267.0ms	(cbrt (fma -4 (* c a) (* b b)))
244.0ms	(cbrt (fma -4 (* c a) (* b b)))

simplify3.6s

Counts

68 → 68

Iterations

Iter	Nodes
5	6589
4	1938
3	624
2	228
1	102
0	53

prune896.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

regimes385.0ms

Accuracy

88.6% (0.8b remaining)

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

bsearch148.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	4.1813913858897907e+68

simplify7.0ms

Iterations

Iter	Nodes
2	37
1	37
0	32

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	8699×	body	80	valid
571.0ms	2954×	body	80	nan