Details

sample66.0ms

Algorithm

intervals

Results

47.0ms

268×

body

valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
1.0b	(fma a c (* b d))
24.6b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

Calls

3 calls:

0.0ms	(fma d d (* c c))
0.0ms	(fma a c (* b d))
4.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

series222.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma d d (* c c))
48.0ms	(fma a c (* b d))
128.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify1.3s

Counts

61 → 61

Iterations

Iter	Nodes
4	3360
3	977
2	322
1	123
0	75

prune697.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 24.1b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma a c (* b d))
16.9b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.5b	(sqrt (fma d d (* c c)))
31.5b	(sqrt (fma d d (* c c)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma a c (* b d))
160.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
49.0ms	(sqrt (fma d d (* c c)))
59.0ms	(sqrt (fma d d (* c c)))

simplify1.1s

Counts

99 → 99

Iterations

Iter	Nodes
4	2805
3	970
2	305
1	146
0	91

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
1.0b	(fma a c (* b d))
16.9b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.5b	(sqrt (fma d d (* c c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

9.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
58.0ms	(fma a c (* b d))
137.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
73.0ms	(sqrt (fma d d (* c c)))

simplify1.1s

Counts

191 → 191

Iterations

Iter	Nodes
3	3771
2	1077
1	483
0	231

prune2.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
0.2b	(/ 1 (/ (hypot d c) (fma b d (* c a))))
0.8b	(fma b d (* c a))
16.9b	(/ (hypot d c) (fma b d (* c a)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 323

Calls

4 calls:

21.0ms	(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
6.0ms	(/ 1 (/ (hypot d c) (fma b d (* c a))))
0.0ms	(fma b d (* c a))
5.0ms	(/ (hypot d c) (fma b d (* c a)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
145.0ms	(/ 1 (/ (hypot d c) (fma b d (* c a))))
47.0ms	(fma b d (* c a))
115.0ms	(/ (hypot d c) (fma b d (* c a)))

simplify1.5s

Counts

335 → 335

Iterations

Iter	Nodes
2	3263
1	1236
0	462

prune3.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.4b

regimes375.0ms

Accuracy

28.4% (10.5b remaining)

Error of 12.9b against oracle of 2.4b and baseline of 17.0b

bsearch105.0ms

Steps

Iters	Range		Point
7	1.1552701116243735e+166	2.1229772983211598e+168	1.1770311826568578e+166
9	-5.0081114852453345e+138	-9.278525860478265e+132	-1.284532853290371e+137

simplify3.0ms

Iterations

Iter	Nodes
2	25
1	25
0	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8470×

body

valid