Details

sample38.0ms

Algorithm

intervals

Results

21.0ms

269×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize34.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma a c (* b d))
25.2b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

1.0ms	(fma a c (* b d))
10.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

series199.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(fma a c (* b d))
132.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify3.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	3488
3	1019
2	285
1	109
0	65

prune407.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma a c (* b d))
14.5b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
29.5b	(sqrt (fma d d (* c c)))
29.5b	(sqrt (fma d d (* c c)))

rewrite12.0ms

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))
6.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma a c (* b d))
145.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
50.0ms	(sqrt (fma d d (* c c)))
76.0ms	(sqrt (fma d d (* c c)))

simplify3.3s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
4	2818
3	974
2	304
1	146
0	91

prune696.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
0.3b	(fma a c (* b d))
14.5b	(/ (fma a c (* b d)) (hypot d c))
29.5b	(sqrt (fma d d (* c c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `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 → 173

Calls

4 calls:

26.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
0.0ms	(fma a c (* b d))
10.0ms	(/ (fma a c (* b d)) (hypot d c))
3.0ms	(sqrt (fma d d (* c c)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
44.0ms	(fma a c (* b d))
147.0ms	(/ (fma a c (* b d)) (hypot d c))
66.0ms	(sqrt (fma d d (* c c)))

simplify2.1s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
3	3013
2	1041
1	468
0	230

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.3b	(fma a c (* b d))
14.5b	(/ (fma a c (* b d)) (hypot d c))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 114

Calls

3 calls:

14.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
1.0ms	(fma a c (* b d))
11.0ms	(/ (fma a c (* b d)) (hypot d c))

series426.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
52.0ms	(fma a c (* b d))
174.0ms	(/ (fma a c (* b d)) (hypot d c))

simplify2.6s

Counts

123 → 123

Iterations

Iter	Nodes
done	5007
3	3530
2	910
1	347
0	162

prune588.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

regimes313.0ms

Accuracy

18.6% (8.9b remaining)

Error of 14.7b against oracle of 5.8b and baseline of 16.8b

bsearch44.0ms

Steps

Iters	Range		Point
9	4.230872522382776e+160	1.60249842060193e+167	9.842459121637509e+163

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample868.0ms

Algorithm

intervals

Results

649.0ms

8499×

body

valid