Details

sample59.0ms

Algorithm

intervals

Results

40.0ms

269×

body

valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize49.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
0.5b	(fma a c (* b d))
29.8b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite11.0ms

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))
9.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma d d (* c c))
45.0ms	(fma a c (* b d))
128.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify971.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	2004
4	2004
3	1082
2	340
1	123
0	75

prune783.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 29.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma a c (* b d))
16.8b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.8b	(sqrt (fma d d (* c c)))
31.8b	(sqrt (fma d d (* c c)))

rewrite23.0ms

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))
16.0ms	(/ (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)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma a c (* b d))
202.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
71.0ms	(sqrt (fma d d (* c c)))
65.0ms	(sqrt (fma d d (* c c)))

simplify1.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	2004
4	2004
3	974
2	304
1	146
0	91

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
0.5b	(fma a c (* b d))
16.8b	(/ (fma a c (* b d)) (hypot d c))
31.8b	(sqrt (fma d d (* c c)))

rewrite20.0ms

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:

9.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (hypot d c))
2.0ms	(sqrt (fma d d (* c c)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
61.0ms	(fma a c (* b d))
154.0ms	(/ (fma a c (* b d)) (hypot d c))
81.0ms	(sqrt (fma d d (* c c)))

simplify1.1s

Counts

185 → 185

Iterations

Iter	Nodes
done	2001
3	2001
2	1041
1	468
0	230

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.5b	(fma a c (* b d))
16.8b	(/ (fma a c (* b d)) (hypot d c))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

0.0ms	(hypot d c)
12.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.0ms	(fma a c (* b d))
4.0ms	(/ (fma a c (* b d)) (hypot d c))

series451.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(hypot d c)
152.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
50.0ms	(fma a c (* b d))
182.0ms	(/ (fma a c (* b d)) (hypot d c))

simplify831.0ms

Counts

137 → 137

Iterations

Iter	Nodes
done	2025
3	2025
2	923
1	359
0	170

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

regimes282.0ms

Accuracy

32.9% (7.2b remaining)

Error of 12.9b against oracle of 5.7b and baseline of 16.4b

bsearch119.0ms

Steps

Iters	Range		Point
9	1.6933955445897368e+221	1.4196464610458346e+230	1.7195081298008246e+221
9	-4.2516442886911883e+123	-3.786455365439721e+118	-1.8277997780989823e+123

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8488×

body

valid