Details

sample53.0ms

Algorithm

intervals

Results

25.0ms

263×

body

valid

simplify71.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune68.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize130.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.0b	(fma d d (* c c))
27.3b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite17.0ms

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:

1.0ms	(fma a c (* b d))
1.0ms	(fma d d (* c c))
12.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

series387.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(fma a c (* b d))
89.0ms	(fma d d (* c c))
215.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify6.6s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
4	3559
3	1103
2	331
1	123
0	75

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 27.0b

localize138.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
18.4b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
28.3b	(sqrt (fma d d (* c c)))
28.3b	(sqrt (fma d d (* c c)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 254

Calls

4 calls:

56.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
14.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
4.0ms	(sqrt (fma d d (* c c)))
5.0ms	(sqrt (fma d d (* c c)))

series733.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
279.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
93.0ms	(sqrt (fma d d (* c c)))
97.0ms	(sqrt (fma d d (* c c)))

simplify8.4s

Counts

266 → 266

Iterations

Iter	Nodes
done	5022
3	4606
2	1144
1	547
0	262

prune4.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.0b

localize119.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (hypot d c) (fma b d (* c a))) (hypot d c))
0.3b	(/ 1 (* (/ (hypot d c) (fma b d (* c a))) (hypot d c)))
0.8b	(fma b d (* c a))
18.5b	(/ (hypot d c) (fma b d (* c a)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
27×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`associate-l`
11×	`div-exp`
9×	`pow1`
8×	`prod-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*l/` `pow-flip` `unswap-sqr`
1×	`associate-/r/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 112

Calls

4 calls:

35.0ms	(* (/ (hypot d c) (fma b d (* c a))) (hypot d c))
50.0ms	(/ 1 (* (/ (hypot d c) (fma b d (* c a))) (hypot d c)))
3.0ms	(fma b d (* c a))
13.0ms	(/ (hypot d c) (fma b d (* c a)))

series810.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (/ (hypot d c) (fma b d (* c a))) (hypot d c))
363.0ms	(/ 1 (* (/ (hypot d c) (fma b d (* c a))) (hypot d c)))
66.0ms	(fma b d (* c a))
184.0ms	(/ (hypot d c) (fma b d (* c a)))

simplify6.6s

Counts

124 → 124

Iterations

Iter	Nodes
done	5089
3	3448
2	1114
1	310
0	137

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.9b

localize96.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma d b (* c a)) (hypot d c)) (hypot d c))
0.8b	(fma d b (* c a))
18.4b	(/ (fma d b (* c a)) (hypot d c))

rewrite50.0ms

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:

25.0ms	(/ (/ (fma d b (* c a)) (hypot d c)) (hypot d c))
1.0ms	(fma d b (* c a))
12.0ms	(/ (fma d b (* c a)) (hypot d c))

series506.0ms

Counts

3 → 9

Calls

3 calls:

238.0ms	(/ (/ (fma d b (* c a)) (hypot d c)) (hypot d c))
70.0ms	(fma d b (* c a))
198.0ms	(/ (fma d b (* c a)) (hypot d c))

simplify5.1s

Counts

123 → 123

Iterations

Iter	Nodes
done	5008
3	3150
2	860
1	337
0	164

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.6b

regimes1.1s

Accuracy

32.8% (8.3b remaining)

Error of 13.5b against oracle of 5.2b and baseline of 17.6b

bsearch71.0ms

Steps

Iters	Range		Point
2	1.449336560724627e+77	1.6993258300219904e+77	1.66807717135982e+77
8	-1.0307498481855882e+125	-6.599110238462854e+121	-9.494881135626707e+123

simplify11.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample1.3s

Algorithm

intervals

Results

752.0ms

8425×

body

valid