Details

sample31.0ms

Algorithm

intervals

Results

21.0ms

268×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize35.0ms

Local error

Found 1 expressions with local error:

27.8b

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 30

Calls

1 calls:

9.0ms

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

series160.0ms

Counts

1 → 3

Calls

1 calls:

159.0ms

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

simplify1.1s

Counts

33 → 33

Iterations

Iter	Nodes
4	2413
3	689
2	227
1	95
0	59

prune188.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
18.6b	(/ (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)))

rewrite44.0ms

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:

20.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
10.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
3.0ms	(sqrt (fma d d (* c c)))
3.0ms	(sqrt (fma d d (* c c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
145.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
47.0ms	(sqrt (fma d d (* c c)))
63.0ms	(sqrt (fma d d (* c c)))

simplify1.8s

Counts

266 → 266

Iterations

Iter	Nodes
3	4174
2	1184
1	542
0	262

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma b d (* c a))
0.1b	(/ (hypot d c) (/ (fma b d (* c a)) (hypot d c)))
1.2b	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
18.6b	(/ (fma b d (* c a)) (hypot d c))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 321

Calls

4 calls:

0.0ms	(fma b d (* c a))
6.0ms	(/ (hypot d c) (/ (fma b d (* c a)) (hypot d c)))
14.0ms	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
5.0ms	(/ (fma b d (* c a)) (hypot d c))

series593.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma b d (* c a))
119.0ms	(/ (hypot d c) (/ (fma b d (* c a)) (hypot d c)))
224.0ms	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
189.0ms	(/ (fma b d (* c a)) (hypot d c))

simplify7.2s

Counts

333 → 333

Iterations

Iter	Nodes
2	2985
1	1161
0	442

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma b d (* c a))
0.0b	(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
0.2b	(/ 1 (/ (hypot d c) (fma b d (* c a))))
18.7b	(/ (hypot d c) (fma b d (* c a)))

rewrite48.0ms

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:

0.0ms	(fma b d (* c a))
22.0ms	(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
9.0ms	(/ 1 (/ (hypot d c) (fma b d (* c a))))
4.0ms	(/ (hypot d c) (fma b d (* c a)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma b d (* c a))
224.0ms	(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
151.0ms	(/ 1 (/ (hypot d c) (fma b d (* c a))))
117.0ms	(/ (hypot d c) (fma b d (* c a)))

simplify12.7s

Counts

335 → 335

Iterations

Iter	Nodes
2	3109
1	1230
0	462

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

regimes265.0ms

Accuracy

31.5% (7.8b remaining)

Error of 13.0b against oracle of 5.1b and baseline of 16.6b

bsearch82.0ms

Steps

Iters	Range		Point
11	3.256921449474541e+176	7.122284858877049e+195	4.711008584896772e+178
6	-8.126158358066474e+96	-1.2737663299885354e+96	-7.67400831190257e+96

simplify3.0ms

Iterations

Iter	Nodes
2	20
1	20
0	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

843.0ms

8453×

body

valid