Details

sample59.0ms

Algorithm

intervals

Results

40.0ms

268×

body

valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.9b

localize33.0ms

Local error

Found 1 expressions with local error:

24.9b

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

rewrite9.0ms

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:

8.0ms

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

series105.0ms

Counts

1 → 3

Calls

1 calls:

105.0ms

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

simplify988.0ms

Counts

33 → 33

Iterations

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

prune405.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.4b

localize21.0ms

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))))
15.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
28.2b	(sqrt (fma d d (* c c)))
28.2b	(sqrt (fma d d (* c c)))

rewrite26.0ms

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:

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

series386.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
131.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
77.0ms	(sqrt (fma d d (* c c)))
70.0ms	(sqrt (fma d d (* c c)))

simplify1.8s

Counts

266 → 266

Iterations

Iter	Nodes
3	4174
2	1184
1	542
0	262

prune3.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (hypot d c) (/ (fma b d (* c a)) (hypot d c)))
0.4b	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
0.5b	(fma b d (* c a))
15.3b	(/ (fma b d (* c a)) (hypot d c))

rewrite51.0ms

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:

12.0ms	(/ (hypot d c) (/ (fma b d (* c a)) (hypot d c)))
19.0ms	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
0.0ms	(fma b d (* c a))
8.0ms	(/ (fma b d (* c a)) (hypot d c))

series633.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (hypot d c) (/ (fma b d (* c a)) (hypot d c)))
282.0ms	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
56.0ms	(fma b d (* c a))
152.0ms	(/ (fma b d (* c a)) (hypot d c))

simplify5.1s

Counts

333 → 333

Iterations

Iter	Nodes
2	2932
1	1159
0	442

prune3.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize20.0ms

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))))
0.5b	(fma b d (* c a))
15.4b	(/ (hypot d c) (fma b d (* c a)))

rewrite49.0ms

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:

12.0ms	(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
14.0ms	(/ 1 (/ (hypot d c) (fma b d (* c a))))
0.0ms	(fma b d (* c a))
10.0ms	(/ (hypot d c) (fma b d (* c a)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (/ 1 (/ (hypot d c) (fma b d (* c a)))) (hypot d c))
137.0ms	(/ 1 (/ (hypot d c) (fma b d (* c a))))
67.0ms	(fma b d (* c a))
128.0ms	(/ (hypot d c) (fma b d (* c a)))

simplify13.2s

Counts

335 → 335

Iterations

Iter	Nodes
2	3177
1	1235
0	462

prune2.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.6b

regimes291.0ms

Accuracy

37.3% (7.4b remaining)

Error of 12.5b against oracle of 5.1b and baseline of 16.9b

bsearch92.0ms

Steps

Iters	Range		Point
7	2.1102039645699546e+151	5.958060973732056e+152	6.134295887350108e+151
9	-1.5743457092445136e+146	-1.7745971881998158e+137	-2.052205868896771e+142

simplify3.0ms

Iterations

Iter	Nodes
2	22
1	22
0	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

893.0ms

8476×

body

valid