Details

sample57.0ms

Algorithm

intervals

Results

41.0ms

270×

body

valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma a c (* b d))
28.2b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite5.0ms

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:

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

series216.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(fma a c (* b d))
153.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify1.2s

Counts

47 → 47

Iterations

Iter	Nodes
4	3544
3	1049
2	283
1	108
0	65

prune542.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 27.8b

localize26.0ms

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))))
18.7b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
33.4b	(sqrt (fma d d (* c c)))
33.4b	(sqrt (fma d d (* c c)))

rewrite22.0ms

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:

10.0ms	(/ (/ (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)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
182.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
58.0ms	(sqrt (fma d d (* c c)))
55.0ms	(sqrt (fma d d (* c c)))

simplify1.9s

Counts

266 → 266

Iterations

Iter	Nodes
3	4174
2	1184
1	542
0	262

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.8b

localize18.0ms

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)))
0.6b	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
18.7b	(/ (fma b d (* c a)) (hypot d c))

rewrite30.0ms

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)))
9.0ms	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
8.0ms	(/ (fma b d (* c a)) (hypot d c))

series681.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma b d (* c a))
155.0ms	(/ (hypot d c) (/ (fma b d (* c a)) (hypot d c)))
288.0ms	(/ 1 (/ (hypot d c) (/ (fma b d (* c a)) (hypot d c))))
185.0ms	(/ (fma b d (* c a)) (hypot d c))

simplify6.2s

Counts

333 → 333

Iterations

Iter	Nodes
2	2985
1	1161
0	442

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 100

Calls

3 calls:

0.0ms	(fma b d (* c a))
13.0ms	(* (/ 1 (hypot d c)) (/ (fma b d (* c a)) (hypot d c)))
4.0ms	(/ (fma b d (* c a)) (hypot d c))

series375.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(fma b d (* c a))
189.0ms	(* (/ 1 (hypot d c)) (/ (fma b d (* c a)) (hypot d c)))
143.0ms	(/ (fma b d (* c a)) (hypot d c))

simplify6.4s

Counts

109 → 109

Iterations

Iter	Nodes
3	3853
2	1104
1	361
0	142

prune752.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.4b

regimes278.0ms

Accuracy

35.5% (7.6b remaining)

Error of 12.7b against oracle of 5.2b and baseline of 16.9b

bsearch105.0ms

Steps

Iters	Range		Point
9	5.794242328935301e+149	4.804137794702964e+156	3.85213929759163e+150
5	-2.3145197442357917e+201	-5.993537297213248e+200	-1.1964723101605788e+201

simplify10.0ms

Iterations

Iter	Nodes
4	31
3	31
2	28
1	25
0	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

947.0ms

8484×

body

valid