Details

sample46.0ms

Algorithm

intervals

Results

25.0ms

270×

body

valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma c c (* d d))
0.5b	(fma a c (* b d))
24.7b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma c c (* d d))
0.0ms	(fma a c (* b d))
6.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

series632.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(fma c c (* d d))
442.0ms	(fma a c (* b d))
147.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify2.7s

Counts

58 → 58

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	73	833
1	114	819
2	291	707
3	786	707
4	2294	707
done	5001	707

prune220.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
0.5b	(fma a c (* d b))
14.7b	(/ (fma a c (* d b)) (hypot d c))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
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` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

47.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
0.0ms	(fma a c (* d b))
5.0ms	(/ (fma a c (* d b)) (hypot d c))

series476.0ms

Counts

3 → 9

Calls

3 calls:

237.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
47.0ms	(fma a c (* d b))
192.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify3.6s

Counts

106 → 106

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	138	1895
1	326	1763
2	1071	1527
3	3993	1527
done	5001	1494

prune353.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.5b	(fma a c (* d b))
14.7b	(/ (fma a c (* d b)) (hypot d c))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

26.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.0ms	(fma a c (* d b))
6.0ms	(/ (fma a c (* d b)) (hypot d c))

series388.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
44.0ms	(fma a c (* d b))
191.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify1.6s

Counts

120 → 120

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	159	2484
1	320	2423
2	700	2246
3	2024	2192
done	5000	2130

prune439.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot d c) (fma a c (* d b)))) (hypot d c))
0.2b	(/ 1 (/ (hypot d c) (fma a c (* d b))))
0.5b	(fma a c (* d b))
14.8b	(/ (hypot d c) (fma a c (* d b)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
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` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 319

Calls

4 calls:

26.0ms	(/ (/ 1 (/ (hypot d c) (fma a c (* d b)))) (hypot d c))
11.0ms	(/ 1 (/ (hypot d c) (fma a c (* d b))))
0.0ms	(fma a c (* d b))
12.0ms	(/ (hypot d c) (fma a c (* d b)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (/ 1 (/ (hypot d c) (fma a c (* d b)))) (hypot d c))
176.0ms	(/ 1 (/ (hypot d c) (fma a c (* d b))))
47.0ms	(fma a c (* d b))
108.0ms	(/ (hypot d c) (fma a c (* d b)))

simplify1.3s

Counts

331 → 331

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	457	8797
1	1011	7708
2	1898	7150
done	5000	6968

prune710.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.1b

Details

sample46.0ms

simplify16.0ms

prune12.0ms

localize17.0ms

rewrite7.0ms

series632.0ms

simplify2.7s

prune220.0ms

localize14.0ms

rewrite59.0ms

series476.0ms

simplify3.6s

prune353.0ms

localize16.0ms

rewrite42.0ms

series388.0ms

simplify1.6s

prune439.0ms

localize18.0ms

rewrite70.0ms

series522.0ms

simplify1.3s

prune710.0ms

regimes222.0ms

bsearch1.0ms