Details

sample28.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	11	14
1	16	13
2	26	12
3	32	12
done	32	12

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z z (fma x x (* y y)))
0.0b	(fma x x (* y y))
0.1b	(/ (fma z z (fma x x (* y y))) 3.0)
34.1b	(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`sqrt-prod`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `fma-udef` `div-inv`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 76

Calls

4 calls:

0.0ms	(fma z z (fma x x (* y y)))
0.0ms	(fma x x (* y y))
5.0ms	(/ (fma z z (fma x x (* y y))) 3.0)
4.0ms	(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series465.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma z z (fma x x (* y y)))
43.0ms	(fma x x (* y y))
83.0ms	(/ (fma z z (fma x x (* y y))) 3.0)
278.0ms	(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify3.6s

Counts

88 → 88

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	118	1382
1	183	1320
2	420	1191
3	1240	1191
4	4822	1191
done	5000	1191

prune474.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z z (fma x x (* y y)))
0.0b	(fma x x (* y y))
0.3b	(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
34.0b	(sqrt (fma z z (fma x x (* y y))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`sqrt-prod`
17×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`pow1`
8×	`unswap-sqr`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-unprod` `sqrt-div` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 82

Calls

4 calls:

1.0ms	(fma z z (fma x x (* y y)))
1.0ms	(fma x x (* y y))
43.0ms	(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
3.0ms	(sqrt (fma z z (fma x x (* y y))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(fma z z (fma x x (* y y)))
65.0ms	(fma x x (* y y))
324.0ms	(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
172.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify2.3s

Counts

94 → 94

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	122	1456
1	204	1335
2	437	1247
3	1257	1247
done	5000	1247

prune408.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z z (fma x x (* y y)))
0.0b	(fma x x (* y y))
0.3b	(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
34.0b	(sqrt (fma z z (fma x x (* y y))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 98

Calls

4 calls:

0.0ms	(fma z z (fma x x (* y y)))
0.0ms	(fma x x (* y y))
8.0ms	(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
2.0ms	(sqrt (fma z z (fma x x (* y y))))

series687.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma z z (fma x x (* y y)))
56.0ms	(fma x x (* y y))
385.0ms	(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
179.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify3.0s

Counts

110 → 110

Iterations

Useful iterations: 3 (253.0ms)

Iter	Nodes	Cost
0	127	2025
1	189	1846
2	385	1763
3	951	1761
4	3414	1761
done	5000	1761

prune399.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.2b

localize9.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ z (sqrt 3.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 41

Calls

1 calls:

13.0ms

(/ z (sqrt 3.0))

series75.0ms

Counts

1 → 3

Calls

1 calls:

75.0ms

(/ z (sqrt 3.0))

simplify6.9s

Counts

44 → 44

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	68	381
1	105	344
2	190	334
3	301	332
4	504	332
5	763	332
6	1424	332
7	4858	332
done	5002	332

prune108.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 16.2b

Details

sample28.0ms

simplify23.0ms

prune13.0ms

localize20.0ms

rewrite12.0ms

series465.0ms

simplify3.6s

prune474.0ms

localize29.0ms

rewrite52.0ms

series627.0ms

simplify2.3s

prune408.0ms

localize20.0ms

rewrite14.0ms

series687.0ms

simplify3.0s

prune399.0ms

localize9.0ms

rewrite16.0ms

series75.0ms

simplify6.9s

prune108.0ms

regimes2.0ms