Details

sample105.0ms

Algorithm

intervals

Results

71.0ms

627×

body

valid

simplify5.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	12	17
1	26	16
2	50	15
3	86	15
4	151	15
5	303	15
6	932	15
7	3961	15
done	5001	15

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
0.3b	(pow (fma a a (* b b)) 2.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `unpow-prod-down` `pow-unpow`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `sqr-pow`

Counts

2 → 29

Calls

2 calls:

0.0ms	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
3.0ms	(pow (fma a a (* b b)) 2.0)

series252.0ms

Counts

2 → 6

Calls

2 calls:

102.0ms	(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
150.0ms	(pow (fma a a (* b b)) 2.0)

simplify2.2s

Counts

35 → 35

Iterations

Useful iterations: 3 (176.0ms)

Iter	Nodes	Cost
0	72	472
1	140	456
2	316	408
3	875	404
4	2644	404
done	5000	404

prune178.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))))
13.5b	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.5b	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.5b	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

19.0ms	(* (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))))
2.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
2.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
2.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

315.0ms	(* (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))))
328.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
295.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
282.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

simplify1.4s

Counts

93 → 93

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	106	2580
1	208	2420
2	530	2217
3	1449	1816
done	5001	1778

prune513.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

12.9b	(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.5b	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.5b	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.5b	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

1.0ms	(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

279.0ms	(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
328.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
336.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
307.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

simplify3.8s

Counts

66 → 66

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	82	1350
1	165	1302
2	387	1202
3	1078	1121
4	4410	1103
done	5001	1103

prune539.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (fma a a (* b b)) 2.0)
0.9b	(pow (sqrt (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))) 4)
13.5b	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.5b	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
9×	`cbrt-prod`
7×	`pow1`
6×	`add-exp-log` `pow-unpow` `sqrt-prod`
5×	`pow-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`pow-to-exp` `sqrt-pow1` `pow-exp` `sqr-pow`
1×	`pow1/2` `sqrt-pow2`

Counts

4 → 74

Calls

4 calls:

3.0ms	(pow (fma a a (* b b)) 2.0)
5.0ms	(pow (sqrt (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))) 4)
1.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

178.0ms	(pow (fma a a (* b b)) 2.0)
416.0ms	(pow (sqrt (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))) 4)
311.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
299.0ms	(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

simplify1.5s

Counts

86 → 86

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	168	1743
1	350	1652
2	830	1474
3	2401	1339
done	5000	1317

prune548.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	12	15
done	12	15

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.3s

20344×

body

valid