Details

sample86.0ms

Algorithm

intervals

Results

61.0ms

612×

body

valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5072
7	4067
6	961
5	271
4	143
3	86
2	50
1	26
0	12

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a a (* b b))
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

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

Counts

3 → 39

Calls

3 calls:

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

series317.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(fma a a (* b b))
89.0ms	(fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0))
167.0ms	(pow (fma a a (* b b)) 2.0)

simplify3.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	5003
4	3639
3	1121
2	366
1	159
0	78

prune327.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (fma a a (* b b)) 2.0)
0.3b	(pow (fma a a (* b b)) 2.0)
13.2b	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
13.2b	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`pow-unpow` `unpow-prod-down` `add-exp-log` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

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

series809.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(pow (fma a a (* b b)) 2.0)
139.0ms	(pow (fma a a (* b b)) 2.0)
230.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
291.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

simplify1.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	1468
2	467
1	178
0	84

prune632.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

13.2b	(sqrt (fma 4.0 (* b b) (* (* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0))) (cbrt (pow (fma a a (* b b)) 2.0)))))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

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

series1.0s

Counts

4 → 12

Calls

4 calls:

298.0ms	(sqrt (fma 4.0 (* b b) (* (* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0))) (cbrt (pow (fma a a (* b b)) 2.0)))))
242.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
225.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
244.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	1272
2	432
1	176
0	95

prune815.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize143.0ms

Local error

Found 4 expressions with local error:

13.2b	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
13.2b	(sqrt (fma 4.0 (* b b) (* (* (cbrt (pow (fma a a (* b b)) 2.0)) (* (cbrt (pow (sqrt (fma a a (* b b))) 2.0)) (cbrt (pow (sqrt (fma a a (* b b))) 2.0)))) (cbrt (pow (fma a a (* b b)) 2.0)))))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))
19.6b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

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

series1.0s

Counts

4 → 12

Calls

4 calls:

238.0ms	(sqrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
288.0ms	(sqrt (fma 4.0 (* b b) (* (* (cbrt (pow (fma a a (* b b)) 2.0)) (* (cbrt (pow (sqrt (fma a a (* b b))) 2.0)) (cbrt (pow (sqrt (fma a a (* b b))) 2.0)))) (cbrt (pow (fma a a (* b b)) 2.0)))))
254.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
235.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	1373
2	474
1	202
0	113

prune893.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes481.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	12
0	12

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.2s

20694×

body

valid