Details

sample112.0ms

Algorithm

intervals

Results

84.0ms

621×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3560
3	785
2	201
1	58
0	19

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1))
0.0b	(fma a -12 4)
0.0b	(fma (fma 4 a 4) (* a a) (fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

0.0ms	(fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1))
0.0ms	(fma a -12 4)
0.0ms	(fma (fma 4 a 4) (* a a) (fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

series345.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1))
35.0ms	(fma a -12 4)
119.0ms	(fma (fma 4 a 4) (* a a) (fma (* b b) (fma a -12 4) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
101.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

simplify1.3s

Counts

56 → 56

Iterations

Iter	Nodes
done	5002
3	1525
2	371
1	143
0	80

prune315.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.2b	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
15.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
87.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
103.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
227.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

simplify2.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5016
4	2580
3	812
2	310
1	142
0	71

prune688.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.2b	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
0.2b	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`cbrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
8×	`add-exp-log` `unswap-sqr`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 108

Calls

4 calls:

0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
24.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
17.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
98.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
216.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
224.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

simplify3.0s

Counts

120 → 120

Iterations

Iter	Nodes
done	5016
4	2580
3	812
2	310
1	142
0	71

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize132.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
0.2b	(cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1))))
0.2b	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
0.2b	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
33×	`cbrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
13×	`pow1/3`
12×	`swap-sqr` `associate-r` `associate-l`
8×	`add-exp-log` `unswap-sqr`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`fma-udef`

Counts

4 → 109

Calls

4 calls:

0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
4.0ms	(cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1))))
8.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
9.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

series881.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)
264.0ms	(cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1))))
258.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
232.0ms	(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) -1)))

simplify2.5s

Counts

121 → 121

Iterations

Iter	Nodes
done	5002
4	2859
3	900
2	357
1	161
0	83

prune941.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes354.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	13
0	13

end0.0ms

sample3.4s

Algorithm

intervals

Results

3.0s

20480×

body

valid