Details

sample128.0ms

Algorithm

intervals

Results

98.0ms

709×

body

valid

simplify5.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	178	28
3	545	28
4	1672	28
5	4797	28
done	5000	28

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.1b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b	(* (* b b) (- 1.0 (* 3.0 a)))
0.3b	(pow (fma a a (* b b)) 2.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`pow-to-exp` `flip3--` `pow-pow` `associate-l` `pow-exp` `*-commutative` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
34.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms	(pow (fma a a (* b b)) 2.0)

series563.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
81.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
98.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
205.0ms	(pow (fma a a (* b b)) 2.0)

simplify3.9s

Counts

84 → 84

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	160	1452
1	378	1411
2	1146	1221
3	4227	1207
done	5000	1207

prune595.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

26.0ms	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
12.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
3.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

297.0ms	(* (cbrt (pow (fma a a (* b b)) 2.0)) (cbrt (pow (fma a a (* b b)) 2.0)))
271.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
260.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
323.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify3.6s

Counts

129 → 129

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	122	2774
1	211	2629
2	498	2385
3	1126	2197
4	3057	2186
done	5000	2122

prune955.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

11.5b	(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
11.5b	(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
2.0ms	(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
2.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
3.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

240.0ms	(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
247.0ms	(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
264.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
289.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify1.8s

Counts

80 → 80

Iterations

Useful iterations: 3 (180.0ms)

Iter	Nodes	Cost
0	91	1292
1	162	1262
2	328	1148
3	790	1136
4	2347	1136
done	5000	1136

prune714.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

1.4b	(sqrt (cbrt (pow (fma a a (* b b)) 2.0)))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))
21.4b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

31×	`cbrt-prod`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
10×	`sqrt-prod`
5×	`pow1` `sqr-pow`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1`
1×	`pow1/2`

Counts

4 → 77

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

255.0ms	(sqrt (cbrt (pow (fma a a (* b b)) 2.0)))
261.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
283.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
253.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.1s

Counts

89 → 89

Iterations

Useful iterations: 3 (174.0ms)

Iter	Nodes	Cost
0	91	1287
1	157	1240
2	309	1143
3	706	1106
4	1880	1106
done	5001	1106

prune722.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes262.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	28
1	20	28
done	20	28

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.0s

20340×

body

valid