Details

sample59.0ms

Algorithm

intervals

Results

39.0ms

691×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	158	28
3	446	28
4	1227	28
5	3539	28
done	5000	28

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(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	(pow (fma a a (* b b)) 2.0)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite17.0ms

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))))
1.0ms	(pow (fma a a (* b b)) 2.0)
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
64.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
127.0ms	(pow (fma a a (* b b)) 2.0)
60.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify802.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	160	1452
1	388	1423
2	1597	1221
done	5000	1221

prune302.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
9.4b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
9.4b	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `prod-diff`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
60.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
224.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
214.0ms	(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify858.0ms

Counts

108 → 108

Iterations

Useful iterations: done (854.0ms)

Iter	Nodes	Cost
0	130	2220
1	326	2078
2	1254	1844
done	5001	1840

prune451.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))
19.0b	(cbrt (pow (fma a a (* b b)) 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
1.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
1.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

series587.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
173.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
176.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
178.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify662.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	131	1430
1	312	1413
2	1172	1248
done	5000	1248

prune458.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

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:

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

series713.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
185.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
181.0ms	(cbrt (pow (fma a a (* b b)) 2.0))
174.0ms	(cbrt (pow (fma a a (* b b)) 2.0))

simplify2.4s

Counts

80 → 80

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	58	1188
1	104	1172
2	229	1064
3	773	1052
4	2709	1052
done	5000	1052

prune474.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes178.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	57
1	22	57
done	22	57

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

21017×

body

valid