Details

sample134.0ms

Algorithm

intervals

Results

88.0ms

650×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (316.0ms)

Iter	Nodes	Cost
0	19	31
1	84	29
2	1076	28
done	5000	28

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

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))
0.0b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.2b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(pow (fma a a (* b b)) 2.0)

rewrite75.0ms

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))))
66.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms	(pow (fma a a (* b b)) 2.0)

series593.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
107.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
83.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
231.0ms	(pow (fma a a (* b b)) 2.0)

simplify1.9s

Counts

84 → 84

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	160	1452
1	1062	1401
done	5001	1219

prune430.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (fma a a (* b b)) 2.0)
0.4b	(pow (fma a a (* b b)) 2.0)
8.6b	(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)))
8.6b	(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)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `unpow-prod-down` `pow-unpow` `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:

3.0ms	(pow (fma a a (* b b)) 2.0)
3.0ms	(pow (fma a a (* b b)) 2.0)
2.0ms	(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)))
10.0ms	(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)))

series1.0s

Counts

4 → 12

Calls

4 calls:

177.0ms	(pow (fma a a (* b b)) 2.0)
191.0ms	(pow (fma a a (* b b)) 2.0)
330.0ms	(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)))
340.0ms	(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)))

simplify1.6s

Counts

80 → 80

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	100	1654
1	373	1496
done	5000	1388

prune568.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (fma a a (* b b)) 2.0)
8.6b	(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)))
9.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
9.2b	(cbrt (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

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

Counts

4 → 60

Calls

4 calls:

5.0ms	(pow (fma a a (* b b)) 2.0)
3.0ms	(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)))
2.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
2.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

218.0ms	(pow (fma a a (* b b)) 2.0)
294.0ms	(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)))
455.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
525.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify1.6s

Counts

72 → 72

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	151	2123
1	595	2034
done	5001	1804

prune726.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

8.6b	(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)))
9.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
9.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
9.2b	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite6.0ms

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:

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

series2.0s

Counts

4 → 12

Calls

4 calls:

295.0ms	(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)))
416.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
857.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
458.0ms	(cbrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify1.5s

Counts

66 → 66

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	116	2515
1	429	2434
done	5000	2137

prune588.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes274.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.6s

Algorithm

intervals

Results

3.8s

20563×

body

valid