Details

sample120.0ms

Algorithm

intervals

Results

84.0ms

650×

body

valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (333.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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)

rewrite76.0ms

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:

1.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
1.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
67.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms	(pow (fma a a (* b b)) 2.0)

series462.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
76.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
92.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
167.0ms	(pow (fma a a (* b b)) 2.0)

simplify2.0s

Counts

84 → 84

Iterations

Useful iterations: done (2.0s)

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

prune410.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

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)))

rewrite18.0ms

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:

10.0ms	(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)))
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)))

series944.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(pow (fma a a (* b b)) 2.0)
139.0ms	(pow (fma a a (* b b)) 2.0)
348.0ms	(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)))
293.0ms	(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)))

simplify1.5s

Counts

80 → 80

Iterations

Useful iterations: done (1.5s)

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

prune682.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize90.0ms

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)))

rewrite15.0ms

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:

6.0ms	(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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

213.0ms	(pow (fma a a (* b b)) 2.0)
335.0ms	(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)))
353.0ms	(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)))
360.0ms	(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)))

simplify1.8s

Counts

72 → 72

Iterations

Useful iterations: done (1.8s)

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

prune709.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize84.0ms

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)))

rewrite10.0ms

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:

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)))
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)))

series1.6s

Counts

4 → 12

Calls

4 calls:

327.0ms	(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)))
434.0ms	(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)))
399.0ms	(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)))
404.0ms	(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)))

simplify1.3s

Counts

66 → 66

Iterations

Useful iterations: done (1.3s)

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

prune678.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes294.0ms

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

sample4.5s

Algorithm

intervals

Results

3.7s

20563×

body

valid