Details

sample88.0ms

Algorithm

intervals

Results

7.0ms	84×	body	1280	valid
5.0ms	197×	body	80	valid
4.0ms	47×	body	640	valid
1.0ms	25×	body	320	valid
1.0ms	12×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	5	122
1	15	122
2	40	122
3	113	122
4	254	122
5	404	122
6	609	122
7	893	122
8	1588	122
9	4098	122
done	5000	122

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ x 1.0) (+ x 1.0))
2.6b	(- (* (+ x 1.0) (+ x 1.0)) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`pow1`
7×	`add-cube-cbrt`
6×	`flip3-+` `swap-sqr` `flip-+` `distribute-lft-out`
4×	`frac-times` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
3×	`prod-diff`
2×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-l/` `associate--l+` `associate-r/` `log1p-expm1-u`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `difference-of-squares` `unswap-sqr`

Counts

2 → 63

Calls

2 calls:

24.0ms	(* (+ x 1.0) (+ x 1.0))
16.0ms	(- (* (+ x 1.0) (+ x 1.0)) 1.0)

series83.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(* (+ x 1.0) (+ x 1.0))
64.0ms	(- (* (+ x 1.0) (+ x 1.0)) 1.0)

simplify1.1s

Counts

69 → 69

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	106	15739
1	336	11418
2	1118	10715
done	5003	10675

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 2.0 x (* x x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 2.0 x (* x x))

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(fma 2.0 x (* x x))

simplify4.6s

Counts

13 → 13

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	17	2454
1	29	1866
2	76	1866
3	259	1866
4	1119	1866
5	4191	1866
done	5000	1866

prune38.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 2.0 x (* x x))
0.0b	(fma 2.0 x (* x x))
0.2b	(* (sqrt (fma 2.0 x (* x x))) (sqrt (fma 2.0 x (* x x))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
18×	`pow1` `sqrt-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`associate-r` `associate-l`
5×	`add-cbrt-cube` `add-exp-log` `pow-prod-up`
4×	`unswap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 71

Calls

3 calls:

0.0ms	(fma 2.0 x (* x x))
0.0ms	(fma 2.0 x (* x x))
12.0ms	(* (sqrt (fma 2.0 x (* x x))) (sqrt (fma 2.0 x (* x x))))

series167.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma 2.0 x (* x x))
56.0ms	(fma 2.0 x (* x x))
56.0ms	(* (sqrt (fma 2.0 x (* x x))) (sqrt (fma 2.0 x (* x x))))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: 3 (267.0ms)

Iter	Nodes	Cost
0	62	17531
1	102	12237
2	259	12237
3	1102	12197
done	5002	12197

prune162.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (fma 2.0 x (* x x))))
0.1b	(sqrt (sqrt (fma 2.0 x (* x x))))
0.2b	(* (sqrt (sqrt (fma 2.0 x (* x x)))) (sqrt (fma 2.0 x (* x x))))
0.2b	(* (sqrt (sqrt (fma 2.0 x (* x x)))) (* (sqrt (sqrt (fma 2.0 x (* x x)))) (sqrt (fma 2.0 x (* x x)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

59×	`sqrt-pow1`
54×	`pow1`
52×	`sqrt-prod`
36×	`add-sqr-sqrt` `pow-prod-up`
35×	`pow1/2`
18×	`associate-l`
16×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow-prod-down`
7×	`associate-r`
6×	`pow-plus` `unswap-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `cube-unmult` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`

Counts

4 → 136

Calls

4 calls:

2.0ms	(sqrt (sqrt (fma 2.0 x (* x x))))
2.0ms	(sqrt (sqrt (fma 2.0 x (* x x))))
14.0ms	(* (sqrt (sqrt (fma 2.0 x (* x x)))) (sqrt (fma 2.0 x (* x x))))
32.0ms	(* (sqrt (sqrt (fma 2.0 x (* x x)))) (* (sqrt (sqrt (fma 2.0 x (* x x)))) (sqrt (fma 2.0 x (* x x)))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (sqrt (fma 2.0 x (* x x))))
82.0ms	(sqrt (sqrt (fma 2.0 x (* x x))))
115.0ms	(* (sqrt (sqrt (fma 2.0 x (* x x)))) (sqrt (fma 2.0 x (* x x))))
54.0ms	(* (sqrt (sqrt (fma 2.0 x (* x x)))) (* (sqrt (sqrt (fma 2.0 x (* x x)))) (sqrt (fma 2.0 x (* x x)))))

simplify2.2s

Counts

148 → 148

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	178	41485
1	442	34042
2	1086	30742
3	4020	30127
done	5000	30002

prune340.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	97
done	4	97

end0.0ms

sample687.0ms

Algorithm

intervals

Results

245.0ms	2247×	body	1280	valid
128.0ms	1688×	body	640	valid
124.0ms	5551×	body	80	valid
63.0ms	818×	body	320	valid
13.0ms	414×	body	160	valid