Details

sample67.0ms

Algorithm

intervals

Results

23.0ms	296×	body	80	nan
14.0ms	272×	body	80	valid

simplify236.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	7	8
1	13	8
2	25	7
3	44	7
4	65	7
5	88	7
6	105	7
7	126	7
8	149	7
9	156	7
10	171	7
done	171	7

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma y (sqrt x) (- 1.0 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma y (sqrt x) (- 1.0 x))

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

(fma y (sqrt x) (- 1.0 x))

simplify1.2s

Counts

13 → 13

Iterations

Useful iterations: 4 (414.0ms)

Iter	Nodes	Cost
0	26	126
1	53	123
2	119	109
3	312	109
4	1214	106
done	5000	106

prune74.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* y (sqrt x)) (- 1.0 x))
0.2b	(* y (sqrt x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `associate-+r+` `*-un-lft-identity`
9×	`prod-diff`
7×	`add-log-exp`
6×	`associate-r`
4×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
3×	`associate-l`
2×	`expm1-log1p-u` `sum-log` `log1p-expm1-u` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `sub-neg` `fma-def` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 51

Calls

2 calls:

26.0ms	(+ (* y (sqrt x)) (- 1.0 x))
11.0ms	(* y (sqrt x))

series130.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ (* y (sqrt x)) (- 1.0 x))
81.0ms	(* y (sqrt x))

simplify3.5s

Counts

57 → 57

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	124	606
1	320	505
2	785	453
3	2725	433
done	5000	416

prune158.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqrt-prod`
25×	`add-sqr-sqrt`
18×	`associate-r`
15×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`*-commutative`

Counts

4 → 96

Calls

4 calls:

3.0ms	(sqrt (sqrt x))
5.0ms	(sqrt (sqrt x))
27.0ms	(* y (sqrt (sqrt x)))
57.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(sqrt (sqrt x))
217.0ms	(sqrt (sqrt x))
102.0ms	(* y (sqrt (sqrt x)))
65.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify3.3s

Counts

108 → 108

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	138	963
1	354	754
2	1000	688
3	3003	671
done	5001	659

prune341.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (sqrt x)))
0.2b	(* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x)))))
0.3b	(* (* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt x)))
0.5b	(* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))

rewrite523.0ms

Algorithm

rewrite-expression-head

Rules

186×	`sqrt-prod`
87×	`add-sqr-sqrt`
81×	`sqrt-pow1`
52×	`pow1`
27×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
24×	`swap-sqr`
22×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
17×	`unswap-sqr`
16×	`associate-l` `pow-prod-down`
13×	`pow-prod-up`
10×	`prod-exp` `cbrt-unprod`
7×	`pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `*-commutative`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 184

Calls

4 calls:

8.0ms	(sqrt (sqrt (sqrt x)))
98.0ms	(* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x)))))
358.0ms	(* (* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt x)))
40.0ms	(* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(sqrt (sqrt (sqrt x)))
114.0ms	(* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x)))))
64.0ms	(* (* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt x)))
216.0ms	(* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))

simplify2.0s

Counts

196 → 196

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	224	2772
1	507	1311
2	1602	1183
done	5000	1160

prune468.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	9	8
done	9	8

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	8533×	body	80	valid
391.0ms	8577×	body	80	nan
0.0ms	1×	body	1280	valid