Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	269×	body	80	valid
5.0ms	256×	body	80	nan

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	13	4
1	25	3
2	44	3
3	69	3
4	102	3
5	171	3
6	192	3
7	225	3
8	316	3
9	351	3
10	351	3

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.3b	(* y (sqrt x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

1 → 24

Calls

1 calls:

5.0ms

(* y (sqrt x))

series45.0ms

Counts

1 → 3

Calls

1 calls:

45.0ms

(* y (sqrt x))

simplify97.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	154	119
1	632	106
2	3199	100
3	5002	100

prune57.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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)))

rewrite22.0ms

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:

2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
10.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (sqrt x))
138.0ms	(sqrt (sqrt x))
79.0ms	(* y (sqrt (sqrt x)))
44.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	351	553
1	1519	488
2	5001	461

prune227.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (cbrt (pow (sqrt (sqrt x)) 3)))
0.5b	(cbrt (pow (sqrt (sqrt x)) 3))
0.8b	(pow (sqrt (sqrt x)) 3)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

66×	`sqrt-prod`
48×	`cbrt-prod`
36×	`add-sqr-sqrt` `associate-r`
30×	`add-cube-cbrt` `*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
14×	`pow1`
12×	`add-exp-log`
10×	`add-cbrt-cube`
5×	`pow-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3` `unswap-sqr` `sqr-pow`
2×	`pow1/2` `*-commutative`
1×	`pow-to-exp` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 149

Calls

4 calls:

7.0ms	(* y (sqrt (sqrt x)))
14.0ms	(* (* y (sqrt (sqrt x))) (cbrt (pow (sqrt (sqrt x)) 3)))
4.0ms	(cbrt (pow (sqrt (sqrt x)) 3))
4.0ms	(pow (sqrt (sqrt x)) 3)

series442.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* y (sqrt (sqrt x)))
39.0ms	(* (* y (sqrt (sqrt x))) (cbrt (pow (sqrt (sqrt x)) 3)))
133.0ms	(cbrt (pow (sqrt (sqrt x)) 3))
190.0ms	(pow (sqrt (sqrt x)) 3)

simplify74.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	542	928
1	2529	784
2	5001	740

prune307.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(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))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

175×	`sqrt-prod`
85×	`add-sqr-sqrt`
76×	`sqrt-pow1`
51×	`pow1`
26×	`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×	`*-commutative`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 178

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
16.0ms	(* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x)))))
24.0ms	(* (* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt x)))
14.0ms	(* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(sqrt (sqrt x))
79.0ms	(* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x)))))
39.0ms	(* (* y (* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))) (sqrt (sqrt x)))
138.0ms	(* (sqrt (sqrt (sqrt x))) (sqrt (sqrt (sqrt x))))

simplify76.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	488	1130
1	2306	874
2	5002	859

prune301.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample625.0ms

Algorithm

intervals

Results

188.0ms	8521×	body	80	valid
162.0ms	8588×	body	80	nan
0.0ms	1×	body	160	valid