Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	277×	body	80	valid
5.0ms	238×	body	80	nan

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.3b	(* y (sqrt x))

rewrite5.0ms

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))

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(* y (sqrt x))

simplify98.0ms

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

prune56.0ms

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

rewrite29.0ms

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:

1.0ms	(sqrt (sqrt x))
1.0ms	(sqrt (sqrt x))
7.0ms	(* y (sqrt (sqrt x)))
17.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (sqrt x))
135.0ms	(sqrt (sqrt x))
82.0ms	(* y (sqrt (sqrt x)))
46.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	351	549
1	1519	488
2	5001	461

prune261.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ 1 x) -1/4)
0.1b	(sqrt (sqrt x))
0.3b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (pow (/ 1 x) -1/4))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
34×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `unpow-prod-down` `-un-lft-identity` `associate-r*`
22×	`sqrt-prod`
19×	`prod-exp`
18×	`times-frac`
12×	`pow-exp`
11×	`add-cbrt-cube`
10×	`pow1`
6×	`div-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `pow-unpow` `pow-pow` `1-exp` `unswap-sqr`
2×	`rem-sqrt-square` `pow1/2` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 125

Calls

4 calls:

4.0ms	(pow (/ 1 x) -1/4)
1.0ms	(sqrt (sqrt x))
7.0ms	(* y (sqrt (sqrt x)))
23.0ms	(* (* y (sqrt (sqrt x))) (pow (/ 1 x) -1/4))

series474.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(pow (/ 1 x) -1/4)
137.0ms	(sqrt (sqrt x))
79.0ms	(* y (sqrt (sqrt x)))
83.0ms	(* (* y (sqrt (sqrt x))) (pow (/ 1 x) -1/4))

simplify74.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	641	800
1	2914	727
2	5001	710

prune314.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.3b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (* (pow (/ 1 x) -1/8) (pow (/ 1 x) -1/8)))
0.5b	(* (pow (/ 1 x) -1/8) (pow (/ 1 x) -1/8))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

335×	`add-exp-log`
220×	`prod-exp`
144×	`pow-exp`
100×	`add-sqr-sqrt`
86×	`unpow-prod-down`
72×	`div-exp`
56×	`times-frac`
54×	`*-un-lft-identity`
42×	`add-cube-cbrt`
36×	`pow-to-exp` `rec-exp` `1-exp`
28×	`unswap-sqr`
27×	`associate-r`
22×	`sqrt-prod`
21×	`associate-l`
20×	`add-cbrt-cube`
19×	`swap-sqr`
14×	`sqr-pow`
13×	`pow1`
10×	`cbrt-unprod`
6×	`div-inv`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`rem-sqrt-square` `pow1/2`
1×	`pow2` `pow-sqr` `pow-prod-up`

Counts

4 → 270

Calls

4 calls:

1.0ms	(sqrt (sqrt x))
7.0ms	(* y (sqrt (sqrt x)))
37.0ms	(* (* y (sqrt (sqrt x))) (* (pow (/ 1 x) -1/8) (pow (/ 1 x) -1/8)))
34.0ms	(* (pow (/ 1 x) -1/8) (pow (/ 1 x) -1/8))

series483.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(sqrt (sqrt x))
80.0ms	(* y (sqrt (sqrt x)))
83.0ms	(* (* y (sqrt (sqrt x))) (* (pow (/ 1 x) -1/8) (pow (/ 1 x) -1/8)))
177.0ms	(* (pow (/ 1 x) -1/8) (pow (/ 1 x) -1/8))

simplify103.0ms

Algorithm

egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	975	1939
1	3728	1682
2	5002	1644

prune413.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes76.0ms

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

sample627.0ms

Algorithm

intervals

Results

182.0ms	8562×	body	80	valid
175.0ms	8597×	body	80	nan
0.0ms	1×	body	160	valid