Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	271×	body	80	valid
8.0ms	261×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`prod-diff`
7×	`add-log-exp`
6×	`associate-r`
5×	`fma-def`
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-+l-` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 55

Calls

2 calls:

16.0ms	(+ (- 1.0 x) (* y (sqrt x)))
4.0ms	(* y (sqrt x))

series81.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ (- 1.0 x) (* y (sqrt x)))
40.0ms	(* y (sqrt x))

simplify39.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	273	339
1	1115	252
2	5002	244

prune141.0ms

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)))

rewrite27.0ms

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))
6.0ms	(* y (sqrt (sqrt x)))
16.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(sqrt (sqrt x))
130.0ms	(sqrt (sqrt x))
78.0ms	(* y (sqrt (sqrt x)))
44.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (37.0ms)

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

prune235.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt x) (cbrt x))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(cbrt x)

series729.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* (cbrt x) (cbrt x))
176.0ms	(cbrt x)
180.0ms	(cbrt x)
176.0ms	(cbrt x)

simplify94.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune352.0ms

Pruning

5 alts after pruning (2 fresh and 3 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)))
0.6b	(cbrt (pow (sqrt (sqrt x)) 3))
0.7b	(pow (sqrt (sqrt x)) 3)

rewrite45.0ms

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:

10.0ms	(* y (sqrt (sqrt x)))
24.0ms	(* (* y (sqrt (sqrt x))) (cbrt (pow (sqrt (sqrt x)) 3)))
3.0ms	(cbrt (pow (sqrt (sqrt x)) 3))
3.0ms	(pow (sqrt (sqrt x)) 3)

series450.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* y (sqrt (sqrt x)))
40.0ms	(* (* y (sqrt (sqrt x))) (cbrt (pow (sqrt (sqrt x)) 3)))
139.0ms	(cbrt (pow (sqrt (sqrt x)) 3))
189.0ms	(pow (sqrt (sqrt x)) 3)

simplify75.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (65.0ms)

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

prune299.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes62.0ms

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

sample1.1s

Algorithm

intervals

Results

472.0ms	8620×	body	80	nan
349.0ms	8558×	body	80	valid
0.0ms	1×	body	320	valid