Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	276×	body	80	valid
5.0ms	289×	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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify43.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (16.0ms)

Iter	Nodes	Cost
0	64	71
1	162	57
2	476	55
3	1755	54
4	5001	54

prune34.0ms

Pruning

5 alts after pruning (4 fresh and 1 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))

rewrite42.0ms

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:

31.0ms	(+ (- 1.0 x) (* y (sqrt x)))
9.0ms	(* y (sqrt x))

series73.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (- 1.0 x) (* y (sqrt x)))
41.0ms	(* 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

prune140.0ms

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)))

rewrite55.0ms

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))
12.0ms	(* y (sqrt (sqrt x)))
36.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (sqrt x))
135.0ms	(sqrt (sqrt x))
76.0ms	(* y (sqrt (sqrt x)))
37.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (39.0ms)

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

prune217.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

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))

rewrite69.0ms

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:

6.0ms	(pow (/ 1 x) -1/4)
2.0ms	(sqrt (sqrt x))
12.0ms	(* y (sqrt (sqrt x)))
44.0ms	(* (* y (sqrt (sqrt x))) (pow (/ 1 x) -1/4))

series469.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(pow (/ 1 x) -1/4)
128.0ms	(sqrt (sqrt x))
77.0ms	(* y (sqrt (sqrt x)))
81.0ms	(* (* y (sqrt (sqrt x))) (pow (/ 1 x) -1/4))

simplify74.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (65.0ms)

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

prune301.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes72.0ms

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

sample690.0ms

Algorithm

intervals

Results

181.0ms	8569×	body	80	valid
157.0ms	8548×	body	80	nan
0.0ms	1×	body	640	valid