Details

sample35.0ms

Algorithm

intervals

Results

12.0ms	275×	body	80	valid
8.0ms	278×	body	80	nan

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	5
1	51	4
2	86	4
3	126	4
4	151	4
5	169	4
6	185	4
7	187	4
8	187	4

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* y (sqrt z)))
0.2b	(* y (sqrt z))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

2.0ms	(+ x (* y (sqrt z)))
5.0ms	(* y (sqrt z))

series74.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ x (* y (sqrt z)))
43.0ms	(* y (sqrt z))

simplify116.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	231	204
1	879	180
2	4188	173
3	5001	170

prune122.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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 z))
1.0ms	(sqrt (sqrt z))
7.0ms	(* y (sqrt (sqrt z)))
18.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt (sqrt z))
138.0ms	(sqrt (sqrt z))
82.0ms	(* y (sqrt (sqrt z)))
42.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

simplify48.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	351	553
1	1510	488
2	5001	461

prune276.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ 1 z) -1/4)
0.1b	(sqrt (sqrt z))
0.2b	(* y (pow (/ 1 z) -1/4))
0.3b	(* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt z)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
38×	`add-sqr-sqrt`
29×	`unpow-prod-down`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt` `associate-r`
20×	`times-frac`
19×	`prod-exp` `sqrt-prod`
12×	`pow-exp`
11×	`add-cbrt-cube`
10×	`pow1`
6×	`div-exp`
5×	`unswap-sqr`
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` `sqr-pow`
2×	`rem-sqrt-square` `pow1/2` `*-commutative` `div-inv`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 127

Calls

4 calls:

4.0ms	(pow (/ 1 z) -1/4)
1.0ms	(sqrt (sqrt z))
19.0ms	(* y (pow (/ 1 z) -1/4))
23.0ms	(* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt z)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(pow (/ 1 z) -1/4)
140.0ms	(sqrt (sqrt z))
64.0ms	(* y (pow (/ 1 z) -1/4))
87.0ms	(* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt z)))

simplify68.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	590	778
1	2623	697
2	5001	686

prune356.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (sqrt (sqrt z)))
0.2b	(* y (pow (/ 1 z) -1/4))
0.3b	(* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt (sqrt z))))
0.3b	(* (* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt (sqrt z)))) (sqrt (sqrt (sqrt z))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
57×	`sqrt-prod`
41×	`associate-r`
40×	`prod-exp`
37×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`add-cbrt-cube`
16×	`unpow-prod-down`
14×	`pow1`
12×	`pow-exp`
11×	`times-frac`
10×	`cbrt-unprod`
9×	`sqrt-pow1`
6×	`div-exp`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `rem-sqrt-square` `rec-exp` `pow1/2` `1-exp` `*-commutative`
2×	`sqr-pow`
1×	`div-inv`

Counts

4 → 138

Calls

4 calls:

2.0ms	(sqrt (sqrt (sqrt z)))
16.0ms	(* y (pow (/ 1 z) -1/4))
25.0ms	(* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt (sqrt z))))
88.0ms	(* (* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt (sqrt z)))) (sqrt (sqrt (sqrt z))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(sqrt (sqrt (sqrt z)))
68.0ms	(* y (pow (/ 1 z) -1/4))
109.0ms	(* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt (sqrt z))))
88.0ms	(* (* (* y (pow (/ 1 z) -1/4)) (sqrt (sqrt (sqrt z)))) (sqrt (sqrt (sqrt z))))

simplify81.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	691	1202
1	3188	1015
2	5002	1013

prune412.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes233.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample978.0ms

Algorithm

intervals

Results

408.0ms	8523×	body	80	valid
232.0ms	8227×	body	80	nan