Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	288×	body	80	nan
10.0ms	273×	body	80	valid

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 2

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(fma (sqrt z) y 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:

1.0ms

(fma (sqrt z) y x)

series62.0ms

Counts

1 → 3

Calls

1 calls:

62.0ms

(fma (sqrt z) y x)

simplify58.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 4 (56.0ms)

Iter	Nodes	Cost
0	70	58
1	176	50
2	528	50
3	1813	46
4	5001	43

prune35.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	10	3	13
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	11	4	15

Merged error: 0.1b

Counts

15 → 4

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b	(* y (sqrt z))

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 z))

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(* y (sqrt z))

simplify89.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	154	119
1	621	106
2	3007	100
3	5001	100

prune60.0ms

Filtered

27 candidates to 18 candidates (66.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	22	5	27
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	24	7	31

Merged error: 0.0b

Counts

31 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt z))
0.1b	(sqrt (sqrt z))
0.2b	(* y (sqrt (sqrt z)))
0.4b	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

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 z))
2.0ms	(sqrt (sqrt z))
6.0ms	(* y (sqrt (sqrt z)))
9.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (sqrt z))
134.0ms	(sqrt (sqrt z))
78.0ms	(* y (sqrt (sqrt z)))
43.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

simplify45.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	351	549
1	1510	488
2	5001	461

prune221.0ms

Filtered

108 candidates to 68 candidates (63.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	108	7	115

Merged error: 0b

Counts

115 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ 1 z) -1/4)
0.1b	(sqrt (sqrt z))
0.2b	(* y (sqrt (sqrt z)))
0.4b	(* (* y (sqrt (sqrt z))) (pow (/ 1 z) -1/4))

rewrite32.0ms

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:

5.0ms	(pow (/ 1 z) -1/4)
2.0ms	(sqrt (sqrt z))
10.0ms	(* y (sqrt (sqrt z)))
12.0ms	(* (* y (sqrt (sqrt z))) (pow (/ 1 z) -1/4))

series655.0ms

Counts

4 → 12

Calls

4 calls:

354.0ms	(pow (/ 1 z) -1/4)
133.0ms	(sqrt (sqrt z))
82.0ms	(* y (sqrt (sqrt z)))
87.0ms	(* (* y (sqrt (sqrt z))) (pow (/ 1 z) -1/4))

simplify73.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	641	800
1	2905	727
2	5001	710

prune256.0ms

Filtered

137 candidates to 83 candidates (60.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	137	7	144

Merged error: 0b

Counts

144 → 7

regimes225.0ms

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

sample933.0ms

Algorithm

intervals

Results

302.0ms	8544×	body	80	valid
279.0ms	8499×	body	80	nan