Details

sample24.0ms

Algorithm

intervals

Results

12.0ms

389×

body

valid

simplify289.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	16	6
1	33	4
2	56	4
3	76	3
4	88	3
5	131	3
6	236	3
7	328	3
8	343	3
9	443	3
10	797	3
11	3499	3
12	5001	3

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: 0.1b

Counts

2 → 2

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 3 (* z z) (* x y))

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 3 (* z z) (* x y))

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

(fma 3 (* z z) (* x y))

simplify53.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	33	59
1	79	52
2	256	52
3	1025	52
4	5001	52

prune35.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	11	4	15

Merged error: 0.1b

Counts

15 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x y) (* z z)) (* z z))
0.0b	(+ (* x y) (* z z))
0.1b	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
7×	`fma-def`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate-+l+`

Counts

3 → 51

Calls

3 calls:

6.0ms	(+ (+ (* x y) (* z z)) (* z z))
4.0ms	(+ (* x y) (* z z))
9.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series127.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (+ (* x y) (* z z)) (* z z))
37.0ms	(+ (* x y) (* z z))
46.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify135.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	235	373
1	1084	317
2	4667	293
3	5001	292

prune116.0ms

Filtered

60 candidates to 47 candidates (78.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	57	7	64

Merged error: 0.0b

Counts

64 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (+ (* x y) (* z z)) (* z z))) (cbrt (+ (+ (* x y) (* z z)) (* z z))))
1.5b	(cbrt (+ (+ (* x y) (* z z)) (* z z)))
1.5b	(cbrt (+ (+ (* x y) (* z z)) (* z z)))
1.5b	(cbrt (+ (+ (* x y) (* z z)) (* z z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

13.0ms	(* (cbrt (+ (+ (* x y) (* z z)) (* z z))) (cbrt (+ (+ (* x y) (* z z)) (* z z))))
5.0ms	(cbrt (+ (+ (* x y) (* z z)) (* z z)))
5.0ms	(cbrt (+ (+ (* x y) (* z z)) (* z z)))
7.0ms	(cbrt (+ (+ (* x y) (* z z)) (* z z)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (cbrt (+ (+ (* x y) (* z z)) (* z z))) (cbrt (+ (+ (* x y) (* z z)) (* z z))))
129.0ms	(cbrt (+ (+ (* x y) (* z z)) (* z z)))
133.0ms	(cbrt (+ (+ (* x y) (* z z)) (* z z)))
132.0ms	(cbrt (+ (+ (* x y) (* z z)) (* z z)))

simplify101.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	313	1501
1	1045	1404
2	4169	1296
3	5001	1288

prune302.0ms

Filtered

107 candidates to 86 candidates (80.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	106	8	114

Merged error: 0b

Counts

114 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x y) (* z z))
0.3b	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
1.1b	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
1.1b	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`+-commutative` `fma-def` `sum-log` `fma-udef`

Counts

4 → 60

Calls

4 calls:

4.0ms	(+ (* x y) (* z z))
1.0ms	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
5.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
5.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* x y) (* z z))
168.0ms	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
97.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
101.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

simplify94.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	227	611
1	921	525
2	3494	517
3	5001	508

prune166.0ms

Filtered

72 candidates to 61 candidates (84.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	72	8	80

Merged error: 0b

Counts

80 → 8

regimes197.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	3
1	8	3

end0.0ms

sample647.0ms

Algorithm

intervals

Results

389.0ms

12183×

body

valid