Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

372×

body

valid

simplify349.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

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	441	3
10	793	3
11	3482	3
12	5001	3

prune5.0ms

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

localize6.0ms

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))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

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

simplify76.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	33	59
1	79	52
2	256	52
3	1024	52
4	5001	52

prune28.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	9	4	13
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	10	5	15

Merged error: 0.0b

Counts

15 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3 (* z z)) (* x y))
0.2b	(* 3 (* z z))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
36×	`associate-r`
28×	`fma-def`
23×	`*-un-lft-identity`
16×	`associate-l`
15×	`add-cube-cbrt`
14×	`unswap-sqr`
8×	`swap-sqr`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`*-commutative`
4×	`distribute-lft-out` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

2 → 84

Calls

2 calls:

28.0ms	(+ (* 3 (* z z)) (* x y))
12.0ms	(* 3 (* z z))

series67.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ (* 3 (* z z)) (* x y))
26.0ms	(* 3 (* z z))

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	232	238
1	1013	217
2	5001	207

prune121.0ms

Filtered

90 candidates to 57 candidates (63.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	90	5	95

Merged error: 0b

Counts

95 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* (fabs z) 3) (sqrt (* z z))) (* x y))
0.2b	(* (* (fabs z) 3) (sqrt (* z z)))
16.4b	(sqrt (* z z))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
65×	`sqrt-prod`
51×	`associate-r`
48×	`associate-l`
47×	`fma-def`
46×	`unswap-sqr`
39×	`*-un-lft-identity`
27×	`add-cube-cbrt`
16×	`pow1`
14×	`swap-sqr`
12×	`*-commutative`
8×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-pow1` `distribute-lft-out`
5×	`rem-sqrt-square` `add-log-exp`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `pow1/2` `sum-log` `pow-sqr` `pow-prod-up` `flip-+`

Counts

3 → 160

Calls

3 calls:

47.0ms	(+ (* (* (fabs z) 3) (sqrt (* z z))) (* x y))
15.0ms	(* (* (fabs z) 3) (sqrt (* z z)))
5.0ms	(sqrt (* z z))

series103.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* (* (fabs z) 3) (sqrt (* z z))) (* x y))
48.0ms	(* (* (fabs z) 3) (sqrt (* z z)))
9.0ms	(sqrt (* z z))

simplify75.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	346	662
1	1277	601
2	5001	553

prune282.0ms

Filtered

169 candidates to 112 candidates (66.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	169	5	174

Merged error: 0b

Counts

174 → 5

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (* (cbrt 3) (cbrt 3)) (* (cbrt 3) (* z z)) (* x y))
0.3b	(* (cbrt 3) (* z z))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
18×	`associate-r`
13×	`unswap-sqr`
10×	`add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`cbrt-prod`
7×	`pow1` `add-exp-log`
6×	`cbrt-unprod`
5×	`swap-sqr`
4×	`*-commutative`
3×	`pow-prod-down` `prod-exp`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

2 → 59

Calls

2 calls:

1.0ms	(fma (* (cbrt 3) (cbrt 3)) (* (cbrt 3) (* z z)) (* x y))
13.0ms	(* (cbrt 3) (* z z))

series139.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(fma (* (cbrt 3) (cbrt 3)) (* (cbrt 3) (* z z)) (* x y))
48.0ms	(* (cbrt 3) (* z z))

simplify160.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (154.0ms)

Iter	Nodes	Cost
0	199	365
1	806	317
2	4275	299
3	5001	297

prune98.0ms

Filtered

65 candidates to 39 candidates (60.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	65	5	70

Merged error: 0b

Counts

70 → 5

regimes113.0ms

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

sample535.0ms

Algorithm

intervals

Results

299.0ms

12071×

body

valid