Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

269×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 30.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
29.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
37.0ms	(- (* x.im y.re) (* x.re y.im))
83.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5002	491

prune173.0ms

Filtered

64 candidates to 50 candidates (78.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	9	65

Merged error: 29.3b

Counts

65 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
18.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* x.im y.re) (* x.re y.im))
109.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune254.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Merged error: 28.4b

Counts

107 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
18.8b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
32.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
17.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* x.im y.re) (* x.re y.im))
115.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	378	916
1	1785	831
2	5001	807

prune240.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	107	8	115

Merged error: 28.4b

Counts

115 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
18.7b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
32.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
100×	`add-sqr-sqrt`
98×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
27×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp`
7×	`pow1`
6×	`sqrt-div` `div-inv`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 193

Calls

4 calls:

15.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
8.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im))))
75.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	574	2905
1	2449	2677
2	5002	2540

prune336.0ms

Filtered

205 candidates to 107 candidates (52.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	205	8	213

Merged error: 28.4b

Counts

213 → 8

regimes126.0ms

Accuracy

0% (2.9b remaining)

Error of 26.1b against oracle of 23.2b and baseline of 26.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

sample570.0ms

Algorithm

intervals

Results

361.0ms

8456×

body

valid