Details

sample22.0ms

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: 25.3b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
24.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series119.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- (* 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)))

simplify99.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	251	464
1	938	427
2	3504	426
3	5001	426

prune149.0ms

Filtered

50 candidates to 39 candidates (78.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	39	11	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	12	51

Merged error: 24.4b

Counts

51 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(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:

39.0ms	(- (* x.im y.re) (* x.re y.im))
108.0ms	(/ (- (* 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)))

simplify98.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (27.0ms)

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

prune255.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	98	12	110

Merged error: 21.2b

Counts

110 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
16.8b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(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))
18.0ms	(* (- (* 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)))

series218.0ms

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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (37.0ms)

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

prune249.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	107	12	119

Merged error: 21.2b

Counts

119 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
16.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

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))
12.0ms	(/ (- (* 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)))

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)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

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

prune235.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	96	14	110

Merged error: 21.2b

Counts

110 → 14

regimes287.0ms

Accuracy

38% (2.0b remaining)

Error of 24.9b against oracle of 22.9b and baseline of 26.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	39
1	36	39
2	36	39

end0.0ms

sample573.0ms

Algorithm

intervals

Results

364.0ms

8478×

body

valid