Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

272×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

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: 26.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.1b	(- (* x.im y.re) (* x.re y.im))
26.0b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

260×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
92×	`associate-l`
88×	`times-frac`
65×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
26×	`swap-sqr`
24×	`add-cube-cbrt`
11×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1`
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 → 160

Calls

3 calls:

17.0ms	(+ (* y.re y.re) (* y.im y.im))
16.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* y.re y.re) (* y.im y.im))
45.0ms	(- (* x.im y.re) (* x.re y.im))
101.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	391	1751
1	1460	1703
2	5001	1701

prune239.0ms

Filtered

169 candidates to 72 candidates (42.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	9	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Merged error: 25.6b

Counts

170 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

314×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
121×	`times-frac`
112×	`sqrt-prod`
108×	`associate-l`
70×	`distribute-lft-out`
52×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
42×	`add-cube-cbrt`
28×	`swap-sqr`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
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 → 220

Calls

4 calls:

15.0ms	(- (* x.im y.re) (* x.re y.im))
39.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
20.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* x.im y.re) (* x.re y.im))
135.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify133.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	416	2698
1	1181	2613
2	3957	2607
3	5001	2602

prune326.0ms

Filtered

232 candidates to 99 candidates (42.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	224	8	232
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	231	10	241

Merged error: 22.8b

Counts

241 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
14.9b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

149×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
66×	`sqrt-prod`
51×	`associate-l`
40×	`distribute-lft-out`
39×	`associate-r`
37×	`times-frac`
34×	`frac-times` `add-cube-cbrt`
33×	`associate-/r*`
19×	`flip3--` `flip--`
17×	`associate-*r/`
16×	`swap-sqr`
13×	`add-exp-log` `unswap-sqr`
10×	`associate-/l*`
9×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`sqrt-div` `add-log-exp`
4×	`prod-exp` `clear-num`
3×	`frac-2neg` `flip3-+` `un-div-inv` `flip-+`
2×	`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` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 186

Calls

4 calls:

15.0ms	(- (* x.im y.re) (* x.re y.im))
51.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
22.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* x.im y.re) (* x.re y.im))
127.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	528	1852
1	2052	1781
2	5001	1721

prune559.0ms

Filtered

198 candidates to 98 candidates (49.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	198	10	208

Merged error: 22.8b

Counts

208 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
14.9b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

314×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
121×	`times-frac`
112×	`sqrt-prod`
108×	`associate-l`
70×	`distribute-lft-out`
52×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
42×	`add-cube-cbrt`
28×	`swap-sqr`
11×	`associate-/r` `associate-/l`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 219

Calls

4 calls:

14.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* x.im y.re) (* x.re y.im))
94.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	340	2691
1	919	2630
2	2600	2630
3	5001	2630

prune330.0ms

Filtered

231 candidates to 100 candidates (43.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	231	10	241

Merged error: 22.8b

Counts

241 → 10

regimes161.0ms

Accuracy

0% (3.3b remaining)

Error of 26.0b against oracle of 22.7b and baseline of 26.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

sample564.0ms

Algorithm

intervals

Results

339.0ms

8490×

body

valid