Details

sample29.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify11.0ms

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

prune3.0ms

Filtered

1 candidates to 0 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: 30.2b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* 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)))

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

series40.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
30.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify98.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	251	464
1	938	427
2	3490	426
3	5002	426

prune85.0ms

Filtered

50 candidates to 39 candidates (22.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	9	51

Merged error: 29.4b

Counts

51 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
18.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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))
8.0ms	(/ (- (* 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)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
33.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify98.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3340	845
3	5003	845

prune118.0ms

Filtered

98 candidates to 75 candidates (23.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	1	6	7
Picked	1	0	1
Done	1	0	1
Total	97	10	107

Merged error: 26.9b

Counts

107 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
18.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 161

Calls

4 calls:

23.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
8.0ms	(/ (- (* 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)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
34.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	582	2518
1	2638	2255
2	5001	2130

prune156.0ms

Filtered

173 candidates to 114 candidates (34.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	172	11	183

Merged error: 26.9b

Counts

183 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.3b	(- (* x.im y.re) (* x.re y.im))
29.6b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
13.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series42.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(- (* x.im y.re) (* x.re y.im))
27.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify44.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	343	778
1	1563	685
2	5002	657

prune68.0ms

Filtered

96 candidates to 59 candidates (38.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	96	11	107

Merged error: 26.9b

Counts

107 → 11

regimes453.0ms

Accuracy

37.7% (1.6b remaining)

Error of 25.4b against oracle of 23.8b and baseline of 26.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	27
1	32	27
2	32	27

end0.0ms

sample708.0ms

Algorithm

intervals

Results

375.0ms

8460×

body

valid

Details

sample29.0ms

simplify11.0ms

prune3.0ms

localize9.0ms

rewrite12.0ms

series40.0ms

simplify98.0ms

prune85.0ms

localize13.0ms

rewrite20.0ms

series54.0ms

simplify98.0ms

prune118.0ms

localize13.0ms

rewrite45.0ms

series74.0ms

simplify74.0ms

prune156.0ms

localize10.0ms

rewrite23.0ms

series42.0ms

simplify44.0ms

prune68.0ms

regimes453.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample708.0ms

Profiling