Details

sample32.0ms

Algorithm

intervals

Results

12.0ms

266×

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

prune4.0ms

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: 25.6b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (* x.im y.re) (* x.re y.im))
25.1b	(/ (- (* 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)))

series38.0ms

Counts

2 → 6

Calls

2 calls:

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

prune88.0ms

Filtered

50 candidates to 39 candidates (22.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	8	51

Merged error: 24.9b

Counts

51 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (* x.im y.re) (* x.re y.im))
15.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(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)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* 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)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (27.0ms)

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

prune129.0ms

Filtered

98 candidates to 75 candidates (23.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	95	11	106

Merged error: 22.1b

Counts

106 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (* x.im y.re) (* x.re y.im))
15.9b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `associate-/r*` `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 → 85

Calls

4 calls:

5.0ms	(- (* 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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
24.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	264	887
1	808	842
2	2343	837
3	5001	837

prune120.0ms

Filtered

97 candidates to 74 candidates (23.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	97	11	108

Merged error: 22.1b

Counts

108 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

8.3b	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

137×	`add-sqr-sqrt`
108×	`sqrt-prod`
99×	`times-frac`
57×	`*-un-lft-identity`
45×	`add-cube-cbrt`
33×	`associate-r` `associate-l`
28×	`unswap-sqr`
26×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`sqrt-div`
9×	`pow1`
8×	`div-exp` `prod-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 163

Calls

4 calls:

33.0ms	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
5.0ms	(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)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	568	3021
1	2570	2733
2	5001	2579

prune129.0ms

Filtered

175 candidates to 103 candidates (41.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	175	11	186

Merged error: 22.1b

Counts

186 → 11

regimes486.0ms

Accuracy

38.5% (1.8b remaining)

Error of 25.0b against oracle of 23.2b and baseline of 26.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	34
1	37	34
2	37	34

end0.0ms

sample708.0ms

Algorithm

intervals

Results

380.0ms

8453×

body

valid

Details

sample32.0ms

simplify11.0ms

prune4.0ms

localize13.0ms

rewrite12.0ms

series38.0ms

simplify98.0ms

prune88.0ms

localize12.0ms

rewrite20.0ms

series59.0ms

simplify96.0ms

prune129.0ms

localize13.0ms

rewrite23.0ms

series46.0ms

simplify68.0ms

prune120.0ms

localize15.0ms

rewrite52.0ms

series46.0ms

simplify72.0ms

prune129.0ms

regimes486.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample708.0ms

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