Details

sample29.0ms

Algorithm

intervals

Results

11.0ms

270×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune7.0ms

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: 29.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
28.4b	(/ (+ (* x.re y.re) (* x.im 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×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

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

series35.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2837	412
3	5001	412

prune141.0ms

Filtered

48 candidates to 38 candidates (20.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Merged error: 28.2b

Counts

49 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
16.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* x.re y.re) (* x.im y.im))
33.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

simplify81.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune362.0ms

Filtered

96 candidates to 74 candidates (22.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 25.4b

Counts

101 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
16.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

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

9.0ms	(+ (* x.re y.re) (* x.im y.im))
33.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

simplify81.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune363.0ms

Filtered

96 candidates to 74 candidates (22.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	96	8	104

Merged error: 25.4b

Counts

104 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* y.re y.re) (* y.im y.im))
8.9b	(+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re))
22.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re)))
38.2b	(* (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re))) (- (* y.re y.re) (* y.im y.im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1`
4×	`flip3-+` `associate-r` `associate-/r/` `flip-+`
3×	`sub-neg` `flip3--` `associate-/r` `flip--` `associate-/l`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative`

Counts

4 → 98

Calls

4 calls:

3.0ms	(- (* y.re y.re) (* y.im y.im))
5.0ms	(+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re)))
14.0ms	(* (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re))) (- (* y.re y.re) (* y.im y.im)))

series133.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* y.re y.re) (* y.im y.im))
14.0ms	(+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re))
55.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re)))
55.0ms	(* (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* (neg (pow y.im 3)) y.im) (* (pow y.re 3) y.re))) (- (* y.re y.re) (* y.im y.im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	493	1528
1	2729	1229
2	5002	1202

prune482.0ms

Filtered

110 candidates to 85 candidates (22.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	110	8	118

Merged error: 25.4b

Counts

118 → 8

regimes451.0ms

Accuracy

4.5% (2.9b remaining)

Error of 26.5b against oracle of 23.5b and baseline of 26.6b

bsearch35.0ms

Steps

Iters	Range		Point
6	1.3653351403313602e+73	1.322226463547956e+74	7.546018787528083e+73

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	18
1	21	18

end0.0ms

sample721.0ms

Algorithm

intervals

Results

361.0ms

8458×

body

valid

Details

sample29.0ms

simplify3.0ms

prune7.0ms

localize9.0ms

rewrite12.0ms

series35.0ms

simplify80.0ms

prune141.0ms

localize11.0ms

rewrite20.0ms

series56.0ms

simplify81.0ms

prune362.0ms

localize15.0ms

rewrite20.0ms

series54.0ms

simplify81.0ms

prune363.0ms

localize21.0ms

rewrite34.0ms

series133.0ms

simplify91.0ms

prune482.0ms

regimes451.0ms

bsearch35.0ms

simplify1.0ms

end0.0ms

sample721.0ms

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