Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

272×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	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: 26.3b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
25.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

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

series115.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
85.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (23.0ms)

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

prune158.0ms

Filtered

48 candidates to 38 candidates (79.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	38	10	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	10	49

Merged error: 25.5b

Counts

49 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
16.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite37.0ms

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:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
16.0ms	(/ (+ (* 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)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* x.re y.re) (* x.im y.im))
105.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify92.0ms

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

prune250.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	96	10	106

Merged error: 23.0b

Counts

106 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
16.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.6b	(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`
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))
9.0ms	(/ (+ (* 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)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
106.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify84.0ms

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

prune251.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	95	11	106

Merged error: 23.0b

Counts

106 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

8.4b	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
31.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

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:

32.0ms	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	579	3020
1	3448	2732
2	5003	2578

prune393.0ms

Filtered

175 candidates to 104 candidates (59.4%)

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: 23.0b

Counts

186 → 11

regimes235.0ms

Accuracy

26.9% (2.3b remaining)

Error of 25.4b against oracle of 23.1b and baseline of 26.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	27
1	33	27
2	33	27

end0.0ms

sample569.0ms

Algorithm

intervals

Results

363.0ms

8465×

body

valid

Details

sample22.0ms

simplify4.0ms

prune2.0ms

localize9.0ms

rewrite13.0ms

series115.0ms

simplify83.0ms

prune158.0ms

localize21.0ms

rewrite37.0ms

series231.0ms

simplify92.0ms

prune250.0ms

localize13.0ms

rewrite21.0ms

series210.0ms

simplify84.0ms

prune251.0ms

localize15.0ms

rewrite53.0ms

series244.0ms

simplify78.0ms

prune393.0ms

regimes235.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample569.0ms

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