Details

sample22.0ms

Algorithm

intervals

Results

12.0ms

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

prune5.0ms

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: 28.5b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
28.0b	(/ (- (* x.im y.re) (* x.re 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×	`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)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- (* x.im y.re) (* x.re y.im))
86.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (26.0ms)

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

prune138.0ms

Filtered

50 candidates to 39 candidates (78.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	8	51

Merged error: 27.8b

Counts

51 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.5b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* x.im y.re) (* x.re y.im))
108.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	304	912
1	990	857
2	3340	845
3	5003	845

prune241.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	95	11	106

Merged error: 24.6b

Counts

106 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b

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

17.6b

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

20.2b

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-/r/`
7×	`add-cube-cbrt`
6×	`times-frac` `associate-/r*`
5×	`add-log-exp`
4×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv`
3×	`pow1` `distribute-rgt-out--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

3 → 65

Calls

3 calls:

14.0ms

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

6.0ms

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

6.0ms

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

series215.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms

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

47.0ms

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

44.0ms

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

simplify42.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	342	669
1	1537	598
2	5001	598

prune155.0ms

Filtered

74 candidates to 54 candidates (73.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	7	2	9
Picked	1	0	1
Done	1	0	1
Total	79	6	85

Merged error: 23.6b

Counts

85 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im)))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
3.0b	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
17.6b	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
19.0b	(/ y.re (+ (* y.re y.re) (* y.im y.im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

11.0ms	(- (* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im)))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im)))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
42.0ms	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
46.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	402	894
1	1834	805
2	5001	805

prune231.0ms

Filtered

112 candidates to 82 candidates (73.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	112	6	118

Merged error: 23.6b

Counts

118 → 6

regimes146.0ms

Accuracy

22.2% (2.2b remaining)

Error of 24.4b against oracle of 22.2b and baseline of 25.0b

bsearch69.0ms

Steps

Iters	Range		Point
6	6.032929379497232e+122	9.237392696154721e+123	1.1328506141572114e+123
7	-1.2506657699217206e-26	-7.609180663877619e-29	-9.630646419521664e-28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	39
1	34	39

end0.0ms

sample613.0ms

Algorithm

intervals

Results

398.0ms

8467×

body

valid

Details

sample22.0ms

simplify11.0ms

prune5.0ms

localize10.0ms

rewrite13.0ms

series122.0ms

simplify101.0ms

prune138.0ms

localize12.0ms

rewrite22.0ms

series214.0ms

simplify96.0ms

prune241.0ms

localize11.0ms

rewrite29.0ms

series215.0ms

simplify42.0ms

prune155.0ms

localize11.0ms

rewrite37.0ms

series253.0ms

simplify52.0ms

prune231.0ms

regimes146.0ms

bsearch69.0ms

simplify2.0ms

end0.0ms

sample613.0ms

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