Details

sample26.0ms

Algorithm

intervals

Results

15.0ms

272×

body

valid

simplify10.0ms

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

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: 24.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
23.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
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)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(- (* x.im y.re) (* x.re y.im))
84.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5001	491

prune164.0ms

Filtered

64 candidates to 50 candidates (78.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	9	65

Merged error: 23.4b

Counts

65 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* 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))))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b	(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`
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))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify97.0ms

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

prune232.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	96	11	107

Merged error: 20.7b

Counts

107 → 11

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)))))
15.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite46.0ms

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

series328.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (/ 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)))))
111.0ms	(/ (- (* x.im y.re) (* x.re 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)))

simplify72.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	582	2520
1	2665	2255
2	5003	2140

prune340.0ms

Filtered

173 candidates to 112 candidates (64.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	172	12	184

Merged error: 20.7b

Counts

184 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
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))))
15.6b	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
16.5b	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
15.0ms	(- (/ (* 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)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
114.0ms	(- (/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im))) (/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im))))
45.0ms	(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	385	746
1	1875	664
2	5002	660

prune180.0ms

Filtered

88 candidates to 65 candidates (73.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	6	3	9
Picked	1	0	1
Done	1	1	2
Total	92	8	100

Merged error: 18.9b

Counts

100 → 8

regimes173.0ms

Accuracy

66.4% (0.9b remaining)

Error of 23.0b against oracle of 22.1b and baseline of 24.7b

bsearch69.0ms

Steps

Iters	Range		Point
6	1.4692372860321438e+56	1.5715651896237286e+57	9.046605254534478e+56
6	-4.2568175387433725e+35	-5.141442709397297e+34	-1.9332834244083665e+35

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	28
1	37	28

end0.0ms

sample590.0ms

Algorithm

intervals

Results

376.0ms

8478×

body

valid

Details

sample26.0ms

simplify10.0ms

prune2.0ms

localize9.0ms

rewrite16.0ms

series148.0ms

simplify39.0ms

prune164.0ms

localize12.0ms

rewrite21.0ms

series210.0ms

simplify97.0ms

prune232.0ms

localize13.0ms

rewrite46.0ms

series328.0ms

simplify72.0ms

prune340.0ms

localize11.0ms

rewrite32.0ms

series227.0ms

simplify45.0ms

prune180.0ms

regimes173.0ms

bsearch69.0ms

simplify2.0ms

end0.0ms

sample590.0ms

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