Details

analyze532.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample42.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify161.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	15

prune4.0ms

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:

0.5b	(- (* 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 → 43

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)))

series39.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5676	845

prune96.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	39	10	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	10	50

Merged error: 23.3b

Counts

50 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b	(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 → 85

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)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ (- (* 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)))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5760	1553

prune132.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 23.3b

Counts

107 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

9.4b	(* y.im (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`sqrt-prod`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `unswap-sqr`
2×	`prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

11.0ms	(* y.im (/ x.re (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)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* y.im (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
8.0ms	(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)))

simplify38.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4989	1084
1	4989	1084

prune127.0ms

Filtered

75 candidates to 101 candidates (-34.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	101	9	110

Merged error: 23.3b

Counts

110 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

11.1b	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* y.re x.im) (* y.im x.re)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
27.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
53×	`times-frac`
37×	`*-un-lft-identity`
33×	`add-cube-cbrt` `associate-r`
27×	`sqrt-prod`
26×	`add-exp-log`
18×	`cbrt-prod`
16×	`add-cbrt-cube`
13×	`associate-l`
12×	`unswap-sqr`
8×	`div-exp` `prod-exp`
7×	`pow1`
6×	`cbrt-div`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `cbrt-unprod` `flip-+` `add-log-exp`
2×	`rec-exp` `pow1/3` `1-exp` `associate-/r/` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 123

Calls

4 calls:

24.0ms	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* y.re x.im) (* y.im x.re)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* y.re x.im) (* y.im x.re)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
20.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5230	3266

prune147.0ms

Filtered

98 candidates to 135 candidates (-37.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	135	9	144

Merged error: 23.3b

Counts

144 → 9

regimes321.0ms

Accuracy

-22.6% (1.1b remaining)

Error of 23.5b against oracle of 22.4b and baseline of 23.3b

bsearch59.0ms

Steps

Iters	Range		Point
8	1.4763116773215927e-209	2.0507023818615214e-206	2.2944353920244916e-209
10	-1.3197247523846362e-242	-9.057696839308776e-253	-2.7466643681102755e-252

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	81
1	85	81

end0.0ms

sample1.2s

Algorithm

intervals

Results

315.0ms

8000×

body

valid

Details

analyze532.0ms

sample42.0ms

simplify161.0ms

prune4.0ms

localize10.0ms

rewrite13.0ms

series39.0ms

simplify62.0ms

prune96.0ms

localize15.0ms

rewrite22.0ms

series56.0ms

simplify51.0ms

prune132.0ms

localize14.0ms

rewrite25.0ms

series33.0ms

simplify38.0ms

prune127.0ms

localize19.0ms

rewrite40.0ms

series230.0ms

simplify65.0ms

prune147.0ms

regimes321.0ms

bsearch59.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling