Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample24.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

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: 30.0b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series23.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5218	1035

prune178.0ms

Filtered

46 candidates to 69 candidates (-50.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	53	16	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	16	70

Merged error: 7.1b

Counts

70 → 16

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
28.8b	(log (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
82×	`add-sqr-sqrt`
54×	`sqrt-prod`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 153

Calls

3 calls:

22.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series50.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
21.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4936	2822
1	4936	2822

prune330.0ms

Filtered

96 candidates to 162 candidates (-68.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	152	10	162
Fresh	11	4	15
Picked	1	0	1
Done	0	0	0
Total	164	14	178

Merged error: 6.9b

Counts

178 → 14

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
0.3b	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
28.8b	(log (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
46×	`times-frac`
45×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
29×	`associate-l` `add-cbrt-cube`
26×	`associate-r` `sqrt-prod`
22×	`prod-exp`
18×	`pow1`
12×	`cbrt-unprod`
11×	`div-exp`
8×	`log-pow`
6×	`cbrt-undiv`
5×	`associate-*r/` `unswap-sqr`
4×	`pow-prod-down`
3×	`rec-exp` `log-prod` `1-exp` `un-div-inv` `add-log-exp`
2×	`frac-times` `log-div` `*-commutative` `div-inv`
1×	`flip3-+` `rem-log-exp` `associate-*l/` `flip-+`

Counts

3 → 122

Calls

3 calls:

13.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
11.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(log (+ (* re re) (* im im)))

series53.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
24.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
9.0ms	(log (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5202	1839

prune250.0ms

Filtered

74 candidates to 131 candidates (-77.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	131	14	145

Merged error: 6.9b

Counts

145 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
0.4b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
28.8b	(log (+ (* re re) (* im im)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-prod`
112×	`times-frac`
107×	`add-sqr-sqrt`
69×	`add-cube-cbrt` `*-un-lft-identity`
60×	`associate-l`
42×	`pow1`
31×	`log-pow`
29×	`associate-r`
21×	`add-exp-log`
20×	`add-cbrt-cube`
12×	`unswap-sqr`
10×	`sqrt-div`
7×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`frac-times` `associate-*r/`
4×	`log-div` `pow-prod-down` `associate-l/` `div-inv` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `log-prod` `div-exp`
2×	`flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`frac-2neg` `rem-log-exp` `clear-num`

Counts

4 → 207

Calls

4 calls:

26.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
18.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
26.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
22.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
10.0ms	(log (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4940	4416
1	4940	4416

prune547.0ms

Filtered

135 candidates to 219 candidates (-62.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	5	7	12
Picked	0	1	1
Done	0	1	1
Total	218	15	233

Merged error: 6.8b

Counts

233 → 15

regimes863.0ms

Accuracy

58% (10.4b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 32.3b

bsearch24.0ms

Steps

Iters	Range		Point
8	4.727307915167732e+107	1.1550816695436949e+111	1.3191085918819207e+109
2	-8.431524114725349e+108	-7.594310835311773e+108	-8.117569134945259e+108

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	68
1	50	68

end0.0ms

sample638.0ms

Algorithm

intervals

Results

502.0ms

8000×

body

valid

Details

analyze5.0ms

sample24.0ms

simplify2.0ms

prune4.0ms

localize14.0ms

rewrite12.0ms

series23.0ms

simplify61.0ms

prune178.0ms

localize13.0ms

rewrite41.0ms

series50.0ms

simplify80.0ms

prune330.0ms

localize15.0ms

rewrite33.0ms

series53.0ms

simplify49.0ms

prune250.0ms

localize15.0ms

rewrite64.0ms

series106.0ms

simplify72.0ms

prune547.0ms

regimes863.0ms

bsearch24.0ms

simplify1.0ms

end0.0ms

sample638.0ms

Profiling