Details

analyze4.0ms

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

sample22.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify3.0ms

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: 34.5b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

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)))

series30.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5218	1035

prune152.0ms

Filtered

46 candidates to 69 candidates (-50.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	55	14	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	14	70

Merged error: 7.3b

Counts

70 → 14

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 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)))
33.1b	(log (+ (* re re) (* im im)))

rewrite39.0ms

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:

21.0ms	(* (/ 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)))

series58.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
27.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
10.0ms	(log (+ (* re re) (* im im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4936	2822
1	4936	2822

prune298.0ms

Filtered

96 candidates to 162 candidates (-68.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	152	10	162
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	163	13	176

Merged error: 7.1b

Counts

176 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.4b	(* (/ (sqrt 1/2) 1) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
0.6b	(/ (log 10.0) (log (+ (* re re) (* im im))))
33.1b	(log (+ (* re re) (* im im)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

532×	`times-frac`
318×	`add-sqr-sqrt`
238×	`*-un-lft-identity`
228×	`add-cube-cbrt`
152×	`sqrt-prod`
125×	`associate-r`
121×	`pow1`
115×	`log-pow`
42×	`add-exp-log`
32×	`add-cbrt-cube`
25×	`unswap-sqr`
24×	`associate-/r*`
22×	`associate-l`
19×	`div-exp`
17×	`div-inv`
13×	`cbrt-undiv`
10×	`associate-/l*`
9×	`prod-exp`
6×	`cbrt-unprod`
4×	`add-log-exp`
3×	`log-prod` `1-exp`
2×	`log-div` `frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `flip3-+` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 410

Calls

4 calls:

12.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
65.0ms	(* (/ (sqrt 1/2) 1) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
4.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
4.0ms	(log (+ (* re re) (* im im)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
31.0ms	(* (/ (sqrt 1/2) 1) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
25.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
9.0ms	(log (+ (* re re) (* im im)))

simplify107.0ms

Algorithm

egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4960	8322
1	4960	8322

prune595.0ms

Filtered

200 candidates to 422 candidates (-111.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	419	3	422
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	419	16	435

Merged error: 7.0b

Counts

435 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
0.3b	(* (/ (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)))
33.1b	(log (+ (* re re) (* im im)))

rewrite63.0ms

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:

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))))))
24.0ms	(* (/ (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:

27.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
45.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
25.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4940	4416
1	4940	4416

prune497.0ms

Filtered

134 candidates to 219 candidates (-63.4%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	3	11	14
Picked	0	1	1
Done	0	1	1
Total	217	18	235

Merged error: 7.0b

Counts

235 → 18

regimes805.0ms

Accuracy

54.8% (10.8b remaining)

Error of 18.2b against oracle of 7.4b and baseline of 31.3b

bsearch77.0ms

Steps

Iters	Range		Point
7	2.727763882729661e+135	4.3919554010441137e+136	5.509693746587087e+135
9	1.7725555918785836e-276	1.3763447895164663e-269	2.424827901233389e-276
8	-1.5674558434495267e-199	-2.081266212082811e-203	-1.8632042262810938e-201
9	-6.723965022024421e+129	-4.5947852851516383e+123	-1.0802856481292018e+127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	124
1	73	124

end0.0ms

sample594.0ms

Algorithm

intervals

Results

459.0ms

8000×

body

valid

Details

analyze4.0ms

sample22.0ms

simplify3.0ms

prune4.0ms

localize11.0ms

rewrite13.0ms

series30.0ms

simplify65.0ms

prune152.0ms

localize15.0ms

rewrite39.0ms

series58.0ms

simplify83.0ms

prune298.0ms

localize14.0ms

rewrite109.0ms

series88.0ms

simplify107.0ms

prune595.0ms

localize14.0ms

rewrite63.0ms

series106.0ms

simplify70.0ms

prune497.0ms

regimes805.0ms

bsearch77.0ms

simplify2.0ms

end0.0ms

sample594.0ms

Profiling