Details

sample25.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.7b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.3b	(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))
3.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify113.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (106.0ms)

Iter	Nodes	Cost
0	224	668
1	555	635
2	1317	630
3	3981	628
4	5001	627

prune141.0ms

Filtered

69 candidates to 45 candidates (34.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	56	13	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	13	70

Merged error: 6.3b

Counts

70 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
0.7b	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
94×	`log-pow`
79×	`pow1`
64×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
62×	`cbrt-prod`
56×	`unpow-prod-down` `cube-prod`
22×	`sqrt-pow1` `pow1/2`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv`
4×	`sqrt-div` `associate-/r*` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`cbrt-undiv` `cube-div` `cube-mult` `log-div` `flip3-+` `unpow3` `div-sub` `div-exp` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube`

Counts

4 → 211

Calls

4 calls:

7.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
7.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
18.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
43.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	547	2589
1	2273	2460
2	5002	2436

prune265.0ms

Filtered

223 candidates to 95 candidates (57.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	211	12	223
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	217	19	236

Merged error: 6.2b

Counts

236 → 19

localize16.0ms

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)))
30.4b	(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:

23.0ms	(* (/ 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)))
3.0ms	(log (+ (* re re) (* im im)))

series51.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
22.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	528	2102
1	2132	1937
2	5001	1838

prune315.0ms

Filtered

162 candidates to 96 candidates (40.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	7	11	18
Picked	1	0	1
Done	0	0	0
Total	163	18	181

Merged error: 6.1b

Counts

181 → 18

localize19.0ms

Local error

Found 3 expressions with local error:

0.3b

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

14.7b

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

16.7b

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`times-frac`
39×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`log-pow` `add-cbrt-cube`
7×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `pow-pow` `div-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 117

Calls

3 calls:

12.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

4.0ms

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

7.0ms

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series112.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

32.0ms

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

35.0ms

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	478	1721
1	2113	1522
2	5001	1321

prune238.0ms

Filtered

126 candidates to 82 candidates (34.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	126	18	144

Merged error: 6.1b

Counts

144 → 18

regimes1.1s

Accuracy

56.1% (10.6b remaining)

Error of 18.0b against oracle of 7.4b and baseline of 31.6b

bsearch35.0ms

Steps

Iters	Range		Point
5	0.0002914685688501568	0.0007800520059423635	0.0007693426915948314
9	-1.845992504175783e+146	-7.308681746474891e+136	-8.266941515723586e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	33
1	45	33

end0.0ms

sample684.0ms

Algorithm

intervals

Results

467.0ms

8000×

body

valid

Details

sample25.0ms

simplify3.0ms

prune3.0ms

localize10.0ms

rewrite12.0ms

series25.0ms

simplify113.0ms

prune141.0ms

localize14.0ms

rewrite36.0ms

series85.0ms

simplify78.0ms

prune265.0ms

localize16.0ms

rewrite39.0ms

series51.0ms

simplify61.0ms

prune315.0ms

localize19.0ms

rewrite28.0ms

series112.0ms

simplify57.0ms

prune238.0ms

regimes1.1s

bsearch35.0ms

simplify2.0ms

end0.0ms

sample684.0ms

Profiling