Details

sample19.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

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 (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: 35.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

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

series202.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* re re) (* im im))
131.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	256	741
1	895	697
2	2846	694
3	5001	694

prune200.0ms

Filtered

83 candidates to 55 candidates (66.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	72	11	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	11	84

Merged error: 8.4b

Counts

84 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
32.7b	(sqrt (+ (* re re) (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

126×	`pow1`
94×	`log-pow`
72×	`times-frac`
60×	`sqrt-div`
54×	`cbrt-div`
45×	`pow1/3` `pow-prod-up`
34×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
30×	`flip3-+` `pow-plus` `flip-+`
28×	`frac-times`
26×	`log-div` `div-sub`
25×	`pow-prod-down`
18×	`associate-/l*`
15×	`pow-sqr`
14×	`associate-*l/`
10×	`pow2`
9×	`sqrt-prod`
8×	`associate-*r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow3`
4×	`associate-/r*` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 177

Calls

4 calls:

29.0ms	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (log (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im)))))) (log 10.0))
36.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify149.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	480	3559
1	955	3468
2	3016	3076
3	5003	3048

prune384.0ms

Filtered

189 candidates to 92 candidates (48.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	188	12	200

Merged error: 8.4b

Counts

200 → 12

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)
32.7b	(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:

8.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3))
141.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
233.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	554	2577
1	2292	2448
2	5001	2428

prune356.0ms

Filtered

223 candidates to 93 candidates (41.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	214	9	223
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	217	18	235

Merged error: 8.2b

Counts

235 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
0.7b	(pow (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3) 3)
0.7b	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
146×	`unpow-prod-down` `cube-prod`
130×	`log-pow`
107×	`pow1`
88×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
30×	`sqrt-pow1` `pow1/2`
13×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`pow-exp`
7×	`div-inv`
6×	`pow-unpow` `associate-/l*`
4×	`cube-mult` `sqrt-div` `unpow3` `associate-/r*` `add-log-exp` `sqr-pow`
3×	`cube-div` `pow-to-exp` `div-exp` `sqrt-prod` `rem-cube-cbrt`
2×	`cbrt-undiv` `log-div` `pow-pow` `flip3-+` `div-sub` `flip-+`
1×	`rem-sqrt-square` `frac-2neg` `clear-num`

Counts

4 → 284

Calls

4 calls:

7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
15.0ms	(pow (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3) 3)
8.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series770.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
354.0ms	(pow (pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3) 3)
232.0ms	(pow (/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0)) 3)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify144.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	789	3844
1	3906	3574
2	5002	3550

prune438.0ms

Filtered

296 candidates to 103 candidates (34.8%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	290	6	296
Fresh	3	13	16
Picked	0	1	1
Done	0	1	1
Total	293	21	314

Merged error: 8.2b

Counts

314 → 21

regimes1.1s

Accuracy

51.4% (11.9b remaining)

Error of 19.0b against oracle of 7.1b and baseline of 31.6b

bsearch143.0ms

Steps

Iters	Range		Point
9	1.2005221730326856e+90	1.0299998940834712e+95	2.5570395887401012e+92
8	2.555487769507404e-297	9.204367104374754e-295	2.151804293746571e-295
9	-4.0298841896469914e-94	-3.744556309116812e-103	-3.8099669373079583e-103
4	-5.3768555360377445e+54	-3.05695134075892e+54	-5.3041072880298795e+54

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	36
1	46	36

end0.0ms

sample477.0ms

Algorithm

intervals

Results

343.0ms

8000×

body

valid