Details

analyze13.0ms

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

sample38.0ms

Algorithm

intervals

Results

25.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	19
1	12	19

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: 31.8b

Counts

2 → 1

localize11.0ms

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))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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:

6.0ms	(+ (* re re) (* im im))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series59.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ (* re re) (* im im))
38.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
12.0ms	(sqrt (+ (* re re) (* im im)))

simplify113.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4917	1838
1	4917	1838

prune200.0ms

Filtered

56 candidates to 83 candidates (-48.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	14	84

Merged error: 7.3b

Counts

84 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
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)))
30.5b	(log (+ (* re re) (* im im)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 164

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
45.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
14.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
8.0ms	(log (+ (* re re) (* im im)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
24.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
39.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
10.0ms	(log (+ (* re re) (* im im)))

simplify158.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4985	4871
1	4985	4871

prune536.0ms

Filtered

106 candidates to 176 candidates (-66.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	167	9	176
Fresh	8	4	12
Picked	1	0	1
Done	1	0	1
Total	177	13	190

Merged error: 7.2b

Counts

190 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
15.1b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
16.6b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`times-frac`
40×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
13×	`pow1`
12×	`add-exp-log` `unpow-prod-down`
9×	`add-cbrt-cube`
8×	`log-pow`
7×	`distribute-rgt-in` `distribute-lft-in`
6×	`add-log-exp`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-pow` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+`

Counts

4 → 128

Calls

4 calls:

7.0ms	(+ (* re re) (* im im))
21.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
5.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
7.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
57.0ms	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
48.0ms	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
41.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify118.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4980	3541
1	4980	3541

prune415.0ms

Filtered

89 candidates to 140 candidates (-57.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	140	13	153

Merged error: 7.2b

Counts

153 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

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))))))
0.4b	(* (/ (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)))
30.5b	(log (+ (* re re) (* im im)))

rewrite83.0ms

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:

30.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (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))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
8.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
54.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
23.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
10.0ms	(log (+ (* re re) (* im im)))

simplify170.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4936	7205
1	4936	7205

prune653.0ms

Filtered

134 candidates to 219 candidates (-63.4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	215	4	219
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	216	16	232

Merged error: 7.1b

Counts

232 → 16

regimes1.3s

Accuracy

56.9% (10.5b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 31.9b

bsearch63.0ms

Steps

Iters	Range		Point
5	2.3336219094046975e+61	5.24142636471266e+61	5.046704470115603e+61
3	3.98678887242932e-212	5.330876350849332e-212	4.5802341129154857e-212
7	7.579403349765175e-307	3.5175501554820765e-305	1.0310803755509703e-305
7	-5.507180982402261e+50	-3.0613511479002126e+49	-1.863429032795485e+50

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	184
1	87	184

end0.0ms

sample887.0ms

Algorithm

intervals

Results

689.0ms

8000×

body

valid

Details

analyze13.0ms

sample38.0ms

simplify7.0ms

prune4.0ms

localize11.0ms

rewrite22.0ms

series59.0ms

simplify113.0ms

prune200.0ms

localize23.0ms

rewrite84.0ms

series78.0ms

simplify158.0ms

prune536.0ms

localize20.0ms

rewrite44.0ms

series152.0ms

simplify118.0ms

prune415.0ms

localize18.0ms

rewrite83.0ms

series123.0ms

simplify170.0ms

prune653.0ms

regimes1.3s

bsearch63.0ms

simplify4.0ms

end0.0ms

sample887.0ms

Profiling