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

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4795	12
1	4795	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: 34.0b

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))
31.3b	(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:

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

series29.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
18.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify33.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5026	1163

prune174.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	14	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	14	84

Merged error: 8.6b

Counts

84 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
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)))
32.6b	(log (+ (* re re) (* im im)))

rewrite45.0ms

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:

4.0ms	(+ (* re re) (* im im))
24.0ms	(* (/ 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

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
23.0ms	(* (/ 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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4935	2958
1	4935	2958

prune336.0ms

Filtered

106 candidates to 176 candidates (-66.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	167	9	176
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	178	12	190

Merged error: 8.4b

Counts

190 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))
16.5b	(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))
17.3b	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite33.0ms

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:

4.0ms	(+ (* re re) (* im im))
12.0ms	(* (/ 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))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
43.0ms	(* (/ 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)))))
36.0ms	(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4946	2286
1	4946	2286

prune313.0ms

Filtered

93 candidates to 140 candidates (-50.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	140	12	152

Merged error: 8.4b

Counts

152 → 12

localize17.0ms

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)))
32.6b	(log (+ (* re re) (* im im)))

rewrite62.0ms

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:

24.0ms	(* (/ (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)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ (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))))))
21.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
12.0ms	(log (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4937	4523
1	4937	4523

prune551.0ms

Filtered

138 candidates to 219 candidates (-58.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	212	7	219
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	218	13	231

Merged error: 8.3b

Counts

231 → 13

regimes698.0ms

Accuracy

57.1% (10.7b remaining)

Error of 18.1b against oracle of 7.4b and baseline of 32.4b

bsearch65.0ms

Steps

Iters	Range		Point
8	6.368840520044388e+60	3.183045142611172e+65	2.3525407734835714e+65
4	4.1484279821246306e-192	5.904720401622327e-192	4.313080396452539e-192
6	1.4309571442516006e-266	5.9210050687566884e-266	3.871076454381889e-266
9	-1.8871607846355217e+117	-7.003815611847085e+110	-9.309314412837093e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	159	121
1	159	121

end0.0ms

sample631.0ms

Algorithm

intervals

Results

487.0ms

8000×

body

valid

Details

analyze5.0ms

sample24.0ms

simplify95.0ms

prune4.0ms

localize10.0ms

rewrite22.0ms

series29.0ms

simplify33.0ms

prune174.0ms

localize12.0ms

rewrite45.0ms

series58.0ms

simplify68.0ms

prune336.0ms

localize19.0ms

rewrite33.0ms

series116.0ms

simplify37.0ms

prune313.0ms

localize17.0ms

rewrite62.0ms

series103.0ms

simplify77.0ms

prune551.0ms

regimes698.0ms

bsearch65.0ms

simplify2.0ms

end0.0ms

sample631.0ms

Profiling