Details

analyze545.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample41.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
4.0ms	39×	body	80	nan

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	44
1	24	44

prune5.0ms

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: 32.6b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

17.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
29.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4919	3186
1	4919	3186

prune420.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 7.8b

Counts

123 → 14

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
0.6b	(pow (log base) 2)
0.6b	(* (log base) (log base))
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
20×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`log-pow`
6×	`log-prod` `swap-sqr` `associate-/r*`
4×	`unpow-prod-down` `sqrt-div` `associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `flip-+` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

15.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
2.0ms	(pow (log base) 2)
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
15.0ms	(pow (log base) 2)
17.0ms	(* (log base) (log base))
11.0ms	(sqrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4931	3587
1	4931	3587

prune413.0ms

Filtered

77 candidates to 125 candidates (-62.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	122	17	139

Merged error: 7.4b

Counts

139 → 17

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
0.6b	(pow (log base) 2)
0.6b	(pow (log base) 2)
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
9×	`pow1`
8×	`add-exp-log` `unpow-prod-down`
6×	`pow-unpow` `associate-/r*` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r/` `log-pow` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

22.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
5.0ms	(pow (log base) 2)
4.0ms	(pow (log base) 2)
7.0ms	(sqrt (+ (* re re) (* im im)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
15.0ms	(pow (log base) 2)
25.0ms	(pow (log base) 2)
11.0ms	(sqrt (+ (* re re) (* im im)))

simplify113.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5050	3434

prune454.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	3	12	15
Picked	1	0	1
Done	0	1	1
Total	106	19	125

Merged error: 7.4b

Counts

125 → 19

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
25.0ms	(cbrt base)
33.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4880	1150
1	4880	1150

prune90.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	15	17
Picked	0	1	1
Done	0	1	1
Total	76	20	96

Merged error: 7.4b

Counts

96 → 20

regimes895.0ms

Accuracy

55.5% (10.9b remaining)

Error of 18.1b against oracle of 7.2b and baseline of 31.7b

bsearch245.0ms

Steps

Iters	Range		Point
10	252878.24386564383	11998586223306416.0	11842883050065392.0
8	1.537090098485261e-159	1.6251587418475811e-155	1.5668585135104207e-159
7	8.18808488505506e-275	9.467163506654884e-273	1.4536155290271033e-273
7	-4.3211528251435536e-296	-4.604830696025859e-298	-1.644827461981046e-297
5	-1.5491933750956309e-257	-4.982636396466136e-258	-1.0946860890696683e-257
7	-2.1636652401388275e+92	-5.126087455890015e+90	-6.759324946026285e+90

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	296
1	81	296

end0.0ms

sample1.3s

Algorithm

intervals

Results

953.0ms	8000×	body	80	valid
112.0ms	998×	body	80	nan

Details

analyze545.0ms

sample41.0ms

simplify7.0ms

prune5.0ms

localize28.0ms

rewrite51.0ms

series98.0ms

simplify91.0ms

prune420.0ms

localize53.0ms

rewrite34.0ms

series69.0ms

simplify100.0ms

prune413.0ms

localize47.0ms

rewrite44.0ms

series66.0ms

simplify113.0ms

prune454.0ms

localize53.0ms

rewrite14.0ms

series100.0ms

simplify79.0ms

prune90.0ms

regimes895.0ms

bsearch245.0ms

simplify4.0ms

end0.0ms

sample1.3s

Profiling