Details

analyze426.0ms

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

sample40.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
3.0ms	34×	body	80	nan

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	6498	28

prune7.0ms

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: 31.6b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
25.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4937	2018
1	4937	2018

prune272.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	105	17	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	17	123

Merged error: 6.0b

Counts

123 → 17

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `unpow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (log base) 2)
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5122	593

prune201.0ms

Filtered

56 candidates to 76 candidates (-35.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	76	17	93

Merged error: 6.0b

Counts

93 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

12.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
20.0ms	(cbrt base)
21.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4984	1518
1	4984	1518

prune207.0ms

Filtered

63 candidates to 80 candidates (-27.0%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	2	13	15
Picked	0	1	1
Done	0	1	1
Total	78	19	97

Merged error: 6.0b

Counts

97 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
0.5b	(* (log base) (log base))
0.7b	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `sqrt-div` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow1/3` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `flip-+` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

2.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
4.0ms	(* (log base) (log base))
5.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
14.0ms	(* (log base) (log base))
50.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4959	977
1	4959	977

prune139.0ms

Filtered

65 candidates to 102 candidates (-56.9%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	15	16
Picked	1	0	1
Done	0	2	2
Total	101	20	121

Merged error: 6.0b

Counts

121 → 20

regimes638.0ms

Accuracy

57.9% (10.1b remaining)

Error of 17.6b against oracle of 7.5b and baseline of 31.4b

bsearch153.0ms

Steps

Iters	Range		Point
6	1.6163068954604413e+121	1.1957981599759264e+122	2.1436881669277446e+121
6	2.979617081579172e-272	3.6047091854412613e-271	1.0930594691132366e-271
7	-1.2874083495777399e-197	-3.387365660580483e-199	-3.6142519675909714e-198
9	-2.7325672709357337e+92	-1.2195697614174734e+86	-3.4618694274082535e+91

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	219	188
1	219	188

end0.0ms

sample1.1s

Algorithm

intervals

Results

785.0ms	8000×	body	80	valid
88.0ms	993×	body	80	nan

Details

analyze426.0ms

sample40.0ms

simplify101.0ms

prune7.0ms

localize19.0ms

rewrite26.0ms

series65.0ms

simplify65.0ms

prune272.0ms

localize24.0ms

rewrite15.0ms

series32.0ms

simplify51.0ms

prune201.0ms

localize27.0ms

rewrite20.0ms

series95.0ms

simplify72.0ms

prune207.0ms

localize22.0ms

rewrite17.0ms

series90.0ms

simplify53.0ms

prune139.0ms

regimes638.0ms

bsearch153.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling