Details

analyze432.0ms

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

sample38.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
2.0ms	23×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

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: 32.1b

Counts

2 → 1

localize22.0ms

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))
0.5b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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:

9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5011	2020

prune256.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	106	16	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	16	123

Merged error: 8.2b

Counts

123 → 16

localize24.0ms

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))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

12.0ms	(/ (+ (* (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)
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series48.0ms

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

simplify59.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5049	2174

prune285.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	105	19	124

Merged error: 7.8b

Counts

124 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(cbrt (pow (log base) 6))
1.2b	(pow (log base) 6)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(cbrt (pow (log base) 6))
2.0ms	(pow (log base) 6)
4.0ms	(sqrt (+ (* re re) (* im im)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms	(cbrt (pow (log base) 6))
20.0ms	(pow (log base) 6)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5206	835

prune197.0ms

Filtered

58 candidates to 89 candidates (-53.4%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	17	17
Picked	1	0	1
Done	0	1	1
Total	87	21	108

Merged error: 7.8b

Counts

108 → 21

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
0.7b	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

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:

5.0ms	(* (log base) (log base))
2.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
5.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (log base) (log base))
20.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
49.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4962	983
1	4962	983

prune125.0ms

Filtered

65 candidates to 102 candidates (-56.9%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	3	16	19
Picked	0	1	1
Done	0	1	1
Total	100	23	123

Merged error: 7.8b

Counts

123 → 23

regimes685.0ms

Accuracy

57.1% (10.8b remaining)

Error of 18.0b against oracle of 7.2b and baseline of 32.3b

bsearch168.0ms

Steps

Iters	Range		Point
7	4.020849607308691e+46	7.805755577134997e+48	7.632785135818537e+48
9	7.811542171807302e-299	6.896001544541615e-294	8.19756653341619e-297
9	-1.5677216657091108e-228	-8.516245194888362e-234	-8.602224484858101e-234
9	-2.6652187729945484e+142	-6.913356636018319e+134	-9.003963061251663e+137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	131
1	65	131

end0.0ms

sample1.1s

Algorithm

intervals

Results

765.0ms	8000×	body	80	valid
93.0ms	1046×	body	80	nan

Details

analyze432.0ms

sample38.0ms

simplify3.0ms

prune4.0ms

localize22.0ms

rewrite27.0ms

series67.0ms

simplify73.0ms

prune256.0ms

localize24.0ms

rewrite23.0ms

series48.0ms

simplify59.0ms

prune285.0ms

localize22.0ms

rewrite15.0ms

series62.0ms

simplify50.0ms

prune197.0ms

localize23.0ms

rewrite19.0ms

series91.0ms

simplify47.0ms

prune125.0ms

regimes685.0ms

bsearch168.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling