Details

analyze445.0ms

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

sample44.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
4.0ms	41×	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: 32.9b

Counts

2 → 1

localize20.0ms

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))
30.5b	(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:

10.0ms	(/ (+ (* (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:

24.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
23.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5011	2020

prune247.0ms

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: 6.5b

Counts

123 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `unpow-prod-down`
6×	`pow-unpow` `log-prod` `associate-l` `log-pow` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`pow-to-exp` `pow-pow` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms	(pow (log base) 2)
14.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4943	826
1	4943	826

prune220.0ms

Filtered

58 candidates to 93 candidates (-60.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	90	17	107

Merged error: 6.4b

Counts

107 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

10.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms	(pow (log base) 2)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4952	1936
1	4952	1936

prune225.0ms

Filtered

77 candidates to 105 candidates (-36.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	103	19	122

Merged error: 6.4b

Counts

122 → 19

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.9b	(pow (log base) 4)
30.5b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`log-prod`
11×	`log-pow`
10×	`associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `flip3-+` `pow-plus` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 4)
4.0ms	(sqrt (+ (* re re) (* im im)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
17.0ms	(pow (log base) 4)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5046	938

prune138.0ms

Filtered

65 candidates to 109 candidates (-67.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	3	14	17
Picked	1	0	1
Done	0	1	1
Total	108	20	128

Merged error: 6.4b

Counts

128 → 20

regimes730.0ms

Accuracy

57.7% (10.5b remaining)

Error of 17.6b against oracle of 7.0b and baseline of 32.0b

bsearch177.0ms

Steps

Iters	Range		Point
9	3.840972094756766e+119	3.3073318879297013e+124	4.616174933667185e+120
9	1.464576479346357e-146	2.350798320248975e-137	1.4945202169127629e-146
6	1.4464795131731517e-198	1.1705419590286359e-197	4.068189076745448e-198
11	-5.650696852337282e+156	-1.9063733403324737e+126	-1.831379490668168e+128

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	145
1	79	145

end0.0ms

sample1.1s

Algorithm

intervals

Results

819.0ms	8000×	body	80	valid
92.0ms	985×	body	80	nan

Details

analyze445.0ms

sample44.0ms

simplify3.0ms

prune4.0ms

localize20.0ms

rewrite27.0ms

series67.0ms

simplify77.0ms

prune247.0ms

localize24.0ms

rewrite16.0ms

series56.0ms

simplify61.0ms

prune220.0ms

localize21.0ms

rewrite24.0ms

series83.0ms

simplify56.0ms

prune225.0ms

localize27.0ms

rewrite19.0ms

series60.0ms

simplify46.0ms

prune138.0ms

regimes730.0ms

bsearch177.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling