Details

sample89.0ms

Algorithm

intervals

Results

33.0ms	291×	body	80	nan
25.0ms	256×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 32.2b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (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))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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:

12.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series66.0ms

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)))
22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	457	1397
1	1716	1276
2	5001	1225

prune239.0ms

Filtered

122 candidates to 80 candidates (34.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 9.2b

Counts

123 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
16.0ms	(* (log base) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify150.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	273	768
1	973	677
2	4633	614
3	5001	580

prune218.0ms

Filtered

127 candidates to 71 candidates (44.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	126	16	142

Merged error: 9.2b

Counts

142 → 16

localize27.0ms

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)
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

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)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
23.0ms	(cbrt base)
22.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	244	529
1	664	484
2	1904	432
3	5001	430

prune169.0ms

Filtered

77 candidates to 55 candidates (28.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	75	18	93

Merged error: 9.2b

Counts

93 → 18

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (* (log base) (log base)) (* (log base) (log base)))
0.7b	(pow (* (log base) (log base)) 3)
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

137×	`pow1`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
21×	`add-exp-log` `add-cbrt-cube`
20×	`pow-plus`
19×	`add-sqr-sqrt`
18×	`log-prod` `*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`pow2` `distribute-rgt-in` `distribute-lft-in`
10×	`prod-exp` `cbrt-unprod`
7×	`swap-sqr`
6×	`pow-pow` `log-pow`
5×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`sqrt-div` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `cube-prod` `flip-+` `sqr-pow`

Counts

4 → 152

Calls

4 calls:

5.0ms	(* (log base) (log base))
10.0ms	(* (* (log base) (log base)) (* (log base) (log base)))
4.0ms	(pow (* (log base) (log base)) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (log base) (log base))
17.0ms	(* (* (log base) (log base)) (* (log base) (log base)))
23.0ms	(pow (* (log base) (log base)) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	413	620
1	1612	551
2	5001	476

prune182.0ms

Filtered

164 candidates to 69 candidates (57.9%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	1	14	15
Picked	0	1	1
Done	0	2	2
Total	163	19	182

Merged error: 9.2b

Counts

182 → 19

regimes939.0ms

Accuracy

64.2% (8.1b remaining)

Error of 17.8b against oracle of 9.7b and baseline of 32.3b

bsearch108.0ms

Steps

Iters	Range		Point
9	1.2032028654389388e+99	1.4107254938318795e+107	5.2882667626719425e+103
9	-4.438676956255125e+114	-8.599666125943959e+108	-1.4566299232431934e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	41
1	53	41
2	53	41

end0.0ms

sample2.4s

Algorithm

intervals

Results

982.0ms	10689×	body	80	nan
793.0ms	8000×	body	80	valid

Details

sample89.0ms

simplify4.0ms

prune5.0ms

localize20.0ms

rewrite29.0ms

series66.0ms

simplify61.0ms

prune239.0ms

localize23.0ms

rewrite22.0ms

series57.0ms

simplify150.0ms

prune218.0ms

localize27.0ms

rewrite13.0ms

series72.0ms

simplify56.0ms

prune169.0ms

localize30.0ms

rewrite28.0ms

series61.0ms

simplify57.0ms

prune182.0ms

regimes939.0ms

bsearch108.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling