Details

sample63.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
18.0ms	221×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune4.0ms

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: 29.9b

Counts

2 → 1

localize23.0ms

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))
27.7b	(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:

10.0ms	(/ (+ (* (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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (43.0ms)

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

prune221.0ms

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: 7.2b

Counts

123 → 15

localize22.0ms

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))
27.7b	(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:

6.0ms	(* (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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify146.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (138.0ms)

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

prune214.0ms

Filtered

127 candidates to 71 candidates (44.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	125	17	142

Merged error: 7.2b

Counts

142 → 17

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.7b	(cbrt base)
0.7b	(cbrt base)
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (log base) (log base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (log base) (log base))
22.0ms	(cbrt base)
24.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	219	373
1	673	335
2	2751	296
3	5002	279

prune192.0ms

Filtered

85 candidates to 53 candidates (37.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	84	18	102

Merged error: 7.2b

Counts

102 → 18

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
58×	`times-frac`
53×	`*-un-lft-identity`
43×	`add-cube-cbrt`
33×	`pow1`
32×	`associate-r` `associate-l` `sqrt-prod`
30×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`prod-exp`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`

Counts

4 → 174

Calls

4 calls:

26.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
5.0ms	(* (log base) (log base))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (/ 1 (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0)))))
15.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	687	3342
1	3745	2983
2	5001	2817

prune248.0ms

Filtered

186 candidates to 103 candidates (44.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	1	15	16
Picked	1	0	1
Done	0	1	1
Total	185	19	204

Merged error: 7.1b

Counts

204 → 19

regimes887.0ms

Accuracy

58.8% (10.1b remaining)

Error of 17.7b against oracle of 7.6b and baseline of 32.2b

bsearch74.0ms

Steps

Iters	Range		Point
9	1.0672714223471645e+107	5.101610838053785e+112	2.7373554894705896e+112
4	-2.6907717808382143e+96	-1.6058317493978785e+96	-2.4384131374064387e+96

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	57
1	76	57
2	76	57

end0.0ms

sample1.9s

Algorithm

intervals

Results

716.0ms	8000×	body	80	valid
657.0ms	7851×	body	80	nan

Details

sample63.0ms

simplify3.0ms

prune4.0ms

localize23.0ms

rewrite27.0ms

series69.0ms

simplify56.0ms

prune221.0ms

localize22.0ms

rewrite22.0ms

series58.0ms

simplify146.0ms

prune214.0ms

localize32.0ms

rewrite13.0ms

series67.0ms

simplify87.0ms

prune192.0ms

localize23.0ms

rewrite47.0ms

series70.0ms

simplify95.0ms

prune248.0ms

regimes887.0ms

bsearch74.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling