Details

sample74.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
21.0ms	250×	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

prune6.0ms

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: 33.2b

Counts

2 → 1

localize18.0ms

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))
0.6b	(* (log base) (log base))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

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)))

series65.0ms

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)))
21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

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

prune687.0ms

Filtered

122 candidates to 80 candidates (34.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	13	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 7.2b

Counts

123 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log base) (log base)) (* 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))
0.6b	(* (log base) (log base))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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

series86.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (+ (* (log base) (log base)) (* 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))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	464	1397
1	1754	1281
2	5002	1229

prune847.0ms

Filtered

122 candidates to 80 candidates (34.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	117	18	135

Merged error: 7.2b

Counts

135 → 18

localize25.0ms

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))
0.6b	(* (log base) (log base))
30.7b	(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:

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

series66.0ms

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)))

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	457	1398
1	1716	1276
2	5001	1225

prune1.1s

Filtered

122 candidates to 80 candidates (34.4%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	122	18	140

Merged error: 7.2b

Counts

140 → 18

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

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)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify148.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	273	769
1	973	677
2	4633	614
3	5001	580

prune784.0ms

Filtered

127 candidates to 71 candidates (44.1%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	2	13	15
Picked	0	1	1
Done	1	1	2
Total	126	19	145

Merged error: 7.1b

Counts

145 → 19

regimes892.0ms

Accuracy

57% (10.7b remaining)

Error of 18.0b against oracle of 7.4b and baseline of 32.2b

bsearch321.0ms

Steps

Iters	Range		Point
8	5.936133990141283e+82	9.555849306330013e+86	2.2360511850626944e+85
6	5.0919682425458094e-191	7.285182887723109e-190	4.084191447942957e-190
8	-1.9703772701366753e-306	2.12138673346124e-307	-1.2300165181090967e-307
8	-24776207428773.418	-5704240281.847295	-24361133460477.875

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	54
1	64	54
2	64	54

end0.0ms

sample1.9s

Algorithm

intervals

Results

711.0ms	8000×	body	80	valid
649.0ms	7842×	body	80	nan

Details

sample74.0ms

simplify3.0ms

prune6.0ms

localize18.0ms

rewrite28.0ms

series65.0ms

simplify57.0ms

prune687.0ms

localize23.0ms

rewrite25.0ms

series86.0ms

simplify57.0ms

prune847.0ms

localize25.0ms

rewrite26.0ms

series66.0ms

simplify56.0ms

prune1.1s

localize22.0ms

rewrite21.0ms

series56.0ms

simplify148.0ms

prune784.0ms

regimes892.0ms

bsearch321.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling