Details

sample77.0ms

Algorithm

intervals

Results

24.0ms	295×	body	80	nan
23.0ms	256×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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: 32.0b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
29.6b	(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:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
27.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms	(* (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	457	1397
1	1716	1276
2	5001	1225

prune226.0ms

Filtered

122 candidates to 80 candidates (34.4%)

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: 10.0b

Counts

123 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (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))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
32×	`add-cube-cbrt`
31×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 130

Calls

4 calls:

11.0ms	(/ (+ (* (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)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (+ (* (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))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	394	1641
1	1327	1515
2	5002	1483

prune251.0ms

Filtered

142 candidates to 80 candidates (43.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	138	18	156

Merged error: 9.5b

Counts

156 → 18

localize23.0ms

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 (sqrt base))) (* (log base) (log (sqrt base)))) (* 0.0 0.0)))
0.5b	(* (log base) (log (sqrt base)))
0.5b	(* (log base) (log (sqrt base)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

11.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (log (sqrt base))) (* (log base) (log (sqrt base)))) (* 0.0 0.0)))
5.0ms	(* (log base) (log (sqrt base)))
7.0ms	(* (log base) (log (sqrt base)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (log (sqrt base))) (* (log base) (log (sqrt base)))) (* 0.0 0.0)))
9.0ms	(* (log base) (log (sqrt base)))
9.0ms	(* (log base) (log (sqrt base)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify108.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	855	2068
1	4025	1869
2	5001	1841

prune234.0ms

Filtered

126 candidates to 87 candidates (31.0%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	15	16
Picked	0	1	1
Done	0	1	1
Total	126	18	144

Merged error: 9.5b

Counts

144 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(* (log base) (log base))
29.6b	(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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
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 base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
42.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	464	1397
1	1754	1281
2	5002	1234

prune129.0ms

Filtered

122 candidates to 80 candidates (34.4%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	4	11	15
Picked	0	1	1
Done	0	2	2
Total	121	19	140

Merged error: 9.5b

Counts

140 → 19

regimes753.0ms

Accuracy

60.4% (8.9b remaining)

Error of 18.2b against oracle of 9.3b and baseline of 31.8b

bsearch183.0ms

Steps

Iters	Range		Point
11	7.549299852457462e+80	5.4643443444538665e+107	6.095901045752572e+93
10	-3.3800619214856376e-209	-7.618934954794205e-221	-3.3341175859759176e-209
3	-8.404792506580255e-186	-6.680160172052255e-186	-6.755127795124206e-186
10	-2.0931088118525462e+161	-6.035010000962467e+147	-4.8496263671570084e+148

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	80
1	81	80
2	81	80

end0.0ms

sample2.2s

Algorithm

intervals

Results

909.0ms	10867×	body	80	nan
722.0ms	8000×	body	80	valid

Details

sample77.0ms

simplify8.0ms

prune4.0ms

localize19.0ms

rewrite26.0ms

series68.0ms

simplify57.0ms

prune226.0ms

localize24.0ms

rewrite28.0ms

series48.0ms

simplify55.0ms

prune251.0ms

localize23.0ms

rewrite31.0ms

series76.0ms

simplify108.0ms

prune234.0ms

localize20.0ms

rewrite28.0ms

series84.0ms

simplify59.0ms

prune129.0ms

regimes753.0ms

bsearch183.0ms

simplify3.0ms

end0.0ms

sample2.2s

Profiling