Details

sample74.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
22.0ms	257×	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

prune10.0ms

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: 31.6b

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))
29.1b	(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))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (* (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)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

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

prune736.0ms

Filtered

122 candidates to 80 candidates (34.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	106	16	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	16	123

Merged error: 6.7b

Counts

123 → 16

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	176	496
1	464	476
2	1323	470
3	5001	457

prune795.0ms

Filtered

73 candidates to 60 candidates (17.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	73	16	89

Merged error: 6.7b

Counts

89 → 16

localize25.0ms

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))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

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:

30.0ms	(* (/ 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)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (/ 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)))))
14.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify99.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	687	3341
1	3728	2983
2	5001	2817

prune989.0ms

Filtered

186 candidates to 102 candidates (45.2%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	183	19	202

Merged error: 6.6b

Counts

202 → 19

localize31.0ms

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)
29.1b	(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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
21.0ms	(cbrt base)
21.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (48.0ms)

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

prune449.0ms

Filtered

77 candidates to 55 candidates (28.6%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	14	16
Picked	1	0	1
Done	0	2	2
Total	77	19	96

Merged error: 6.6b

Counts

96 → 19

regimes897.0ms

Accuracy

56.3% (10.5b remaining)

Error of 18.1b against oracle of 7.5b and baseline of 31.7b

bsearch246.0ms

Steps

Iters	Range		Point
3	1.271206889782828e+124	1.59796910122065e+124	1.4550106337166028e+124
1	3.2435519224687896e-248	3.3776482887491227e-248	3.3441241971790394e-248
7	-2.182942072178726e-246	-1.163006954732957e-247	-1.972444937254012e-246
10	-6.009142246337554e+160	-4.091974005961926e+146	-2.4647497111965144e+148

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	87
1	86	87
2	86	87

end0.0ms

sample2.0s

Algorithm

intervals

Results

714.0ms	8000×	body	80	valid
654.0ms	7848×	body	80	nan

Details

sample74.0ms

simplify3.0ms

prune10.0ms

localize20.0ms

rewrite27.0ms

series69.0ms

simplify59.0ms

prune736.0ms

localize26.0ms

rewrite19.0ms

series38.0ms

simplify51.0ms

prune795.0ms

localize25.0ms

rewrite50.0ms

series66.0ms

simplify99.0ms

prune989.0ms

localize31.0ms

rewrite13.0ms

series69.0ms

simplify57.0ms

prune449.0ms

regimes897.0ms

bsearch246.0ms

simplify3.0ms

end0.0ms

sample2.0s

Profiling