Details

sample66.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
17.0ms	211×	body	80	nan

simplify4.0ms

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: 31.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.6b	(* (log base) (log base))
29.2b	(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:

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
28.0ms	(/ (+ (* (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)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune229.0ms

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: 6.6b

Counts

123 → 14

localize24.0ms

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))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

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

simplify151.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (140.0ms)

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

prune212.0ms

Filtered

127 candidates to 71 candidates (44.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	125	16	141

Merged error: 6.6b

Counts

141 → 16

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt base)
0.5b	(cbrt base)
0.6b	(* (log base) (log base))
29.2b	(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:

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt base)
22.0ms	(cbrt base)
16.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (83.0ms)

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

prune191.0ms

Filtered

85 candidates to 53 candidates (37.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	85	16	101

Merged error: 6.6b

Counts

101 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log base) (log base))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	185	471
1	587	433
2	2451	416
3	5002	399

prune106.0ms

Filtered

93 candidates to 63 candidates (32.3%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	93	16	109

Merged error: 6.6b

Counts

109 → 16

regimes676.0ms

Accuracy

56.4% (10.7b remaining)

Error of 17.9b against oracle of 7.2b and baseline of 31.8b

bsearch172.0ms

Steps

Iters	Range		Point
3	8.114463514765957e+44	1.0878947445748038e+45	1.0706167200061657e+45
9	-3.4463461352207073e-250	-2.3036737429460782e-256	-2.4570524722393267e-253
8	-9.091281933402102e-158	-2.4160831221231224e-161	-2.4573759973696178e-161
10	-9.890537988017573e+164	-1.5954363105956547e+149	-1.6216658838049843e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	103
1	79	103

end0.0ms

sample2.0s

Algorithm

intervals

Results

706.0ms	8000×	body	80	valid
666.0ms	8036×	body	80	nan

Details

sample66.0ms

simplify4.0ms

prune4.0ms

localize19.0ms

rewrite27.0ms

series71.0ms

simplify58.0ms

prune229.0ms

localize24.0ms

rewrite23.0ms

series58.0ms

simplify151.0ms

prune212.0ms

localize35.0ms

rewrite13.0ms

series67.0ms

simplify91.0ms

prune191.0ms

localize24.0ms

rewrite19.0ms

series36.0ms

simplify83.0ms

prune106.0ms

regimes676.0ms

bsearch172.0ms

simplify2.0ms

end0.0ms

sample2.0s

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