Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	256×	body	80	valid
0.0hr	221×	body	80	nan

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	23	16
1	23	16

prune0.0hr

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

localize0.0hr

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)))

rewrite0.0hr

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:

0.0hr	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.0hr	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0hr	(* (log base) (log base))
0.0hr	(sqrt (+ (* re re) (* im im)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.0hr	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0hr	(* (log base) (log base))
0.0hr	(sqrt (+ (* re re) (* im im)))

simplify0.0hr

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

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

localize0.0hr

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)))

rewrite0.0hr

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:

0.0hr	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0hr	(* (log base) (log base))
0.0hr	(* (log base) (log base))
0.0hr	(sqrt (+ (* re re) (* im im)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0hr	(* (log base) (log base))
0.0hr	(* (log base) (log base))
0.0hr	(sqrt (+ (* re re) (* im im)))

simplify0.0hr

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (0.0hr)

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

prune0.0hr

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

localize0.0hr

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)))

rewrite0.0hr

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:

0.0hr	(* (log base) (log base))
0.0hr	(cbrt base)
0.0hr	(cbrt base)
0.0hr	(sqrt (+ (* re re) (* im im)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (log base) (log base))
0.0hr	(cbrt base)
0.0hr	(cbrt base)
0.0hr	(sqrt (+ (* re re) (* im im)))

simplify0.0hr

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (0.0hr)

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

prune0.0hr

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

localize0.0hr

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)))

rewrite0.0hr

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:

0.0hr	(* (/ 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)))))
0.0hr	(* (log base) (log base))
0.0hr	(* (log base) (log base))
0.0hr	(sqrt (+ (* re re) (* im im)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (/ 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)))))
0.0hr	(* (log base) (log base))
0.0hr	(* (log base) (log base))
0.0hr	(sqrt (+ (* re re) (* im im)))

simplify0.0hr

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

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

regimes0.0hr

Accuracy

58.8% (10.1b remaining)

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

bsearch0.0hr

Steps

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

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

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

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	8000×	body	80	valid
0.0hr	7851×	body	80	nan

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling