Details

sample77.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
25.0ms	277×	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

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: 34.8b

Counts

2 → 1

localize19.0ms

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))
32.2b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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)))

series67.0ms

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))
16.0ms	(* (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

prune222.0ms

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: 7.3b

Counts

123 → 13

localize22.0ms

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))
32.2b	(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:

23.0ms	(* (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)))

simplify146.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (138.0ms)

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

prune213.0ms

Filtered

127 candidates to 71 candidates (44.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	124	16	140

Merged error: 7.3b

Counts

140 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
32.2b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`pow1`
23×	`add-cube-cbrt`
12×	`add-exp-log` `log-prod`
10×	`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×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `rec-exp` `pow-flip` `frac-2neg` `pow-plus` `1-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `inv-pow`

Counts

4 → 112

Calls

4 calls:

5.0ms	(/ 1 (+ (* (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:

25.0ms	(/ 1 (+ (* (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)))

simplify48.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	390	927
1	1463	839
2	5002	778

prune186.0ms

Filtered

124 candidates to 69 candidates (44.4%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	120	20	140

Merged error: 7.3b

Counts

140 → 20

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
32.2b	(sqrt (+ (* re re) (* im im)))
32.2b	(sqrt (+ (* re re) (* im im)))
32.2b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`prod-exp` `cbrt-unprod`
6×	`sqrt-div`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-plus`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 91

Calls

4 calls:

10.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify110.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	339	1175
1	1106	998
2	4574	894
3	5002	894

prune105.0ms

Filtered

103 candidates to 63 candidates (38.8%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	17	17
Picked	0	1	1
Done	0	2	2
Total	102	21	123

Merged error: 7.3b

Counts

123 → 21

regimes648.0ms

Accuracy

56.5% (10.6b remaining)

Error of 17.7b against oracle of 7.2b and baseline of 31.5b

bsearch176.0ms

Steps

Iters	Range		Point
8	1.3938877395240674e+106	4.847750330327718e+109	1.427812133242356e+109
6	1.511438345790827e-253	7.823438580998689e-253	4.21081843927483e-253
9	-6.93456016491827e-231	-1.3255659656892363e-238	-1.7686052380030963e-238
8	-4.2412295018571275e+93	-6.552564865654721e+89	-2.495557459662749e+92

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	80
1	76	80
2	76	80

end0.0ms

sample2.0s

Algorithm

intervals

Results

732.0ms	8000×	body	80	valid
701.0ms	8113×	body	80	nan

Details

sample77.0ms

simplify3.0ms

prune4.0ms

localize19.0ms

rewrite29.0ms

series67.0ms

simplify57.0ms

prune222.0ms

localize22.0ms

rewrite23.0ms

series58.0ms

simplify146.0ms

prune213.0ms

localize21.0ms

rewrite23.0ms

series66.0ms

simplify48.0ms

prune186.0ms

localize24.0ms

rewrite24.0ms

series54.0ms

simplify110.0ms

prune105.0ms

regimes648.0ms

bsearch176.0ms

simplify3.0ms

end0.0ms

sample2.0s

Profiling