Details

sample50.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
15.0ms	234×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	33	16
2	33	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: 34.6b

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)))
0.5b	(* (log base) (log base))
32.0b	(sqrt (+ (* re re) (* im im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

413×	`*-un-lft-identity`
189×	`distribute-lft-out`
182×	`associate-l`
117×	`times-frac`
111×	`pow1`
98×	`swap-sqr` `log-pow`
94×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
26×	`hypot-def`
13×	`associate-/r*`
12×	`log-prod` `*-commutative` `unswap-sqr`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-r` `sqrt-prod`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 273

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
39.0ms	(/ (+ (* (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))
21.0ms	(sqrt (+ (* re re) (* im im)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
107.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
153.0ms	(* (log base) (log base))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	468	3825
1	1797	3485
2	5001	3421

prune425.0ms

Filtered

285 candidates to 104 candidates (63.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	272	13	285
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	273	13	286

Merged error: 0.2b

Counts

286 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (exp (log (hypot re im)))) (log base))
0.4b	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
5.9b	(exp (log (hypot re im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

403×	`*-un-lft-identity`
184×	`distribute-lft-out`
180×	`associate-l`
117×	`times-frac`
111×	`pow1`
102×	`log-pow`
86×	`swap-sqr`
45×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
15×	`log-prod`
13×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`exp-prod` `associate-r`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-sum`
2×	`flip3-+` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `rem-exp-log` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 245

Calls

4 calls:

6.0ms	(* (log (exp (log (hypot re im)))) (log base))
44.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
2.0ms	(exp (log (hypot re im)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (log (exp (log (hypot re im)))) (log base))
117.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
155.0ms	(* (log base) (log base))
55.0ms	(exp (log (hypot re im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	427	3525
1	1603	2952
2	5002	2893

prune398.0ms

Filtered

257 candidates to 92 candidates (64.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	246	11	257
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	257	13	270

Merged error: 0.0b

Counts

270 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (hypot (log base) 0.0) 1))
0.3b	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.4b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

571×	`add-sqr-sqrt`
552×	`associate-/r*`
463×	`times-frac`
431×	`*-un-lft-identity`
374×	`add-cube-cbrt`
361×	`frac-times`
170×	`add-exp-log`
138×	`associate-/l*`
133×	`associate-l`
124×	`associate-r`
102×	`unswap-sqr`
93×	`div-exp`
62×	`prod-exp`
50×	`add-cbrt-cube`
46×	`clear-num`
44×	`frac-2neg`
41×	`1-exp`
31×	`div-inv`
28×	`*-commutative`
22×	`associate-/r/`
20×	`cbrt-undiv`
19×	`associate-r/` `associate-l/`
15×	`rec-exp`
13×	`cbrt-unprod`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`un-div-inv` `remove-double-div`
1×	`pow-flip` `pow-prod-down` `fma-udef` `inv-pow`

Counts

4 → 761

Calls

4 calls:

7.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
60.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
1.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
7.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

366.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
391.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
152.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
384.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))

simplify176.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	3155	13647
1	5001	12456

prune1.1s

Filtered

773 candidates to 287 candidates (62.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	767	6	773
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	775	11	786

Merged error: 0b

Counts

786 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.5b	(cbrt base)
0.5b	(cbrt base)
5.9b	(exp (log (hypot re im)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
524×	`distribute-lft-out`
508×	`associate-l`
207×	`times-frac`
173×	`pow1`
169×	`log-pow`
42×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`associate-/r*`
9×	`associate-/l*`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`log-prod` `exp-sum`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 301

Calls

4 calls:

76.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
3.0ms	(exp (log (hypot re im)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (+ (* (log (exp (log (hypot re im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
185.0ms	(cbrt base)
186.0ms	(cbrt base)
56.0ms	(exp (log (hypot re im)))

simplify86.0ms

Algorithm

egg-herbie

Counts

313 → 313

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	330	6836
1	1128	5868
2	5002	5759

prune391.0ms

Filtered

313 candidates to 77 candidates (75.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	312	1	313
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	314	10	324

Merged error: 0b

Counts

324 → 10

regimes299.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	22
1	31	22

end0.0ms

sample1.4s

Algorithm

intervals

Results

542.0ms	8000×	body	80	valid
507.0ms	7882×	body	80	nan