Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	265×	body	80	nan
18.0ms	256×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	16
1	33	16
2	33	16

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 35.0b

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))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite87.0ms

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:

43.0ms	(/ (+ (* (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))
17.0ms	(sqrt (+ (* re re) (* im im)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
100.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
156.0ms	(* (log base) (log base))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	468	3824
1	1793	3485
2	5001	3407

prune428.0ms

Filtered

285 candidates to 104 candidates (36.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	273	12	285
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	274	12	286

Merged error: 0.2b

Counts

286 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (* (log (sqrt base)) (* 1 (log (hypot re im)))) (* (log (sqrt base)) (* 1 (log (hypot re im))))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt base)) (* 1 (log (hypot re im))))
0.4b	(* (log (sqrt base)) (* 1 (log (hypot re im))))
0.5b	(* (log base) (log base))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

1316×	`*-un-lft-identity`
820×	`distribute-lft-out`
694×	`associate-l`
357×	`pow1`
338×	`log-pow`
325×	`times-frac`
214×	`swap-sqr`
96×	`associate-r`
88×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`*-commutative`
30×	`log-prod`
28×	`distribute-rgt-out`
27×	`distribute-rgt-in` `distribute-lft-in`
25×	`associate-/l*`
22×	`add-exp-log`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
13×	`associate-/r*`
11×	`prod-exp`
7×	`pow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 523

Calls

4 calls:

137.0ms	(/ (+ (+ (* (log (sqrt base)) (* 1 (log (hypot re im)))) (* (log (sqrt base)) (* 1 (log (hypot re im))))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log (sqrt base)) (* 1 (log (hypot re im))))
10.0ms	(* (log (sqrt base)) (* 1 (log (hypot re im))))
5.0ms	(* (log base) (log base))

series815.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (+ (+ (* (log (sqrt base)) (* 1 (log (hypot re im)))) (* (log (sqrt base)) (* 1 (log (hypot re im))))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
178.0ms	(* (log (sqrt base)) (* 1 (log (hypot re im))))
175.0ms	(* (log (sqrt base)) (* 1 (log (hypot re im))))
163.0ms	(* (log base) (log base))

simplify162.0ms

Algorithm

egg-herbie

Counts

535 → 535

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	746	10218
1	3080	7269
2	5001	7173

prune623.0ms

Filtered

535 candidates to 120 candidates (22.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	523	12	535
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	532	15	547

Merged error: 0.0b

Counts

547 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (hypot (log base) 0.0) 1))
0.4b	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma 2 (* (log (sqrt base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
0.4b	(/ (fma 2 (* (log (sqrt base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
0.4b	(* (log (sqrt base)) (log (hypot re im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

277×	`times-frac`
276×	`add-sqr-sqrt`
236×	`*-un-lft-identity`
224×	`add-cube-cbrt`
212×	`associate-/r*`
171×	`frac-times`
106×	`associate-/l*`
85×	`add-exp-log`
58×	`associate-l`
47×	`div-exp`
36×	`clear-num`
34×	`frac-2neg` `add-cbrt-cube`
21×	`prod-exp` `div-inv`
20×	`associate-/r/`
19×	`associate-*l/`
18×	`1-exp`
17×	`associate-r` `unswap-sqr`
13×	`cbrt-undiv`
12×	`pow1`
9×	`rec-exp` `associate-*r/`
7×	`cbrt-unprod`
6×	`log-prod`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`pow-prod-down` `un-div-inv` `*-commutative` `remove-double-div`
1×	`pow-flip` `sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 469

Calls

4 calls:

7.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
33.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma 2 (* (log (sqrt base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
3.0ms	(/ (fma 2 (* (log (sqrt base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
5.0ms	(* (log (sqrt base)) (log (hypot re im)))

series1.5s

Counts

4 → 12

Calls

4 calls:

390.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
439.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma 2 (* (log (sqrt base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))
472.0ms	(/ (fma 2 (* (log (sqrt base)) (log (hypot re im))) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
179.0ms	(* (log (sqrt base)) (log (hypot re im)))

simplify121.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2186	8635
1	5001	7980

prune1.2s

Filtered

481 candidates to 233 candidates (48.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	476	5	481
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	485	11	496

Merged error: 0b

Counts

496 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt base)) (* 1 (log (hypot re im))))
0.5b	(* (log base) (log base))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
24×	`*-un-lft-identity`
22×	`associate-r`
20×	`add-cube-cbrt`
18×	`log-prod`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-exp-log` `associate-l`
11×	`add-cbrt-cube`
10×	`log-pow`
8×	`unswap-sqr`
6×	`cbrt-prod` `swap-sqr` `prod-exp`
4×	`expm1-log1p-u` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow1/3`
1×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `1-exp` `pow-sqr` `pow-prod-up`

Counts

4 → 116

Calls

4 calls:

10.0ms	(* (log (sqrt base)) (* 1 (log (hypot re im))))
5.0ms	(* (log base) (log base))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))

series613.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (log (sqrt base)) (* 1 (log (hypot re im))))
165.0ms	(* (log base) (log base))
133.0ms	(cbrt (hypot re im))
131.0ms	(cbrt (hypot re im))

simplify51.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	456	776
1	1524	680
2	5001	642

prune682.0ms

Filtered

128 candidates to 82 candidates (64.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Merged error: 0b

Counts

139 → 10

regimes275.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	31
1	37	31

end0.0ms

sample1.5s

Algorithm

intervals

Results

578.0ms	8000×	body	80	valid
539.0ms	7955×	body	80	nan