Details

sample58.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
17.0ms	210×	body	80	nan

simplify6.0ms

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 (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: 30.9b

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))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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` `hypot-def` `div-inv`

Counts

4 → 119

Calls

4 calls:

14.0ms	(/ (+ (* (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)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
152.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	467	1408
1	1820	1268
2	5001	1220

prune444.0ms

Filtered

131 candidates to 95 candidates (72.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 0.2b

Counts

132 → 11

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`pow1`
12×	`log-prod`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-r` `associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`flip3-+` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

3 → 99

Calls

3 calls:

9.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log (hypot re im)) (log base))
5.0ms	(* (log base) (log base))

series361.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
100.0ms	(* (log (hypot re im)) (log base))
149.0ms	(* (log base) (log base))

simplify53.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	377	1035
1	1559	925
2	5002	895

prune337.0ms

Filtered

108 candidates to 73 candidates (67.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	95	13	108
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	105	14	119

Merged error: 0.0b

Counts

119 → 14

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
157×	`times-frac`
104×	`add-sqr-sqrt`
93×	`div-exp`
90×	`*-un-lft-identity`
85×	`add-cube-cbrt`
62×	`prod-exp`
50×	`add-cbrt-cube`
44×	`associate-l`
41×	`1-exp`
20×	`cbrt-undiv`
15×	`rec-exp`
14×	`associate-/r*`
13×	`cbrt-unprod`
11×	`div-inv`
7×	`pow1` `associate-r` `unswap-sqr`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 236

Calls

4 calls:

6.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
22.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
4.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

348.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
343.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))
151.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
251.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	940	3390
1	4239	2753
2	5001	2552

prune588.0ms

Filtered

248 candidates to 134 candidates (54.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	243	5	248
Fresh	7	6	13
Picked	0	1	1
Done	0	0	0
Total	250	12	262

Merged error: 0b

Counts

262 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

184×	`times-frac`
140×	`add-sqr-sqrt`
104×	`*-un-lft-identity`
96×	`add-cube-cbrt`
67×	`add-exp-log`
43×	`associate-l`
36×	`div-exp`
32×	`add-cbrt-cube`
16×	`associate-/l*`
15×	`prod-exp` `unswap-sqr`
14×	`div-inv`
13×	`cbrt-undiv` `associate-r`
10×	`pow1` `1-exp`
6×	`associate-/r*` `cbrt-unprod`
5×	`rec-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-flip` `frac-2neg` `clear-num` `inv-pow` `pow-div`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 225

Calls

4 calls:

3.0ms	(/ 1 (hypot (log base) 0.0))
6.0ms	(/ (/ 1 (hypot (log base) 0.0)) (hypot (log base) 0.0))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
19.0ms	(* (/ (/ 1 (hypot (log base) 0.0)) (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

335.0ms	(/ 1 (hypot (log base) 0.0))
385.0ms	(/ (/ 1 (hypot (log base) 0.0)) (hypot (log base) 0.0))
111.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
351.0ms	(* (/ (/ 1 (hypot (log base) 0.0)) (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 1))

simplify87.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	879	3262
1	4186	2722
2	5001	2596

prune568.0ms

Filtered

237 candidates to 143 candidates (60.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	235	2	237
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	239	10	249

Merged error: 0b

Counts

249 → 10

regimes260.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	20
1	29	20

end0.0ms

sample1.8s

Algorithm

intervals

Results

707.0ms	8000×	body	80	valid
668.0ms	8056×	body	80	nan