Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
17.0ms	266×	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 (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: 27.5b

Counts

2 → 1

localize22.0ms

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))
25.4b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-commutative`
5×	`hypot-def`
3×	`flip3-+` `flip-+`
2×	`pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`+-commutative` `pow2` `frac-2neg` `associate-l` `clear-num` `log-pow` `div-inv`

Counts

4 → 19

Calls

4 calls:

9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
3.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(* (log base) (log base))
5.0ms	(sqrt (+ (* re re) (* im im)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
91.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
149.0ms	(* (log base) (log base))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	229	206
1	701	198
2	2482	194
3	5002	186

prune117.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 0.2b

Counts

32 → 8

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`pow2` `frac-2neg` `clear-num` `div-inv`

Counts

3 → 10

Calls

3 calls:

8.0ms	(/ (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
2.0ms	(* (log (hypot im re)) (log base))
3.0ms	(* (log base) (log base))

series356.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(/ (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
100.0ms	(* (log (hypot im re)) (log base))
148.0ms	(* (log base) (log base))

simplify59.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	162	145
1	518	138
2	2015	136
3	5001	128

prune82.0ms

Filtered

19 candidates to 15 candidates (78.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	12	7	19
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	17	10	27

Merged error: 0.1b

Counts

27 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/r/`
4×	`flip3-+` `clear-num` `flip-+` `associate-/l/`
3×	`frac-2neg` `associate-/r*` `div-inv`
2×	`*-commutative`
1×	`pow2` `remove-double-div` `inv-pow`

Counts

4 → 23

Calls

4 calls:

8.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0))))
8.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))
2.0ms	(* (log (hypot im re)) (log base))
3.0ms	(* (log base) (log base))

series514.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0))))
139.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))
96.0ms	(* (log (hypot im re)) (log base))
148.0ms	(* (log base) (log base))

simplify99.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	210	275
1	747	261
2	3580	237
3	5001	230

prune154.0ms

Filtered

35 candidates to 27 candidates (77.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	29	6	35
Fresh	4	4	8
Picked	1	0	1
Done	1	0	1
Total	35	10	45

Merged error: 0.0b

Counts

45 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.4b	(* (/ 1 (fma 0.0 0.0 (pow (log base) 2))) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (hypot im re)) (log base))
0.5b	(pow (log base) 2)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times`
4×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
3×	`associate-*l/`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-r/` `-commutative` `div-inv`
1×	`pow-to-exp` `associate-l` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 25

Calls

4 calls:

2.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
7.0ms	(* (/ 1 (fma 0.0 0.0 (pow (log base) 2))) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))
2.0ms	(* (log (hypot im re)) (log base))
2.0ms	(pow (log base) 2)

series729.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
274.0ms	(* (/ 1 (fma 0.0 0.0 (pow (log base) 2))) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))
96.0ms	(* (log (hypot im re)) (log base))
145.0ms	(pow (log base) 2)

simplify36.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	269	391
1	1143	388
2	5001	388

prune112.0ms

Filtered

37 candidates to 26 candidates (70.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	37	10	47

Merged error: 0.0b

Counts

47 → 10

regimes237.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	12
1	23	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

686.0ms	8000×	body	80	valid
549.0ms	8159×	body	80	nan