Details

sample61.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
19.0ms	210×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	16
1	52	16
2	68	16
3	88	16
4	102	16
5	106	16
6	106	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: 30.8b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (atan2 im re) (log base))
0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

4.0ms	(* (atan2 im re) (log base))
10.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (atan2 im re) (log base))
40.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	466	1254
1	1924	1122
2	5002	1081

prune402.0ms

Filtered

129 candidates to 89 candidates (69.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	122	7	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	7	130

Merged error: 0.1b

Counts

130 → 7

localize6.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (log base))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

7.0ms

(/ (atan2 im re) (log base))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(/ (atan2 im re) (log base))

simplify56.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	105	215
1	272	201
2	673	200
3	1915	198
4	5002	196

prune106.0ms

Filtered

36 candidates to 24 candidates (66.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	30	6	36
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	33	10	43

Merged error: 0.0b

Counts

43 → 10

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ 1 (log base))
0.3b	(* (atan2 im re) (/ 1 (log base)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`associate-r`
15×	`add-exp-log`
12×	`pow1`
9×	`add-cbrt-cube`
7×	`log-pow`
4×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 78

Calls

2 calls:

3.0ms	(/ 1 (log base))
8.0ms	(* (atan2 im re) (/ 1 (log base)))

series187.0ms

Counts

2 → 6

Calls

2 calls:

153.0ms	(/ 1 (log base))
34.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	210	419
1	833	361
2	2681	319
3	5001	312

prune131.0ms

Filtered

84 candidates to 43 candidates (51.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`pow1`
12×	`log-prod`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-r`
7×	`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×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `flip3--` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `div-inv`

Counts

3 → 99

Calls

3 calls:

4.0ms	(* (atan2 im re) (log base))
9.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (log base) (log base))

series209.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* (atan2 im re) (log base))
33.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
149.0ms	(* (log base) (log base))

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	379	1007
1	1679	893
2	5002	851

prune255.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	107	11	118

Merged error: 0b

Counts

118 → 11

regimes196.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	4
1	11	4

end0.0ms

sample1.9s

Algorithm

intervals

Results

796.0ms	8000×	body	80	valid
733.0ms	8056×	body	80	nan