Details

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 46.875%

Guaranteed chance to sample good point: 88.149127%

Results

24.0ms	256×	body	80	valid
1.0ms	14×	body	80	nan

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	44	16
2	56	16
3	74	16
4	80	16
5	80	16

prune4.0ms

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: 31.8b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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×	`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--` `div-inv`

Counts

4 → 108

Calls

4 calls:

8.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (atan2 im re) (log base))
4.0ms	(* (log base) (log base))
3.0ms	(sqrt (+ (* re re) (* im im)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (atan2 im re) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	441	1237
1	1738	1127
2	5001	1101

prune194.0ms

Filtered

75 candidates to 120 candidates (-60.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 0.1b

Counts

121 → 10

localize9.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (/ (+ 0 (log base)) 1))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
93×	`*-un-lft-identity`
57×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`distribute-lft-out`
19×	`associate-/r*`
13×	`pow1`
12×	`log-pow`
8×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`div-exp` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
1×	`frac-2neg` `1-exp` `clear-num` `associate-/r/` `add-log-exp`

Counts

1 → 95

Calls

1 calls:

8.0ms

(/ (atan2 im re) (/ (+ 0 (log base)) 1))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(/ (atan2 im re) (/ (+ 0 (log base)) 1))

simplify68.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	355	941
1	1467	819
2	4142	698
3	5001	698

prune106.0ms

Filtered

37 candidates to 98 candidates (-164.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	97	11	108

Merged error: 0.0b

Counts

108 → 11

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (log base))
0.2b	(* (/ 1 (log base)) (atan2 im re))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 73

Calls

2 calls:

3.0ms	(/ 1 (log base))
7.0ms	(* (/ 1 (log base)) (atan2 im re))

series29.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(/ 1 (log base))
12.0ms	(* (/ 1 (log base)) (atan2 im re))

simplify136.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	202	403
1	785	345
2	1921	301
3	4509	301
4	5001	301

prune96.0ms

Filtered

40 candidates to 79 candidates (-97.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	78	12	90

Merged error: 0.0b

Counts

90 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (/ 1 (pow (log base) 3))) (atan2 im re))
0.3b	(/ 1 (pow (log base) 3))
0.6b	(cbrt (/ 1 (pow (log base) 3)))
0.7b	(pow (log base) 3)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
106×	`add-sqr-sqrt`
101×	`cbrt-prod`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
49×	`associate-l`
46×	`unpow-prod-down` `cube-prod`
29×	`pow1`
22×	`log-pow`
16×	`add-exp-log`
14×	`associate-/r*`
13×	`sqr-pow`
11×	`cube-mult` `unpow3`
10×	`unswap-sqr`
8×	`add-cbrt-cube`
6×	`div-exp`
4×	`pow-to-exp` `pow-exp` `add-log-exp`
3×	`rec-exp` `pow-unpow` `1-exp` `associate-r` `div-inv` `associate-/l*`
2×	`cbrt-div`
1×	`cbrt-undiv` `pow-flip` `pow-pow` `frac-2neg` `pow1/3` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `inv-pow` `rem-cube-cbrt`

Counts

4 → 235

Calls

4 calls:

12.0ms	(* (cbrt (/ 1 (pow (log base) 3))) (atan2 im re))
5.0ms	(/ 1 (pow (log base) 3))
5.0ms	(cbrt (/ 1 (pow (log base) 3)))
2.0ms	(pow (log base) 3)

series69.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (cbrt (/ 1 (pow (log base) 3))) (atan2 im re))
24.0ms	(/ 1 (pow (log base) 3))
16.0ms	(cbrt (/ 1 (pow (log base) 3)))
17.0ms	(pow (log base) 3)

simplify54.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	395	1664
1	1508	1363
2	5002	1312

prune186.0ms

Filtered

101 candidates to 247 candidates (-144.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	246	13	259

Merged error: 0.0b

Counts

259 → 13

regimes356.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b 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

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 46.875%

Guaranteed chance to sample good point: 88.149127%

Results

775.0ms	8000×	body	80	valid
43.0ms	480×	body	80	nan

Details

sample2.5s

simplify9.0ms

prune4.0ms

localize21.0ms

rewrite23.0ms

series40.0ms

simplify60.0ms

prune194.0ms

localize9.0ms

rewrite15.0ms

series10.0ms

simplify68.0ms

prune106.0ms

localize7.0ms

rewrite12.0ms

series29.0ms

simplify136.0ms

prune96.0ms

localize11.0ms

rewrite38.0ms

series69.0ms

simplify54.0ms

prune186.0ms

regimes356.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.6s

Profiling