Details

sample81.0ms

Algorithm

intervals

Results

24.0ms	295×	body	80	nan
23.0ms	256×	body	80	valid

simplify11.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.8b

Counts

2 → 1

localize22.0ms

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)))

rewrite24.0ms

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))
4.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms

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)))
8.0ms	(* (atan2 im re) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (45.0ms)

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

prune182.0ms

Filtered

120 candidates to 75 candidates (37.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	9	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Merged error: 0.1b

Counts

121 → 9

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify67.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	355	942
1	1366	819
2	3942	698
3	5001	698

prune103.0ms

Filtered

98 candidates to 37 candidates (62.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	94	13	107

Merged error: 0.0b

Counts

107 → 13

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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:

5.0ms	(/ 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))

simplify105.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (17.0ms)

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

prune101.0ms

Filtered

79 candidates to 41 candidates (48.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	78	14	92

Merged error: 0.0b

Counts

92 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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:

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

series76.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (pow (log base) 3))
13.0ms	(* (cbrt (/ 1 (pow (log base) 3))) (atan2 im re))
17.0ms	(cbrt (/ 1 (pow (log base) 3)))
21.0ms	(pow (log base) 3)

simplify54.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 2 (35.0ms)

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

prune190.0ms

Filtered

247 candidates to 101 candidates (59.1%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	3	8	11
Picked	0	1	1
Done	0	2	2
Total	247	14	261

Merged error: 0b

Counts

261 → 14

regimes362.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	14	5
2	14	5

end0.0ms

sample2.2s

Algorithm

intervals

Results

905.0ms	10867×	body	80	nan
728.0ms	8000×	body	80	valid

Details

sample81.0ms

simplify11.0ms

prune4.0ms

localize22.0ms

rewrite24.0ms

series41.0ms

simplify56.0ms

prune182.0ms

localize8.0ms

rewrite13.0ms

series11.0ms

simplify67.0ms

prune103.0ms

localize7.0ms

rewrite14.0ms

series29.0ms

simplify105.0ms

prune101.0ms

localize11.0ms

rewrite37.0ms

series76.0ms

simplify54.0ms

prune190.0ms

regimes362.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling