Details

sample75.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
21.0ms	236×	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: 32.9b

Counts

2 → 1

localize19.0ms

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)))
0.3b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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:

9.0ms	(/ (- (* (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))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- (* (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)))

simplify57.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (44.0ms)

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

prune214.0ms

Filtered

75 candidates to 120 candidates (-60.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	107	13	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	13	121

Merged error: 0.1b

Counts

121 → 13

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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:

9.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(/ (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	941
1	1467	819
2	4142	698
3	5001	698

prune133.0ms

Filtered

37 candidates to 98 candidates (-164.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	93	18	111

Merged error: 0.0b

Counts

111 → 18

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (/ 1 base))
0.3b	(/ (neg (atan2 im re)) (log (/ 1 base)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
41×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`log-pow`
26×	`pow1`
21×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`log-prod`
12×	`pow-flip` `inv-pow`
10×	`associate-/l*`
9×	`add-exp-log`
7×	`neg-mul-1`
6×	`associate-/r*`
4×	`rem-log-exp` `add-cbrt-cube`
3×	`div-exp`
2×	`div-inv` `add-log-exp`
1×	`cbrt-undiv` `neg-sub0` `log-div` `rec-exp` `frac-2neg` `1-exp` `div-sub` `distribute-frac-neg` `log-rec` `clear-num`

Counts

2 → 119

Calls

2 calls:

3.0ms	(log (/ 1 base))
6.0ms	(/ (neg (atan2 im re)) (log (/ 1 base)))

series24.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(log (/ 1 base))
13.0ms	(/ (neg (atan2 im re)) (log (/ 1 base)))

simplify96.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	334	929
1	1125	892
2	4345	844
3	5002	830

prune157.0ms

Filtered

65 candidates to 125 candidates (-92.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	9	8	17
Picked	1	0	1
Done	0	0	0
Total	129	14	143

Merged error: 0.0b

Counts

143 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (neg (atan2 im re)) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
0.3b	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
0.6b	(cbrt (/ 1 base))
0.6b	(cbrt (/ 1 base))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
86×	`*-un-lft-identity`
74×	`add-sqr-sqrt` `add-cube-cbrt`
65×	`cbrt-prod`
48×	`log-prod`
32×	`associate-+l+`
24×	`distribute-rgt-out`
21×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
16×	`pow1` `distribute-rgt-in` `associate-+r+` `distribute-lft-in`
12×	`distribute-lft1-in` `log-pow`
10×	`associate-/l*`
7×	`neg-mul-1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `div-inv`
5×	`add-log-exp`
3×	`cbrt-div`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `log-div` `frac-2neg` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `sum-log`

Counts

4 → 199

Calls

4 calls:

10.0ms	(/ (neg (atan2 im re)) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
13.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
2.0ms	(cbrt (/ 1 base))
3.0ms	(cbrt (/ 1 base))

series113.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (neg (atan2 im re)) (+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base)))))
42.0ms	(+ (* 2 (log (cbrt (/ 1 base)))) (log (cbrt (/ 1 base))))
21.0ms	(cbrt (/ 1 base))
22.0ms	(cbrt (/ 1 base))

simplify133.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	541	2363
1	1388	2122
2	4533	1935
3	5002	1874

prune376.0ms

Filtered

154 candidates to 211 candidates (-37.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	206	5	211
Fresh	6	7	13
Picked	0	1	1
Done	0	0	0
Total	212	13	225

Merged error: 0.0b

Counts

225 → 13

regimes422.0ms

Accuracy

0% (0.4b 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	19	11
1	19	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

760.0ms	8000×	body	80	valid
589.0ms	6656×	body	80	nan

Details

sample75.0ms

simplify9.0ms

prune4.0ms

localize19.0ms

rewrite25.0ms

series44.0ms

simplify57.0ms

prune214.0ms

localize9.0ms

rewrite14.0ms

series11.0ms

simplify67.0ms

prune133.0ms

localize8.0ms

rewrite13.0ms

series24.0ms

simplify96.0ms

prune157.0ms

localize12.0ms

rewrite36.0ms

series113.0ms

simplify133.0ms

prune376.0ms

regimes422.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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