Details

analyze432.0ms

Algorithm: search

sample41.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
2.0ms	27×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

prune5.0ms

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: 27.5b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
25.4b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
23.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	457	1397
1	1716	1276
2	5001	1225

prune246.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	107	15	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Merged error: 5.9b

Counts

123 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
25.4b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
32×	`add-cube-cbrt`
31×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 130

Calls

4 calls:

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
14.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	394	1641
1	1327	1515
2	5002	1483

prune293.0ms

Filtered

80 candidates to 142 candidates (-77.5%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	137	20	157

Merged error: 5.5b

Counts

157 → 20

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log base) (* 2 (log (cbrt base))))
0.6b	(cbrt base)
0.6b	(cbrt base)
25.4b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
18×	`cbrt-prod`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
4×	`associate-l` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `log-pow` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

6.0ms	(* (log base) (* 2 (log (cbrt base))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (log base) (* 2 (log (cbrt base))))
21.0ms	(cbrt base)
21.0ms	(cbrt base)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	352	650
1	916	597
2	3877	557
3	5001	534

prune216.0ms

Filtered

57 candidates to 92 candidates (-61.4%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	1	17	18
Picked	0	1	1
Done	0	1	1
Total	90	22	112

Merged error: 5.5b

Counts

112 → 22

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (log base) 3) (log base))
0.5b	(* (log base) (log base))
0.7b	(pow (log base) 3)
25.4b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`pow1`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`associate-l`
12×	`add-exp-log` `log-prod`
11×	`log-pow`
9×	`unpow-prod-down` `cube-prod` `add-cbrt-cube`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
5×	`unswap-sqr`
4×	`prod-exp` `add-log-exp`
3×	`pow-unpow` `sqrt-prod` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-plus` `sqrt-div` `unpow3` `pow-exp` `*-commutative` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `pow-sqr` `flip-+` `rem-cube-cbrt`

Counts

4 → 118

Calls

4 calls:

6.0ms	(* (pow (log base) 3) (log base))
4.0ms	(* (log base) (log base))
2.0ms	(pow (log base) 3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (pow (log base) 3) (log base))
14.0ms	(* (log base) (log base))
17.0ms	(pow (log base) 3)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	334	563
1	1778	487
2	5001	434

prune207.0ms

Filtered

68 candidates to 130 candidates (-91.2%)

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	1	18	19
Picked	0	1	1
Done	0	2	2
Total	128	24	152

Merged error: 5.5b

Counts

152 → 24

regimes1.1s

Accuracy

57.4% (10.5b remaining)

Error of 17.1b against oracle of 6.6b and baseline of 31.3b

bsearch487.0ms

Steps

Iters	Range		Point
9	2.9256188419951653e+84	4.284653959372798e+89	1.6493808279984082e+86
5	-1.2182869830826919e+90	-4.7827119556091316e+89	-6.045769334257274e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	49
1	87	49
2	88	49
3	88	49

end0.0ms

analyze425.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

771.0ms	8000×	body	80	valid
96.0ms	985×	body	80	nan

Details

analyze432.0ms

sample41.0ms

simplify3.0ms

prune5.0ms

localize19.0ms

rewrite25.0ms

series67.0ms

simplify57.0ms

prune246.0ms

localize23.0ms

rewrite27.0ms

series48.0ms

simplify49.0ms

prune293.0ms

localize30.0ms

rewrite15.0ms

series101.0ms

simplify90.0ms

prune216.0ms

localize30.0ms

rewrite20.0ms

series53.0ms

simplify71.0ms

prune207.0ms

regimes1.1s

bsearch487.0ms

simplify2.0ms

end0.0ms

analyze425.0ms

sample1.1s

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