Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune2.0ms

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: 31.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`log-pow`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1` `pow1/2` `associate-/l*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `associate-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`log-div` `div-sub`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 74

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
133.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	256	741
1	895	697
2	2846	694
3	5001	694

prune208.0ms

Filtered

83 candidates to 55 candidates (66.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	68	15	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	15	84

Merged error: 7.2b

Counts

84 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.5b	(/ (log 10.0) (log (+ (* re re) (* im im))))
29.9b	(log (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
47×	`pow1`
43×	`log-pow`
24×	`associate-/r*`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`log-prod`
2×	`log-div` `frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `rem-log-exp` `sum-log` `associate-/r/`

Counts

4 → 159

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
6.0ms	(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
4.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
4.0ms	(log (+ (* re re) (* im im)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
131.0ms	(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
120.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
49.0ms	(log (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	496	1907
1	2084	1806
2	5002	1803

prune338.0ms

Filtered

171 candidates to 109 candidates (63.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	164	7	171
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	174	12	186

Merged error: 7.1b

Counts

186 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
0.4b	(* (sqrt 1/2) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
0.5b	(/ (log 10.0) (log (+ (* re re) (* im im))))
29.9b	(log (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

476×	`times-frac`
249×	`add-sqr-sqrt`
217×	`add-cube-cbrt` `*-un-lft-identity`
135×	`sqrt-prod`
125×	`associate-r`
121×	`pow1`
115×	`log-pow`
24×	`associate-/r*`
21×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`div-inv`
10×	`associate-/l*` `unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l`
4×	`add-log-exp`
3×	`log-prod` `prod-exp` `cbrt-unprod`
2×	`log-div` `frac-2neg` `clear-num` `associate-/r/`
1×	`flip3-+` `associate-r/` `rem-log-exp` `pow-prod-down` `-commutative` `flip-+`

Counts

4 → 368

Calls

4 calls:

8.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
36.0ms	(* (sqrt 1/2) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
4.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
4.0ms	(log (+ (* re re) (* im im)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
210.0ms	(* (sqrt 1/2) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
120.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
51.0ms	(log (+ (* re re) (* im im)))

simplify127.0ms

Algorithm

egg-herbie

Counts

380 → 380

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	867	4966
1	4131	4649
2	5001	4634

prune619.0ms

Filtered

380 candidates to 185 candidates (48.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	374	6	380
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	376	16	392

Merged error: 7.0b

Counts

392 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (log 10.0) (log (+ (* re re) (* im im))))
0.7b	(cbrt (pow (/ (log 10.0) (log (+ (* re re) (* im im)))) 3))
0.8b	(pow (/ (log 10.0) (log (+ (* re re) (* im im)))) 3)
29.9b	(log (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`pow1`
46×	`cbrt-prod`
43×	`log-pow`
40×	`unpow-prod-down` `cube-prod`
10×	`add-exp-log`
9×	`add-cbrt-cube`
5×	`div-inv`
4×	`associate-/r` `associate-/l` `add-log-exp`
3×	`pow-unpow` `log-prod`
2×	`cbrt-undiv` `cube-div` `cube-mult` `log-div` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `rem-log-exp` `clear-num` `rem-cbrt-cube` `flip-+`

Counts

4 → 166

Calls

4 calls:

4.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
6.0ms	(cbrt (pow (/ (log 10.0) (log (+ (* re re) (* im im)))) 3))
6.0ms	(pow (/ (log 10.0) (log (+ (* re re) (* im im)))) 3)
4.0ms	(log (+ (* re re) (* im im)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
127.0ms	(cbrt (pow (/ (log 10.0) (log (+ (* re re) (* im im)))) 3))
203.0ms	(pow (/ (log 10.0) (log (+ (* re re) (* im im)))) 3)
49.0ms	(log (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	461	1932
1	1969	1812
2	5001	1804

prune269.0ms

Filtered

178 candidates to 84 candidates (47.2%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	175	3	178
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	175	19	194

Merged error: 7.0b

Counts

194 → 19

regimes698.0ms

Accuracy

58.1% (10.4b remaining)

Error of 17.5b against oracle of 7.2b and baseline of 31.9b

bsearch152.0ms

Steps

Iters	Range		Point
8	4.322309339102123e+90	3.658317714297881e+94	3.51842597900795e+92
7	8.554373099101626e-290	2.7552220295623955e-288	1.1868703169839283e-289
9	-2.2365661558835998e-197	-6.33701187792121e-204	-3.196517835772386e-203
5	-2.1804788916246727e+94	-8.504827414387646e+93	-2.1469124341159173e+94

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	46
1	58	46

end0.0ms

sample494.0ms

Algorithm

intervals

Results

353.0ms

8000×

body

valid

Details

sample20.0ms

simplify4.0ms

prune2.0ms

localize10.0ms

rewrite16.0ms

series200.0ms

simplify93.0ms

prune208.0ms

localize11.0ms

rewrite24.0ms

series327.0ms

simplify68.0ms

prune338.0ms

localize13.0ms

rewrite74.0ms

series541.0ms

simplify127.0ms

prune619.0ms

localize14.0ms

rewrite26.0ms

series507.0ms

simplify72.0ms

prune269.0ms

regimes698.0ms

bsearch152.0ms

simplify2.0ms

end0.0ms

sample494.0ms

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