Details

sample24.0ms

Algorithm

intervals

Results

15.0ms

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

prune3.0ms

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: 32.1b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

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

series167.0ms

Counts

2 → 6

Calls

2 calls:

132.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify128.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (120.0ms)

Iter	Nodes	Cost
0	221	664
1	556	631
2	1309	628
3	4047	628
4	5001	627

prune179.0ms

Filtered

69 candidates to 45 candidates (65.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 6.9b

Counts

70 → 12

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
30.8b	(log (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
82×	`add-sqr-sqrt`
54×	`sqrt-prod`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 153

Calls

3 calls:

27.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series499.0ms

Counts

3 → 9

Calls

3 calls:

272.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
181.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
46.0ms	(log (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	528	2082
1	2065	1915
2	5001	1832

prune346.0ms

Filtered

162 candidates to 94 candidates (58.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	152	10	162
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	160	14	174

Merged error: 6.8b

Counts

174 → 14

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

15.6b

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

16.5b

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`times-frac`
39×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-unpow` `associate-l` `sqrt-prod`
21×	`log-prod`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`log-pow` `add-cbrt-cube`
7×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `sqr-pow`
3×	`rem-log-exp` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `pow-pow` `div-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 117

Calls

3 calls:

13.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

4.0ms

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

8.0ms

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

series973.0ms

Counts

3 → 9

Calls

3 calls:

386.0ms

(* (/ 1/2 (sqrt (log 10.0))) (log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))))

284.0ms

(log (pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0)))))

302.0ms

(pow (+ (* re re) (* im im)) (/ 1 (sqrt (log 10.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	463	1701
1	1990	1501
2	5001	1318

prune309.0ms

Filtered

126 candidates to 79 candidates (62.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	123	17	140

Merged error: 6.8b

Counts

140 → 17

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
0.4b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
30.8b	(log (+ (* re re) (* im im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-prod`
112×	`times-frac`
107×	`add-sqr-sqrt`
69×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-l`
42×	`pow1`
33×	`associate-r`
31×	`log-pow`
21×	`add-exp-log`
20×	`add-cbrt-cube`
12×	`unswap-sqr`
10×	`sqrt-div`
7×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`frac-times` `associate-*r/`
4×	`log-div` `pow-prod-down` `associate-l/` `div-inv` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `log-prod` `div-exp`
2×	`flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`frac-2neg` `rem-log-exp` `clear-num`

Counts

4 → 207

Calls

4 calls:

23.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
27.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
7.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series924.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
454.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
194.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
46.0ms	(log (+ (* re re) (* im im)))

simplify86.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	640	3173
1	2753	2921
2	5002	2883

prune523.0ms

Filtered

219 candidates to 136 candidates (62.1%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	4	11	15
Picked	0	1	1
Done	0	1	1
Total	217	19	236

Merged error: 6.7b

Counts

236 → 19

regimes945.0ms

Accuracy

56% (10.8b remaining)

Error of 18.3b against oracle of 7.5b and baseline of 32.1b

bsearch190.0ms

Steps

Iters	Range		Point
8	2.1558392991063154e+98	3.0943356273139873e+102	2.1537425348704007e+102
9	-1.0921927090926265e-299	-4.707778381284133e-306	-7.851329880982983e-304
6	-6.699760191485107e-158	-1.388315075739649e-158	-1.4047799893311319e-158
9	-5.7624267828213205e+137	-6.4141430665981575e+128	-9.314131480659566e+128

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	64
1	70	64

end0.0ms

sample613.0ms

Algorithm

intervals

Results

464.0ms

8000×

body

valid