Details

analyze8.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample41.0ms

Algorithm

intervals

Results

26.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

prune7.0ms

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: 29.9b

Counts

2 → 1

localize20.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
27.6b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

13.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
7.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5218	1035

prune147.0ms

Filtered

46 candidates to 69 candidates (-50.0%)

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: 7.1b

Counts

70 → 12

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 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)))
28.7b	(log (+ (* re re) (* im im)))

rewrite39.0ms

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:

23.0ms	(* (/ 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)))

series49.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
21.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4936	2822
1	4936	2822

prune293.0ms

Filtered

96 candidates to 162 candidates (-68.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Merged error: 6.9b

Counts

174 → 11

localize19.0ms

Local error

Found 3 expressions with local error:

0.3b

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

14.0b

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

15.9b

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

rewrite27.0ms

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:

12.0ms

(* (/ 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)))))

7.0ms

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

series108.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms

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

33.0ms

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

34.0ms

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

simplify68.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4904	2099
1	4904	2099

prune257.0ms

Filtered

78 candidates to 126 candidates (-61.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	124	13	137

Merged error: 6.9b

Counts

137 → 13

localize14.0ms

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) 1) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
0.6b	(/ (log 10.0) (log (+ (* re re) (* im im))))
28.7b	(log (+ (* re re) (* im im)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

532×	`times-frac`
318×	`add-sqr-sqrt`
238×	`*-un-lft-identity`
228×	`add-cube-cbrt`
152×	`sqrt-prod`
125×	`associate-r`
121×	`pow1`
115×	`log-pow`
42×	`add-exp-log`
32×	`add-cbrt-cube`
25×	`unswap-sqr`
24×	`associate-/r*`
22×	`associate-l`
19×	`div-exp`
17×	`div-inv`
13×	`cbrt-undiv`
10×	`associate-/l*`
9×	`prod-exp`
6×	`cbrt-unprod`
4×	`add-log-exp`
3×	`log-prod` `1-exp`
2×	`log-div` `frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `flip3-+` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 410

Calls

4 calls:

8.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
53.0ms	(* (/ (sqrt 1/2) 1) (/ (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)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im)))))
25.0ms	(* (/ (sqrt 1/2) 1) (/ (sqrt 1/2) (/ (log 10.0) (log (+ (* re re) (* im im))))))
24.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
9.0ms	(log (+ (* re re) (* im im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4960	8322
1	4960	8322

prune561.0ms

Filtered

200 candidates to 422 candidates (-111.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	418	4	422
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	421	14	435

Merged error: 6.9b

Counts

435 → 14

regimes834.0ms

Accuracy

57% (10.6b remaining)

Error of 17.4b against oracle of 6.8b and baseline of 31.5b

bsearch64.0ms

Steps

Iters	Range		Point
9	2.91496086920264e+30	1.0395323375993686e+36	4.636459646981212e+35
7	5.031538721684922e-197	3.3037526197584205e-195	7.114272991027333e-197
7	-3.421034464204448e-267	-1.4680813468529351e-269	-1.1094194130263304e-267
6	-1.2683204674669225e+84	-3.006257280694689e+83	-1.2212465663556388e+84

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	112
1	66	112

end0.0ms

sample645.0ms

Algorithm

intervals

Results

496.0ms

8000×

body

valid

Details

analyze8.0ms

sample41.0ms

simplify4.0ms

prune7.0ms

localize20.0ms

rewrite23.0ms

series25.0ms

simplify66.0ms

prune147.0ms

localize13.0ms

rewrite39.0ms

series49.0ms

simplify84.0ms

prune293.0ms

localize19.0ms

rewrite27.0ms

series108.0ms

simplify68.0ms

prune257.0ms

localize14.0ms

rewrite94.0ms

series82.0ms

simplify105.0ms

prune561.0ms

regimes834.0ms

bsearch64.0ms

simplify2.0ms

end0.0ms

sample645.0ms

Profiling