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

sample62.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

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: 31.4b

Counts

2 → 1

localize11.0ms

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))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

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)))

series33.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
21.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4916	1166
1	4916	1166

prune173.0ms

Filtered

56 candidates to 83 candidates (-48.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	13	84

Merged error: 8.1b

Counts

84 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
0.5b	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
108×	`add-sqr-sqrt`
78×	`sqrt-prod`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt` `log-pow`
53×	`pow1`
46×	`associate-r`
28×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
16×	`sqrt-pow1` `pow1/2`
15×	`unswap-sqr`
9×	`div-exp`
8×	`prod-exp`
7×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv`
4×	`sqrt-div` `cbrt-unprod`
3×	`flip3-+` `flip-+` `div-inv`
2×	`log-div` `rec-exp` `1-exp` `div-sub`
1×	`+-commutative` `frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative`

Counts

4 → 205

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
29.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
9.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
19.0ms	(* (/ 1 (sqrt (log 10.0))) (/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0))))
23.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (sqrt (log 10.0)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4982	3538
1	4982	3538

prune363.0ms

Filtered

109 candidates to 217 candidates (-99.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	209	8	217
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	212	18	230

Merged error: 8.0b

Counts

230 → 18

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
3.8b	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
46×	`times-frac`
44×	`*-un-lft-identity`
42×	`add-cube-cbrt`
38×	`sqrt-prod`
25×	`pow-unpow` `associate-l`
20×	`log-prod`
18×	`unpow-prod-down`
15×	`pow1`
14×	`add-exp-log`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-cbrt-cube`
7×	`log-pow`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`associate-r` `prod-exp`
3×	`pow-pow` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `pow-exp` `sum-log` `-commutative` `sqrt-pow2`

Counts

4 → 141

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
14.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
9.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
42.0ms	(* (/ 1 (sqrt (log 10.0))) (log (pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))))
37.0ms	(pow (sqrt (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4961	2403
1	4961	2403

prune342.0ms

Filtered

88 candidates to 153 candidates (-73.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	152	19	171

Merged error: 8.0b

Counts

171 → 19

localize14.0ms

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)))))
0.6b	(/ (log 10.0) (log (+ (* re re) (* im im))))
30.2b	(log (+ (* re re) (* im im)))

rewrite25.0ms

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))
7.0ms	(/ 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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
21.0ms	(/ 1/2 (/ (log 10.0) (log (+ (* re re) (* im im)))))
26.0ms	(/ (log 10.0) (log (+ (* re re) (* im im))))
9.0ms	(log (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4972	3107
1	4972	3107

prune216.0ms

Filtered

109 candidates to 171 candidates (-56.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	9	8	17
Picked	0	1	1
Done	0	1	1
Total	174	16	190

Merged error: 8.0b

Counts

190 → 16

regimes1.2s

Accuracy

55.9% (10.8b remaining)

Error of 18.1b against oracle of 7.3b and baseline of 31.7b

bsearch92.0ms

Steps

Iters	Range		Point
8	3.760273602242606e+105	7.037067349760771e+109	7.871445329821158e+108
7	-2.198309510895907e-259	-3.0813968954381045e-261	-1.8532320640870052e-259
6	-6.038978841916928e-179	-4.494600987039991e-180	-1.6831834820475888e-179
9	-7.425132341927507e+32	-4.092514055723384e+25	-7.272468339126353e+32

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	109
1	61	109

end0.0ms

sample1.4s

Algorithm

intervals

Results

443.0ms

8000×

body

valid

Details

analyze8.0ms

sample62.0ms

simplify2.0ms

prune4.0ms

localize11.0ms

rewrite17.0ms

series33.0ms

simplify50.0ms

prune173.0ms

localize15.0ms

rewrite58.0ms

series53.0ms

simplify68.0ms

prune363.0ms

localize23.0ms

rewrite37.0ms

series90.0ms

simplify46.0ms

prune342.0ms

localize14.0ms

rewrite25.0ms

series64.0ms

simplify59.0ms

prune216.0ms

regimes1.2s

bsearch92.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling