Details

sample42.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

prune3.0ms

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: 32.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (sqrt (+ (* re re) (* im im))))
0.7b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

4.0ms	(log (sqrt (+ (* re re) (* im im))))
7.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
3.0ms	(sqrt (+ (* re re) (* im im)))

series34.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify119.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 4 (107.0ms)

Iter	Nodes	Cost
0	232	856
1	572	804
2	1348	793
3	4052	791
4	5002	790

prune178.0ms

Filtered

60 candidates to 91 candidates (-51.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	77	14	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	14	92

Merged error: 8.8b

Counts

92 → 14

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)))
31.3b	(log (+ (* re re) (* im im)))

rewrite40.0ms

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)))

series54.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
22.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
12.0ms	(log (+ (* re re) (* im im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	528	2102
1	2132	1937
2	5001	1838

prune360.0ms

Filtered

96 candidates to 162 candidates (-68.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	164	12	176

Merged error: 8.7b

Counts

176 → 12

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))))))

13.9b

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

18.4b

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

rewrite30.0ms

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)))))

9.0ms

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

series114.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms

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

36.0ms

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

35.0ms

(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	478	1721
1	2113	1522
2	5001	1321

prune292.0ms

Filtered

82 candidates to 126 candidates (-53.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	124	14	138

Merged error: 8.7b

Counts

138 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
1.0b	(sqrt (sqrt (log 10.0)))
1.0b	(sqrt (sqrt (log 10.0)))
31.3b	(log (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
60×	`times-frac`
56×	`add-sqr-sqrt`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`cbrt-prod`
18×	`pow1`
10×	`associate-/r*` `log-pow`
8×	`sqrt-pow1`
7×	`add-exp-log`
6×	`associate-/l*`
5×	`add-cbrt-cube`
4×	`rem-sqrt-square` `pow1/2` `add-log-exp`
3×	`log-prod`
2×	`log-div`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 142

Calls

4 calls:

8.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
2.0ms	(sqrt (sqrt (log 10.0)))
2.0ms	(sqrt (sqrt (log 10.0)))
3.0ms	(log (+ (* re re) (* im im)))

series9.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
0.0ms	(sqrt (sqrt (log 10.0)))
0.0ms	(sqrt (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	279	1327
1	647	1276
2	1708	1194
3	5001	1182

prune383.0ms

Filtered

82 candidates to 148 candidates (-80.5%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	145	17	162

Merged error: 8.6b

Counts

162 → 17

regimes1.1s

Accuracy

56.1% (10.7b remaining)

Error of 18.3b against oracle of 7.6b and baseline of 32.0b

bsearch76.0ms

Steps

Iters	Range		Point
7	2.20140649672281e+130	1.0677592813206312e+132	2.232500477572645e+130
11	5.1798235178893905e-163	1.988786700782574e-127	9.114673635183846e-161
6	-1.3466004809849949e-260	-1.8052437872173091e-261	-2.263966836247413e-261
4	-3.194608663985631e+118	-1.8893531281097833e+118	-2.791497222573345e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	69
1	71	69

end0.0ms

sample673.0ms

Algorithm

intervals

Results

474.0ms

8000×

body

valid

Details

sample42.0ms

simplify3.0ms

prune3.0ms

localize10.0ms

rewrite17.0ms

series34.0ms

simplify119.0ms

prune178.0ms

localize13.0ms

rewrite40.0ms

series54.0ms

simplify59.0ms

prune360.0ms

localize19.0ms

rewrite30.0ms

series114.0ms

simplify57.0ms

prune292.0ms

localize19.0ms

rewrite21.0ms

series9.0ms

simplify55.0ms

prune383.0ms

regimes1.1s

bsearch76.0ms

simplify2.0ms

end0.0ms

sample673.0ms

Profiling