Details

sample25.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	12
1	11	12

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: 32.4b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
29.9b	(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)))

series24.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5218	1035

prune145.0ms

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: 8.2b

Counts

70 → 12

localize12.0ms

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)))
31.1b	(log (+ (* re re) (* im im)))

rewrite42.0ms

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:

24.0ms	(* (/ 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)))

series56.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
26.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
9.0ms	(log (+ (* re re) (* im im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4936	2822
1	4936	2822

prune305.0ms

Filtered

96 candidates to 162 candidates (-68.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	152	10	162
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	161	13	174

Merged error: 8.0b

Counts

174 → 13

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
0.3b	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
31.1b	(log (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
46×	`times-frac`
45×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
29×	`associate-l` `add-cbrt-cube`
26×	`associate-r` `sqrt-prod`
22×	`prod-exp`
18×	`pow1`
12×	`cbrt-unprod`
11×	`div-exp`
8×	`log-pow`
6×	`cbrt-undiv`
5×	`associate-*r/` `unswap-sqr`
4×	`pow-prod-down`
3×	`rec-exp` `log-prod` `1-exp` `un-div-inv` `add-log-exp`
2×	`frac-times` `log-div` `*-commutative` `div-inv`
1×	`flip3-+` `rem-log-exp` `associate-*l/` `flip-+`

Counts

3 → 122

Calls

3 calls:

11.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
14.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
4.0ms	(log (+ (* re re) (* im im)))

series53.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0))))
23.0ms	(* (/ 1/2 (sqrt (log 10.0))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10.0)))))
9.0ms	(log (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5202	1839

prune231.0ms

Filtered

74 candidates to 131 candidates (-77.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	131	13	144

Merged error: 8.0b

Counts

144 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
0.4b	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
0.4b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
31.1b	(log (+ (* re re) (* im im)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-prod`
112×	`times-frac`
107×	`add-sqr-sqrt`
69×	`add-cube-cbrt` `*-un-lft-identity`
60×	`associate-l`
42×	`pow1`
31×	`log-pow`
29×	`associate-r`
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:

27.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
20.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
8.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
4.0ms	(log (+ (* re re) (* im im)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0)))))
27.0ms	(* (sqrt (/ 1/2 (sqrt (log 10.0)))) (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))) (sqrt (/ 1/2 (sqrt (log 10.0))))))
22.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
10.0ms	(log (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4940	4416
1	4940	4416

prune520.0ms

Filtered

135 candidates to 219 candidates (-62.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	211	8	219
Fresh	5	6	11
Picked	0	1	1
Done	1	0	1
Total	217	15	232

Merged error: 8.0b

Counts

232 → 15

regimes709.0ms

Accuracy

56.6% (10.6b remaining)

Error of 18.2b against oracle of 7.6b and baseline of 32.1b

bsearch36.0ms

Steps

Iters	Range		Point
8	1.437665081705215e+76	5.265615968817064e+80	3.112931712533811e+80
7	-6.361697676969315e+93	-3.5977498111597825e+92	-7.300218245200566e+92

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	81
1	59	81

end0.0ms

sample676.0ms

Algorithm

intervals

Results

457.0ms

8000×

body

valid

Details

sample25.0ms

simplify3.0ms

prune3.0ms

localize10.0ms

rewrite13.0ms

series24.0ms

simplify62.0ms

prune145.0ms

localize12.0ms

rewrite42.0ms

series56.0ms

simplify83.0ms

prune305.0ms

localize13.0ms

rewrite34.0ms

series53.0ms

simplify49.0ms

prune231.0ms

localize14.0ms

rewrite69.0ms

series108.0ms

simplify70.0ms

prune520.0ms

regimes709.0ms

bsearch36.0ms

simplify1.0ms

end0.0ms

sample676.0ms

Profiling