Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	197×	body	80	valid
8.0ms	27×	body	2560	valid
3.0ms	9×	body	5120	valid
3.0ms	12×	body	1280	valid
2.0ms	9×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

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: 37.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(- (sqrt (+ (* re re) (* im im))) re)
0.5b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1`
6×	`*-un-lft-identity`
5×	`sqrt-prod` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div`
3×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `distribute-lft-out--`

Counts

3 → 43

Calls

3 calls:

8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
13.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
27.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify32.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5297	602

prune107.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Merged error: 18.3b

Counts

53 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ re (sqrt (+ (* re re) (* im im))))
0.7b	(/ (sqrt (* (* im im) 2.0)) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
29.8b	(sqrt (+ (* re re) (* im im)))
29.9b	(sqrt (* (* im im) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
32×	`sqrt-prod`
28×	`times-frac`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
11×	`pow1`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`sqrt-pow1` `sqrt-div` `associate-/l*`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 93

Calls

4 calls:

6.0ms	(+ re (sqrt (+ (* re re) (* im im))))
13.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (* (* im im) 2.0))

series46.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ re (sqrt (+ (* re re) (* im im))))
28.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (+ re (sqrt (+ (* re re) (* im im))))))
6.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (* (* im im) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5931	1890

prune186.0ms

Filtered

80 candidates to 105 candidates (-31.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	103	9	112

Merged error: 11.0b

Counts

112 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* im im) (* re re)))))))
0.3b	(/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* im im) (* re re))))))
0.6b	(+ re (sqrt (+ (* im im) (* re re))))
29.8b	(sqrt (+ (* im im) (* re re)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

104×	`sqrt-prod`
91×	`*-un-lft-identity`
88×	`times-frac`
78×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
48×	`associate-r`
14×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`sqrt-div` `associate-/l*` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`associate-l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 167

Calls

4 calls:

20.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* im im) (* re re)))))))
10.0ms	(/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* im im) (* re re))))))
6.0ms	(+ re (sqrt (+ (* im im) (* re re))))
4.0ms	(sqrt (+ (* im im) (* re re)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (fabs im) (/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* im im) (* re re)))))))
32.0ms	(/ (sqrt 2.0) (sqrt (+ re (sqrt (+ (* im im) (* re re))))))
8.0ms	(+ re (sqrt (+ (* im im) (* re re))))
7.0ms	(sqrt (+ (* im im) (* re re)))

simplify48.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5000	3248

prune244.0ms

Filtered

102 candidates to 179 candidates (-75.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	178	10	188

Merged error: 0.4b

Counts

188 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 2.0 (+ re (sqrt (+ (* im im) (* re re))))))
0.2b	(* (fabs im) (sqrt (/ 2.0 (+ re (sqrt (+ (* im im) (* re re)))))))
0.6b	(+ re (sqrt (+ (* im im) (* re re))))
29.8b	(sqrt (+ (* im im) (* re re)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqrt-prod`
37×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
8×	`pow1`
7×	`distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+`
3×	`rem-sqrt-square` `associate-l` `unswap-sqr`
2×	`sqrt-pow1` `pow1/2` `div-inv`
1×	`+-commutative` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `-commutative` `cbrt-unprod`

Counts

4 → 96

Calls

4 calls:

8.0ms	(sqrt (/ 2.0 (+ re (sqrt (+ (* im im) (* re re))))))
14.0ms	(* (fabs im) (sqrt (/ 2.0 (+ re (sqrt (+ (* im im) (* re re)))))))
6.0ms	(+ re (sqrt (+ (* im im) (* re re))))
4.0ms	(sqrt (+ (* im im) (* re re)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (/ 2.0 (+ re (sqrt (+ (* im im) (* re re))))))
29.0ms	(* (fabs im) (sqrt (/ 2.0 (+ re (sqrt (+ (* im im) (* re re)))))))
8.0ms	(+ re (sqrt (+ (* im im) (* re re))))
9.0ms	(sqrt (+ (* im im) (* re re)))

simplify24.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	5021	1702

prune157.0ms

Filtered

84 candidates to 108 candidates (-28.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	107	11	118

Merged error: 0.3b

Counts

118 → 11

regimes654.0ms

Accuracy

54.6% (17.2b remaining)

Error of 17.6b against oracle of 0.4b and baseline of 38.3b

bsearch103.0ms

Steps

Iters	Range		Point
9	3.43401543638109e+114	5.025550553073085e+120	4.40956572394349e+116
10	1.3994626587696508e-214	2.9831774035161146e-199	1.4225422339265396e-214
6	-3.9639939611996993e-296	-2.6703687768748694e-297	-7.88936342124095e-297
8	-1.0891331514545633e+114	-3.5827156305380124e+111	-4.6910854621363227e+113

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	91
1	60	91

end0.0ms

sample1.1s

Algorithm

intervals

Results

348.0ms	6084×	body	80	valid
224.0ms	687×	body	2560	valid
116.0ms	427×	body	1280	valid
112.0ms	291×	body	5120	valid
62.0ms	287×	body	640	valid
25.0ms	158×	body	320	valid
7.0ms	66×	body	160	valid

Details

sample40.0ms

simplify3.0ms

prune3.0ms

localize11.0ms

rewrite26.0ms

series42.0ms

simplify32.0ms

prune107.0ms

localize13.0ms

rewrite32.0ms

series46.0ms

simplify44.0ms

prune186.0ms

localize15.0ms

rewrite49.0ms

series78.0ms

simplify48.0ms

prune244.0ms

localize13.0ms

rewrite37.0ms

series74.0ms

simplify24.0ms

prune157.0ms

regimes654.0ms

bsearch103.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling