Details

sample133.0ms

Algorithm

intervals

Results

11.0ms	37×	body	2560	valid
8.0ms	166×	body	80	valid
5.0ms	20×	body	1280	valid
4.0ms	11×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 42.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.6b	(+ (sqrt (+ (* re re) (* im im))) re)
30.4b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

9.0ms	(+ (* re re) (* im im))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	277	428
1	1024	399
2	3458	393
3	5002	391

prune111.0ms

Filtered

63 candidates to 52 candidates (17.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	6	64

Merged error: 21.8b

Counts

64 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (+ (* re re) (* im im))) re)
6.4b	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
19.4b	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
30.4b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
21×	`unpow-prod-down`
20×	`difference-of-squares`
14×	`sqrt-prod`
10×	`distribute-lft-out--`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
7×	`unpow2` `sqr-pow`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `sqrt-div` `div-exp`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `rem-sqrt-square` `frac-2neg` `flip3-+` `diff-log` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 120

Calls

4 calls:

9.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
22.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	440	1427
1	1601	1331
2	5002	1323

prune176.0ms

Filtered

132 candidates to 85 candidates (35.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	132	6	138

Merged error: 16.0b

Counts

138 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
6.4b	(sqrt (* 2.0 (* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))))
30.4b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`-un-lft-identity` `associate-r*`
19×	`times-frac`
16×	`add-cube-cbrt`
13×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-prod` `difference-of-squares`
6×	`add-log-exp`
4×	`sqrt-pow1` `pow-prod-down` `distribute-lft-out--`
3×	`sqrt-div` `associate-r/` `associate-l*`
2×	`flip3--` `pow1/2` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `div-exp` `*-commutative` `flip-+` `div-inv`

Counts

4 → 86

Calls

4 calls:

14.0ms	(* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
24.0ms	(sqrt (* 2.0 (* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	429	793
1	1908	714
2	5003	713

prune125.0ms

Filtered

98 candidates to 72 candidates (26.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Merged error: 14.3b

Counts

104 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
26.7b	(sqrt (* 2.0 (pow im 2)))
30.4b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`times-frac`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp`
4×	`sqrt-div` `associate-/l*`
2×	`flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

15.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (* 2.0 (pow im 2)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (* 2.0 (pow im 2)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	386	1461
1	1401	1391
2	5001	1364

prune163.0ms

Filtered

116 candidates to 81 candidates (30.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	115	8	123

Merged error: 9.6b

Counts

123 → 8

regimes152.0ms

Accuracy

58.1% (10.5b remaining)

Error of 21.4b against oracle of 10.9b and baseline of 36.0b

bsearch71.0ms

Steps

Iters	Range		Point
10	1.7168059376205562e-68	2.1041336759107886e-57	2.3901845536880374e-59
9	-2.0001192140414813e+161	-1.6212848430265458e+153	-1.343225904371213e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	22
1	42	22

end0.0ms

sample1.3s

Algorithm

intervals

Results

293.0ms	5521×	body	80	valid
280.0ms	941×	body	2560	valid
160.0ms	442×	body	5120	valid
139.0ms	580×	body	1280	valid
57.0ms	298×	body	640	valid
22.0ms	142×	body	320	valid
9.0ms	76×	body	160	valid

Details

sample133.0ms

simplify6.0ms

prune3.0ms

localize10.0ms

rewrite26.0ms

series41.0ms

simplify95.0ms

prune111.0ms

localize13.0ms

rewrite39.0ms

series45.0ms

simplify57.0ms

prune176.0ms

localize12.0ms

rewrite38.0ms

series47.0ms

simplify56.0ms

prune125.0ms

localize14.0ms

rewrite31.0ms

series38.0ms

simplify48.0ms

prune163.0ms

regimes152.0ms

bsearch71.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling