Details

sample48.0ms

Algorithm

intervals

Results

15.0ms	181×	body	80	valid
10.0ms	28×	body	2560	valid
6.0ms	15×	body	5120	valid
5.0ms	18×	body	1280	valid
2.0ms	10×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

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)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

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:

2.0ms	(+ (* re re) (* im im))
10.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
12.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* re re) (* im im))
165.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	274	428
1	986	391
2	3089	381
3	5002	379

prune182.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (+ (* re re) (* im im))) re)
7.9b	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
20.6b	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

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:

17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
16.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
20.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
3.0ms	(sqrt (+ (* re re) (* im im)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
186.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
71.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	447	1428
1	1582	1323
2	5001	1313

prune301.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.5b

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)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.8b	(sqrt (* 2.0 (pow im 2)))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

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:

21.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
16.0ms	(- (sqrt (+ (* re re) (* im im))) re)
2.0ms	(sqrt (* 2.0 (pow im 2)))
3.0ms	(sqrt (+ (* re re) (* im im)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
32.0ms	(sqrt (* 2.0 (pow im 2)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	393	1462
1	1376	1383
2	5001	1354

prune317.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
0.4b	(* (sqrt 2.0) (fabs im))
32.7b	(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac` `associate-/r*`
7×	`pow1`
6×	`associate-l` `add-log-exp` `difference-of-squares`
4×	`sqrt-div`
3×	`associate-r` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 87

Calls

4 calls:

23.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(* (sqrt 2.0) (fabs im))
3.0ms	(sqrt (+ (* re re) (* im im)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (* (sqrt 2.0) (fabs im)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
30.0ms	(* (sqrt 2.0) (fabs im))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	450	903
1	1991	826
2	5002	817

prune249.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.8b

regimes138.0ms

Accuracy

50.6% (14.8b remaining)

Error of 22.3b against oracle of 7.5b and baseline of 37.4b

bsearch278.0ms

Steps

Iters	Range		Point
8	3.3685160830587113e-93	1.1118131948146322e-89	6.786381174376227e-92
7	4.321237752559463e-255	8.594462797983843e-254	2.3062092194117723e-254
8	2.555487769507404e-297	9.204367104374754e-295	2.216823154714405e-295
10	-3.744556309116812e-103	-1.0905044694663493e-116	-1.1044329890532487e-116
10	-8.777387788220042e+125	-4.2027485674795273e+114	-8.15615961666859e+125

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	55
1	75	55

end0.0ms

sample1.2s

Algorithm

intervals

Results

429.0ms	5987×	body	80	valid
241.0ms	673×	body	2560	valid
150.0ms	500×	body	1280	valid
136.0ms	312×	body	5120	valid
70.0ms	292×	body	640	valid
27.0ms	153×	body	320	valid
10.0ms	83×	body	160	valid