Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
6.0ms	30×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	12×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

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:

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

series250.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344

prune146.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
5.9b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.5b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
188.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
64.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune277.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (sqrt (+ (* re re) (* im im))) re) im)
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
5.9b	(sqrt (* 2.0 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

9.0ms	(/ (+ (sqrt (+ (* re re) (* im im))) re) im)
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (+ (sqrt (+ (* re re) (* im im))) re) im)
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
187.0ms	(sqrt (* 2.0 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify133.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	375	707
1	1217	653
2	4719	641
3	5003	641

prune228.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
0.4b	(* (sqrt 2.0) (sqrt (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
5.9b	(sqrt (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im)))
31.8b	(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
128×	`*-un-lft-identity`
122×	`sqrt-prod`
119×	`add-sqr-sqrt`
90×	`add-cube-cbrt`
56×	`associate-r`
19×	`distribute-lft-out`
10×	`pow1`
8×	`div-inv` `unswap-sqr`
6×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div`
3×	`pow-prod-down`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`+-commutative` `sqrt-unprod` `associate-r/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod`

Counts

4 → 178

Calls

4 calls:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
24.0ms	(* (sqrt 2.0) (sqrt (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
11.0ms	(sqrt (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
199.0ms	(* (sqrt 2.0) (sqrt (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
123.0ms	(sqrt (/ im (/ (+ (sqrt (+ (* re re) (* im im))) re) im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	781	2448
1	3015	2285
2	5001	2227

prune525.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.5b

regimes451.0ms

Accuracy

50.9% (17.0b remaining)

Error of 19.4b against oracle of 2.4b and baseline of 37.0b

bsearch189.0ms

Steps

Iters	Range		Point
10	9.339102222384328e+136	8.873632187108906e+155	1.3214275905413451e+154
8	7.4027025958194e-290	9.650788373676541e-287	1.1367070531923989e-287
8	-6.894984212414012e-177	-1.644009190884606e-179	-3.8464311801425253e-178
9	-4.331403552570957e+63	-1.1145548392722344e+57	-3.6980740601030615e+63

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	39
1	85	39
2	86	39
3	86	39

end0.0ms

sample660.0ms

Algorithm

intervals

Results

199.0ms	6030×	body	80	valid
142.0ms	729×	body	2560	valid
73.0ms	450×	body	1280	valid
66.0ms	281×	body	5120	valid
33.0ms	268×	body	640	valid
14.0ms	156×	body	320	valid
5.0ms	86×	body	160	valid