Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	198×	body	80	valid
5.0ms	25×	body	2560	valid
2.0ms	14×	body	1280	valid
1.0ms	6×	body	5120	valid
1.0ms	8×	body	640	valid
0.0ms	5×	body	320	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize13.0ms

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)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

2.0ms	(+ (* re re) (* im im))
11.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
17.0ms	(- (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
168.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune178.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
5.8b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
20.7b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite54.0ms

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:

15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(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)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
190.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
66.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

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

prune281.0ms

Filtered

111 candidates to 78 candidates (70.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
5.8b	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
31.0b	(sqrt (+ (* re re) (* im im)))
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

13.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
71.0ms	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
157.0ms	(sqrt (* 2.0 (* (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
36.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify130.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	321	605
1	1109	564
2	4220	551
3	5002	549

prune258.0ms

Filtered

69 candidates to 57 candidates (82.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(* (sqrt 2.0) (fabs (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
31.0b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

21.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(* (sqrt 2.0) (fabs (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
12.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
37.0ms	(* (sqrt 2.0) (fabs (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	435	1256
1	1582	1149
2	5001	1125

prune316.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

regimes138.0ms

Accuracy

42.3% (21.3b remaining)

Error of 21.7b against oracle of 0.4b and baseline of 37.3b

bsearch270.0ms

Steps

Iters	Range		Point
11	3.5318877144286925e+79	5.115290601027986e+108	5.004173400788061e+108
8	5.78828243737659e-174	1.5538611295513305e-171	6.106904356278453e-174
8	2.352857168743782e-242	2.449155213137814e-239	7.173724346810989e-240
4	-8.324161129088754e-267	-5.3907007133187425e-267	-6.631953176532925e-267
10	-6.893918254503549e-96	-4.287114494167576e-108	-3.732260442574711e-107
8	-5.097960459803195e-05	-1.4117940793321767e-07	-1.4315525556785458e-07

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	55
1	101	55
2	102	55
3	102	55

end0.0ms

sample670.0ms

Algorithm

intervals

Results

196.0ms	5993×	body	80	valid
140.0ms	691×	body	2560	valid
75.0ms	492×	body	1280	valid
71.0ms	300×	body	5120	valid
33.0ms	278×	body	640	valid
14.0ms	156×	body	320	valid
5.0ms	90×	body	160	valid