Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
4.0ms	18×	body	2560	valid
3.0ms	18×	body	1280	valid
3.0ms	12×	body	5120	valid
1.0ms	12×	body	640	valid
0.0ms	6×	body	160	valid
0.0ms	3×	body	320	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 (0.0%)

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: 39.0b

Counts

2 → 1

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)))
1.8b	(+ (sqrt (+ (* re re) (* im im))) re)
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

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

series297.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
182.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (88.0ms)

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

prune175.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	5	64

Merged error: 17.1b

Counts

64 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.9b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.7b	(sqrt (+ (* re re) (* im im)))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

15.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series165.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
53.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	268	1096
1	975	974
2	5001	950

prune263.0ms

Filtered

136 candidates to 75 candidates (55.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	135	6	141

Merged error: 17.1b

Counts

141 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
12.5b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
28.7b	(sqrt (+ (* re re) (* im im)))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
16.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
46.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	394	992
1	1342	878
2	5001	845

prune299.0ms

Filtered

103 candidates to 66 candidates (64.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	103	6	109

Merged error: 17.1b

Counts

109 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (+ (* re re) (* im im))) re)
5.2b	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
21.5b	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
16.0ms	(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)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (sqrt (+ (* re re) (* im im))) re)
201.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
78.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (42.0ms)

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

prune285.0ms

Filtered

132 candidates to 85 candidates (64.4%)

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: 13.5b

Counts

138 → 6

regimes108.0ms

Accuracy

49.4% (13.1b remaining)

Error of 27.4b against oracle of 14.4b and baseline of 40.2b

bsearch204.0ms

Steps

Iters	Range		Point
10	1.413974522623055e-130	8.987964064439511e-120	4.932316191053295e-120
7	8.554373099101626e-290	2.7552220295623955e-288	9.458206914580381e-290
9	-2.2365661558835998e-197	-6.33701187792121e-204	-7.458572382736605e-202
10	-4.2374323560179154e+147	-1.6400279301998874e+134	-4.167941501398113e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	35
1	61	35

end0.0ms

sample708.0ms

Algorithm

intervals

Results

211.0ms	5931×	body	80	valid
139.0ms	720×	body	2560	valid
81.0ms	506×	body	1280	valid
71.0ms	298×	body	5120	valid
45.0ms	309×	body	640	valid
14.0ms	148×	body	320	valid
6.0ms	88×	body	160	valid

Details

sample27.0ms

simplify6.0ms

prune3.0ms

localize13.0ms

rewrite23.0ms

series297.0ms

simplify94.0ms

prune175.0ms

localize13.0ms

rewrite42.0ms

series165.0ms

simplify57.0ms

prune263.0ms

localize21.0ms

rewrite35.0ms

series239.0ms

simplify56.0ms

prune299.0ms

localize14.0ms

rewrite44.0ms

series368.0ms

simplify57.0ms

prune285.0ms

regimes108.0ms

bsearch204.0ms

simplify2.0ms

end0.0ms

sample708.0ms

Profiling