Details

sample34.0ms

Algorithm

intervals

Results

9.0ms	187×	body	80	valid
5.0ms	18×	body	2560	valid
4.0ms	18×	body	1280	valid
4.0ms	12×	body	5120	valid
2.0ms	12×	body	640	valid
1.0ms	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

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)))
1.8b	(+ (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)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* re re) (* im im))
170.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (87.0ms)

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

prune164.0ms

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

localize15.0ms

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)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
44.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune255.0ms

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

localize16.0ms

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)))

rewrite36.0ms

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)
17.0ms	(+ (* (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)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
48.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (46.0ms)

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

prune291.0ms

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

localize16.0ms

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)))

rewrite40.0ms

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)
13.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
12.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
195.0ms	(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
68.0ms	(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
38.0ms	(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

prune277.0ms

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

regimes113.0ms

Accuracy

49.4% (13.1b remaining)

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

bsearch221.0ms

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

sample923.0ms

Algorithm

intervals

Results

284.0ms	5931×	body	80	valid
195.0ms	720×	body	2560	valid
115.0ms	506×	body	1280	valid
102.0ms	298×	body	5120	valid
53.0ms	309×	body	640	valid
20.0ms	148×	body	320	valid
8.0ms	88×	body	160	valid