Details

sample34.0ms

Algorithm

intervals

Results

9.0ms	195×	body	80	valid
5.0ms	18×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	10×	body	5120	valid
1.0ms	8×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify5.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 37.9b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`

Counts

2 → 27

Calls

2 calls:

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify80.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	141	198
1	358	186
2	866	182
3	2557	181
4	5001	181

prune75.0ms

Filtered

33 candidates to 29 candidates (12.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	5	34

Merged error: 15.9b

Counts

34 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.6b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

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)))))
15.0ms	(+ (* (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)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

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

prune132.0ms

Filtered

136 candidates to 74 candidates (45.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	136	5	141

Merged error: 15.9b

Counts

141 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (+ (* re re) (* im im))) re)
4.8b	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
21.4b	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
23.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
16.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	362	695
1	1503	628
2	5001	624

prune131.0ms

Filtered

83 candidates to 64 candidates (22.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Merged error: 12.4b

Counts

88 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
0.2b	(- (sqrt (+ (* re re) (* im im))) re)
4.8b	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
17×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
3×	`cbrt-undiv` `sqrt-pow1` `sqrt-div` `div-exp` `associate-/l*`
2×	`pow1/2`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `flip3-+` `diff-log` `associate-*r/` `pow-prod-down` `clear-num` `associate-/r/` `flip--` `flip-+`

Counts

4 → 148

Calls

4 calls:

11.0ms	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
16.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
23.0ms	(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	643	1958
1	3082	1844
2	5002	1831

prune156.0ms

Filtered

160 candidates to 105 candidates (34.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	159	8	167

Merged error: 10.0b

Counts

167 → 8

regimes266.0ms

Accuracy

51.2% (14.1b remaining)

Error of 26.0b against oracle of 11.9b and baseline of 40.8b

bsearch34.0ms

Steps

Iters	Range		Point
8	6.275965676863823e-56	6.73995892514698e-53	8.722237925023642e-55
4	-1.8215798574764598e+151	-1.0517132200168235e+151	-1.2283164429326669e+151

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	20
1	39	20

end0.0ms

sample971.0ms

Algorithm

intervals

Results

286.0ms	6006×	body	80	valid
195.0ms	727×	body	2560	valid
121.0ms	527×	body	1280	valid
88.0ms	266×	body	5120	valid
44.0ms	254×	body	640	valid
19.0ms	146×	body	320	valid
7.0ms	74×	body	160	valid

Details

sample34.0ms

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite12.0ms

series14.0ms

simplify80.0ms

prune75.0ms

localize12.0ms

rewrite43.0ms

series29.0ms

simplify49.0ms

prune132.0ms

localize11.0ms

rewrite35.0ms

series52.0ms

simplify43.0ms

prune131.0ms

localize12.0ms

rewrite46.0ms

series48.0ms

simplify90.0ms

prune156.0ms

regimes266.0ms

bsearch34.0ms

simplify1.0ms

end0.0ms

sample971.0ms

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