Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	199×	body	80	valid
4.0ms	20×	body	2560	valid
3.0ms	14×	body	5120	valid
2.0ms	10×	body	1280	valid
1.0ms	7×	body	640	valid
0.0ms	5×	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 (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: 36.2b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
27.8b	(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)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify79.0ms

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

prune105.0ms

Filtered

33 candidates to 29 candidates (87.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	6	34

Merged error: 15.5b

Counts

34 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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:

16.0ms	(* (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)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
48.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

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

prune279.0ms

Filtered

136 candidates to 73 candidates (53.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	136	6	142

Merged error: 15.5b

Counts

142 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (sqrt (+ (* re re) (* im im))) (* -1 re))
4.9b	(sqrt (* 2.0 (/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) (* -1 re)))))
20.9b	(/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) (* -1 re)))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) (* -1 re))
11.0ms	(sqrt (* 2.0 (/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) (* -1 re)))))
12.0ms	(/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) (* -1 re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (sqrt (+ (* re re) (* im im))) (* -1 re))
192.0ms	(sqrt (* 2.0 (/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) (* -1 re)))))
73.0ms	(/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) (* -1 re)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	417	853
1	1895	747
2	5002	736

prune260.0ms

Filtered

83 candidates to 71 candidates (85.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	2	1	3
Picked	1	0	1
Done	1	1	2
Total	81	8	89

Merged error: 12.7b

Counts

89 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ im (/ (+ (sqrt (+ (* re re) (* im im))) (* -1 re)) im))
1.0b	(+ (sqrt (+ (* re re) (* im im))) (* -1 re))
4.9b	(sqrt (* 2.0 (* 1 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) (* -1 re)) im)))))
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
48×	`add-sqr-sqrt`
47×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/r*`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`div-inv`
4×	`sqrt-pow1` `sqrt-prod`
3×	`cbrt-undiv` `sqrt-div` `div-exp` `pow-prod-down` `associate-/l*`
2×	`mul-1-neg` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `unsub-neg` `clear-num` `sum-log` `associate-/r/`

Counts

4 → 111

Calls

4 calls:

9.0ms	(/ im (/ (+ (sqrt (+ (* re re) (* im im))) (* -1 re)) im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) (* -1 re))
15.0ms	(sqrt (* 2.0 (* 1 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) (* -1 re)) im)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ im (/ (+ (sqrt (+ (* re re) (* im im))) (* -1 re)) im))
46.0ms	(+ (sqrt (+ (* re re) (* im im))) (* -1 re))
201.0ms	(sqrt (* 2.0 (* 1 (/ im (/ (+ (sqrt (+ (* re re) (* im im))) (* -1 re)) im)))))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	600	1515
1	3015	1400
2	5002	1396

prune365.0ms

Filtered

123 candidates to 97 candidates (78.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	124	7	131

Merged error: 10.6b

Counts

131 → 7

regimes326.0ms

Accuracy

61.6% (10.1b remaining)

Error of 22.1b against oracle of 12.0b and baseline of 38.3b

bsearch116.0ms

Steps

Iters	Range	Point
6	1.4561095946501342e+101	1.441855190865374e+102	1.4134443734559052e+102
8	4.782480876373509e-275	5.044371448511112e-272	5.292717122801934e-275
6	-3.245969229886643e+141	-4.4689590379865175e+140	-2.97507766284173e+141

Iters

Range

Point

1.4561095946501342e+101

1.441855190865374e+102

1.4134443734559052e+102

4.782480876373509e-275

5.044371448511112e-272

5.292717122801934e-275

-3.245969229886643e+141

-4.4689590379865175e+140

-2.97507766284173e+141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	31
1	67	31
2	67	31

end0.0ms

sample690.0ms

Algorithm

intervals

Results

198.0ms	5977×	body	80	valid
158.0ms	755×	body	2560	valid
76.0ms	312×	body	5120	valid
72.0ms	461×	body	1280	valid
35.0ms	285×	body	640	valid
14.0ms	150×	body	320	valid
4.0ms	60×	body	160	valid