Details

analyze14.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

sample19.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 41.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
38.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series55.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(+ (* x x) (* y y))
13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
27.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5298	1461

prune151.0ms

Filtered

72 candidates to 90 candidates (-25.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 21.9b

Counts

91 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))
0.4b	(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))))
38.4b	(sqrt (+ (* x x) (+ (* y y) (* z z))))
38.4b	(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

150×	`sqrt-prod`
130×	`add-sqr-sqrt`
106×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
47×	`cbrt-prod`
43×	`associate-r`
24×	`unswap-sqr`
13×	`associate-l`
10×	`pow1` `sqrt-div`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+` `div-inv`
2×	`rem-sqrt-square` `associate-/l/`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 189

Calls

4 calls:

9.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))
34.0ms	(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))))
5.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))
5.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))
47.0ms	(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))))
18.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))
18.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify96.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5103	6176

prune373.0ms

Filtered

134 candidates to 201 candidates (-50.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	200	8	208

Merged error: 21.9b

Counts

208 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
0.5b	(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))))
38.4b	(sqrt (+ (* x x) (+ (* y y) (* z z))))
38.4b	(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

574×	`sqrt-prod`
344×	`add-sqr-sqrt`
284×	`times-frac`
154×	`add-cube-cbrt` `*-un-lft-identity`
73×	`swap-sqr`
43×	`associate-r` `associate-l`
36×	`unswap-sqr`
21×	`pow1`
10×	`sqrt-pow1` `pow1/2` `sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`pow-prod-up` `div-inv`
4×	`add-log-exp`
3×	`flip3-+` `pow-prod-down` `pow-sqr` `flip-+`
2×	`rem-sqrt-square` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sqrt-undiv` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 316

Calls

4 calls:

10.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
49.0ms	(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))))
5.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))
5.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
32.0ms	(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))))
19.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))
19.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify103.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4987	9005
1	4987	9005

prune351.0ms

Filtered

149 candidates to 328 candidates (-120.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	324	4	328
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	326	10	336

Merged error: 21.8b

Counts

336 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y y) (* z z))
0.4b	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
5.9b	(exp (log (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))))
38.4b	(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

81×	`sqrt-prod`
72×	`times-frac`
60×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
40×	`log-prod` `exp-sum`
6×	`pow1` `add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`exp-prod` `sqrt-div`
3×	`flip3-+` `flip-+`
2×	`div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `log-div` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `exp-diff` `div-exp` `clear-num` `sum-log` `log-pow` `rem-exp-log`

Counts

4 → 142

Calls

4 calls:

4.0ms	(+ (* y y) (* z z))
9.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
12.0ms	(exp (log (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))))
5.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y y) (* z z))
33.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
30.0ms	(exp (log (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))))
18.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify57.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5089	3156

prune169.0ms

Filtered

86 candidates to 154 candidates (-79.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	0	6	6
Picked	1	0	1
Done	0	3	3
Total	151	13	164

Merged error: 21.8b

Counts

164 → 13

regimes1.1s

Accuracy

56.6% (8.7b remaining)

Error of 26.9b against oracle of 18.3b and baseline of 38.3b

bsearch150.0ms

Steps

Iters	Range		Point
9	1.5396218463340147e+70	1.8958865676517938e+76	1.867342135659763e+76
9	7.935462177585739e-80	4.8846517773126523e-73	9.272670595575633e-80
8	3.1045049859459322e-130	2.431020967004791e-126	2.5655741827255853e-127
7	-3.157571037515737e+148	-1.9319386193317015e+146	-3.2904042320875013e+146

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	79
1	51	79

end0.0ms

analyze14.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

sample524.0ms

Algorithm

intervals

Results

372.0ms

8000×

body

valid

Details

analyze14.0ms

sample19.0ms

simplify3.0ms

prune6.0ms

localize9.0ms

rewrite29.0ms

series55.0ms

simplify46.0ms

prune151.0ms

localize16.0ms

rewrite63.0ms

series115.0ms

simplify96.0ms

prune373.0ms

localize13.0ms

rewrite97.0ms

series101.0ms

simplify103.0ms

prune351.0ms

localize15.0ms

rewrite36.0ms

series87.0ms

simplify57.0ms

prune169.0ms

regimes1.1s

bsearch150.0ms

simplify1.0ms

end0.0ms

analyze14.0ms

sample524.0ms

Profiling