Details

analyze14.0ms

Algorithm: search

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	7

prune3.0ms

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: 38.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

7.0ms	(+ (* x x) (* y y))
9.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series46.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
28.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	294	707
1	1224	644
2	4391	642
3	5001	640

prune135.0ms

Filtered

60 candidates to 74 candidates (-23.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 18.0b

Counts

75 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`sqrt-div`
8×	`pow1` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `associate-r/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
14.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series54.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
30.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify120.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	318	859
1	1226	828
2	4716	804
3	5001	796

prune111.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Merged error: 18.0b

Counts

91 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.4b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
35.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

152×	`sqrt-prod`
122×	`add-sqr-sqrt`
84×	`times-frac`
55×	`*-un-lft-identity`
47×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
11×	`pow1`
9×	`sqrt-div`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
4×	`add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`flip3-+` `flip-+`
1×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

7.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
25.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
28.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
22.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify63.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	420	2977
1	1428	2846
2	5001	2796

prune205.0ms

Filtered

108 candidates to 168 candidates (-55.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	168	7	175

Merged error: 18.0b

Counts

175 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
0.3b	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
1.0b	(/ 1 (sqrt 3.0))
35.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

170×	`sqrt-prod`
148×	`add-sqr-sqrt`
120×	`times-frac`
83×	`*-un-lft-identity`
75×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
12×	`add-exp-log` `associate-/r*`
11×	`pow1`
10×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`sqrt-div` `div-inv`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`rem-sqrt-square` `pow-flip` `div-exp` `pow-prod-down`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rec-exp` `flip3-+` `sqrt-unprod` `1-exp` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `inv-pow`

Counts

4 → 212

Calls

4 calls:

9.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
24.0ms	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
4.0ms	(/ 1 (sqrt 3.0))
7.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

series93.0ms

Counts

4 → 10

Calls

4 calls:

19.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
31.0ms	(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
0.0ms	(/ 1 (sqrt 3.0))
43.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	452	2919
1	1938	2730
2	5001	2684

prune327.0ms

Filtered

128 candidates to 222 candidates (-73.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	216	6	222
Fresh	0	3	3
Picked	0	1	1
Done	1	2	3
Total	217	12	229

Merged error: 17.9b

Counts

229 → 12

regimes1.0s

Accuracy

58.8% (8.0b remaining)

Error of 26.4b against oracle of 18.4b and baseline of 37.9b

bsearch124.0ms

Steps

Iters	Range		Point
10	4.1203749417012695e+113	1.1958722659400257e+126	2.031375809460608e+124
8	1.0867654425715706e-166	1.1901818990911824e-163	1.3412928175691604e-166
7	3.402453077673389e-218	2.1407623947411836e-216	2.106912008082555e-216
3	-4.136693631811351e+106	-3.3709217465401843e+106	-4.070165636541658e+106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	21
1	43	21
2	43	21

end0.0ms

analyze14.0ms

Algorithm: search

sample677.0ms

Algorithm

intervals

Results

519.0ms

8000×

body

valid

Details

analyze14.0ms

sample20.0ms

simplify6.0ms

prune3.0ms

localize9.0ms

rewrite23.0ms

series46.0ms

simplify122.0ms

prune135.0ms

localize12.0ms

rewrite25.0ms

series54.0ms

simplify120.0ms

prune111.0ms

localize14.0ms

rewrite50.0ms

series112.0ms

simplify63.0ms

prune205.0ms

localize17.0ms

rewrite54.0ms

series93.0ms

simplify70.0ms

prune327.0ms

regimes1.0s

bsearch124.0ms

simplify2.0ms

end0.0ms

analyze14.0ms

sample677.0ms

Profiling