Details

sample29.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	6
1	20	6
2	22	6
3	22	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

2.0ms	(+ (* x x) (* y y))
12.0ms	(+ (+ (* x x) (* y y)) (* z z))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series169.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
41.0ms	(+ (+ (* x x) (* y y)) (* z z))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify90.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	209	340
1	959	320
2	3316	316
3	5001	315

prune123.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

7.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
12.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
98.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
104.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	159	669
1	506	638
2	1776	636
3	5002	632

prune237.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.2b

localize18.0ms

Local error

Found 4 expressions with local error:

5.3b	(pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1/3)
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`sqrt-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
6×	`unpow-prod-down` `sqrt-div`
5×	`add-exp-log`
4×	`sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `pow-pow` `flip3-+` `flip-+`
1×	`pow-to-exp` `unpow1/3` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

14.0ms	(pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1/3)
12.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1/3)
98.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify99.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	210	642
1	757	590
2	3038	588
3	5001	588

prune251.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.2b

localize28.0ms

Local error

Found 4 expressions with local error:

5.5b	(pow (pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

16×	`unpow-prod-down`
15×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
7×	`pow1`
6×	`add-exp-log` `pow-unpow` `sqrt-div`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-to-exp` `sqr-pow`
1×	`pow-pow`

Counts

4 → 74

Calls

4 calls:

28.0ms	(pow (pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
17.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series692.0ms

Counts

4 → 12

Calls

4 calls:

378.0ms	(pow (pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
103.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
108.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
103.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify66.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	243	969
1	652	907
2	2348	905
3	5002	899

prune295.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.2b

regimes331.0ms

Accuracy

64% (7.1b remaining)

Error of 25.8b against oracle of 18.7b and baseline of 38.4b

bsearch68.0ms

Steps

Iters	Range		Point
7	4.587345188449012e+110	2.3696968284357086e+112	2.155295414164648e+112
9	-5.346835466478784e+105	-6.133687488484069e+100	-4.341981727027803e+105

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	7
1	21	7

end0.0ms

sample736.0ms

Algorithm

intervals

Results

569.0ms

8000×

body

valid