Details

sample17.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify7.0ms

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: 37.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite67.0ms

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:

27.0ms	(+ (+ (* x x) (* y y)) (* z z))
7.0ms	(+ (* x x) (* y y))
31.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series169.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (+ (* x x) (* y y)) (* z z))
33.0ms	(+ (* x x) (* y y))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify87.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (83.0ms)

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

prune120.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
0.3b	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
36.3b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
36.3b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

30.0ms	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
75.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
16.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
16.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
145.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
109.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
112.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	320	1178
1	1304	1101
2	5001	1084

prune294.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite107.0ms

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:

18.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
28.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
30.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
29.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms	(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

prune219.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 18.0b

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 18.0b

regimes346.0ms

Accuracy

64.6% (7.0b remaining)

Error of 25.3b against oracle of 18.3b and baseline of 38.2b

bsearch49.0ms

Steps

Iters	Range		Point
8	1.4676110776348385e+142	1.1574277099819921e+145	5.555039258021857e+144
7	-4.412166578960519e+130	-4.90358144502769e+128	-2.090433146826483e+130

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	7
1	21	7

end0.0ms

sample443.0ms

Algorithm

intervals

Results

226.0ms

8000×

body

valid