Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

496×

body

valid

simplify290.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	14	6
1	29	4
2	50	4
3	70	3
4	82	3
5	125	3
6	229	3
7	321	3
8	336	3
9	436	3
10	790	3
11	3492	3
12	5001	3

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
7×	`fma-def`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate-+l+`

Counts

3 → 51

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* y y))
9.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series103.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
36.0ms	(+ (+ (* x x) (* y y)) (* y y))
40.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify135.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	237	373
1	1141	313
2	4748	287
3	5001	286

prune127.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.1b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.0b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.0b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `sum-log` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`+-commutative` `associate-+l+` `fma-udef`

Counts

4 → 64

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* y y))
1.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* y y))
130.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
49.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify88.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	175	647
1	742	534
2	3044	495
3	5001	493

prune224.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
0.2b	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
5.0b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
5.0b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-log-exp`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `sum-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `hypot-def`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 114

Calls

4 calls:

9.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
18.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
7.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
7.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
39.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
49.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
55.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify52.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	232	1434
1	1052	1249
2	5001	1189

prune262.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

5.0b	(sqrt (* (* (cbrt (+ (+ (* x x) (* y y)) (* y y))) (cbrt (+ (+ (* x x) (* y y)) (* y y)))) (cbrt (+ (+ (* x x) (* y y)) (* y y)))))
5.5b	(cbrt (+ (+ (* x x) (* y y)) (* y y)))
5.5b	(cbrt (+ (+ (* x x) (* y y)) (* y y)))
5.5b	(cbrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

23.0ms	(sqrt (* (* (cbrt (+ (+ (* x x) (* y y)) (* y y))) (cbrt (+ (+ (* x x) (* y y)) (* y y)))) (cbrt (+ (+ (* x x) (* y y)) (* y y)))))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* y y)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (* (* (cbrt (+ (+ (* x x) (* y y)) (* y y))) (cbrt (+ (+ (* x x) (* y y)) (* y y)))) (cbrt (+ (+ (* x x) (* y y)) (* y y)))))
107.0ms	(cbrt (+ (+ (* x x) (* y y)) (* y y)))
106.0ms	(cbrt (+ (+ (* x x) (* y y)) (* y y)))
107.0ms	(cbrt (+ (+ (* x x) (* y y)) (* y y)))

simplify155.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	308	2214
1	710	2152
2	3169	2122
3	5001	2094

prune325.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes124.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	10	14

end0.0ms

sample560.0ms

Algorithm

intervals

Results

338.0ms

14218×

body

valid