Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	7
1	27	7
2	33	7
3	34	7
4	34	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
38.8b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite57.0ms

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×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num` `sum-log`

Counts

3 → 72

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
36.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series305.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* x x) (* y y))
62.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
209.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify156.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	310	729
1	1303	650
2	4811	634
3	5001	634

prune297.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
38.8b	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`associate-r`
12×	`add-exp-log` `*-un-lft-identity`
11×	`add-cube-cbrt` `times-frac`
8×	`pow1` `add-cbrt-cube`
6×	`sqrt-div`
5×	`flip3-+` `flip-+` `add-log-exp`
4×	`frac-times` `associate-*l/` `prod-exp`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `unswap-sqr`
2×	`sqrt-pow1` `associate-*r/` `div-exp` `pow-prod-down` `un-div-inv` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `fma-def` `pow1/2` `1-exp` `sum-log` `sqrt-prod` `*-commutative` `div-inv`

Counts

3 → 75

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
42.0ms	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
17.0ms	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series318.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* x x) (* y y))
70.0ms	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
213.0ms	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	409	723
1	2178	618
2	5001	603

prune526.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
38.8b	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

49×	`sqrt-prod`
38×	`add-sqr-sqrt`
36×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
9×	`sqrt-div`
8×	`sqrt-pow1`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `pow1/2` `flip-+`
2×	`hypot-def` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sqrt-undiv` `frac-2neg` `pow-plus` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 122

Calls

4 calls:

24.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
28.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
16.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series794.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
276.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
125.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
124.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify121.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	248	1565
1	762	1485
2	3773	1460
3	5002	1460

prune445.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.3b

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ z (sqrt 3.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
6×	`associate-/r*`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 41

Calls

1 calls:

3.0ms

(/ z (sqrt 3.0))

series68.0ms

Counts

1 → 3

Calls

1 calls:

68.0ms

(/ z (sqrt 3.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (70.0ms)

Iter	Nodes	Cost
0	105	223
1	275	213
2	731	203
3	2029	203
4	5002	202

prune86.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 21.3b

regimes632.0ms

Accuracy

55.3% (8.8b remaining)

Error of 27.4b against oracle of 18.6b and baseline of 38.3b

bsearch126.0ms

Steps

Iters	Range		Point
3	1.5765673566733113e+121	1.9108656425680437e+121	1.597460999541732e+121
9	1.6611258736907357e+60	4.620139067381952e+65	4.545831989981156e+65
10	-3.5223794056915216e+55	-5.778619763743718e+44	-3.4794970398246474e+55

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	15
1	43	15
2	43	15

end0.0ms

sample457.0ms

Algorithm

intervals

Results

282.0ms

8000×

body

valid