Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

11.0ms	(+ (+ (* x x) (* y y)) (* z z))
2.0ms	(+ (* x x) (* y y))
30.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series267.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (+ (* x x) (* y y)) (* z z))
30.0ms	(+ (* x x) (* y y))
46.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
158.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	325	828
1	1345	761
2	5001	755

prune242.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.9b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`flip3-+` `associate-*r/` `sum-log` `flip-+`
3×	`associate-r` `associate-l`
2×	`+-commutative` `sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

12.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
33.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
9.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
31.0ms	(+ (* x x) (* y y))
51.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
170.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify43.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	310	539
1	1615	492
2	5001	492

prune157.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `sum-log` `flip-+`
2×	`+-commutative` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

15.0ms	(+ (+ (* x x) (* y y)) (* z z))
2.0ms	(+ (* x x) (* y y))
22.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
32.0ms	(+ (* x x) (* y y))
216.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
134.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	330	1316
1	1338	1241
2	5002	1218

prune260.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.4b

localize5.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ x (sqrt 3.0))

rewrite4.0ms

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` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

3.0ms

(/ x (sqrt 3.0))

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

(/ x (sqrt 3.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 4 (46.0ms)

Iter	Nodes	Cost
0	103	217
1	273	207
2	729	197
3	2027	197
4	5001	196

prune81.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 11.4b

regimes742.0ms

Accuracy

39.8% (15.4b remaining)

Error of 27.7b against oracle of 12.2b and baseline of 37.9b

bsearch194.0ms

Steps

Iters	Range		Point
10	7.491092794297452e+92	6.705329414328681e+109	4.868546484289821e+107
7	3.937278643333255e-21	3.6395300253035078e-19	4.368495005741588e-21
8	-2.1657762486138537e-223	-1.94649178438058e-226	-5.778603750163605e-226
9	-2.517375459137406e+24	-1134389816868286.8	-1.7101058514616343e+23
10	-1.9275148810805934e+119	-1.770083902157112e+107	-1.798744324637151e+107

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	33
1	59	33
2	62	33
3	62	33

end0.0ms

sample632.0ms

Algorithm

intervals

Results

467.0ms

8000×

body

valid