Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify7.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite65.0ms

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:

3.0ms	(+ (* x x) (* y y))
12.0ms	(+ (+ (* x x) (* y y)) (* z z))
33.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series267.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* x x) (* y y))
38.0ms	(+ (+ (* x x) (* y y)) (* z z))
47.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
157.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (28.0ms)

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

prune251.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
35.4b	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

3.0ms	(+ (* x x) (* y y))
12.0ms	(+ (+ (* x x) (* y y)) (* z z))
51.0ms	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
20.0ms	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
37.0ms	(+ (+ (* x x) (* y y)) (* z z))
48.0ms	(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
161.0ms	(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	407	839
1	2148	760
2	5002	742

prune212.0ms

Filtered

93 candidates to 65 candidates (69.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
0.2b	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
35.4b	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
47×	`cbrt-prod`
46×	`sqrt-prod`
18×	`add-exp-log`
16×	`div-inv`
11×	`add-cbrt-cube`
10×	`associate-/l*`
9×	`add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`pow1` `rem-sqrt-square`
3×	`sum-log` `associate-/l/`
2×	`frac-2neg` `flip3-+` `prod-exp` `clear-num` `cbrt-unprod` `flip-+`
1×	`+-commutative` `associate-+l+` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 169

Calls

4 calls:

12.0ms	(+ (+ (* x x) (* y y)) (* z z))
32.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
36.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
25.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
194.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
128.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
320.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	539	3046
1	2128	2845
2	5001	2818

prune587.0ms

Filtered

181 candidates to 152 candidates (84.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite58.0ms

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:

3.0ms	(+ (* x x) (* y y))
15.0ms	(+ (+ (* x x) (* y y)) (* z z))
24.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* x x) (* y y))
38.0ms	(+ (+ (* x x) (* y y)) (* z z))
208.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
95.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify41.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (29.0ms)

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

prune237.0ms

Filtered

114 candidates to 73 candidates (64.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.4b

regimes370.0ms

Accuracy

64.3% (7.0b remaining)

Error of 25.6b against oracle of 18.6b and baseline of 38.2b

bsearch77.0ms

Steps

Iters	Range		Point
9	1.8130882697008765e+84	7.489722728138725e+90	7.402306065731599e+90
10	-1.041760357593436e+169	-4.358594791243697e+152	-4.904012598659074e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	13
1	40	13
2	40	13

end0.0ms

sample430.0ms

Algorithm

intervals

Results

264.0ms

8000×

body

valid