Details

sample26.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 35.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite50.0ms

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

Counts

3 → 65

Calls

3 calls:

2.0ms	(+ (* x x) (* y y))
32.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series254.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
178.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify126.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	294	707
1	1224	644
2	4405	642
3	5001	640

prune201.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
32.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

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)))

series353.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
223.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
103.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify100.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	294	1188
1	1083	1124
2	4083	1101
3	5001	1101

prune225.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`sqrt-div`
8×	`pow1` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `associate-r/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 75

Calls

3 calls:

2.0ms	(+ (* x x) (* y y))
39.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
178.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
109.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify120.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	318	858
1	1226	828
2	4730	804
3	5002	796

prune201.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 14.2b

localize5.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ 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))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(/ x (sqrt 3.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 4 (44.0ms)

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

prune74.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 14.2b

regimes568.0ms

Accuracy

48.2% (13.2b remaining)

Error of 25.9b against oracle of 12.6b and baseline of 38.2b

bsearch186.0ms

Steps

Iters	Range		Point
9	1.2351546022638887e+92	1.9221479926683782e+97	4.982936361432774e+94
10	7.301571605531334e-229	2.3097359530250173e-211	7.012294660736446e-227
7	-1.415840716860803e-267	-2.9025922612993884e-269	-4.449993086430283e-268
11	-5.765687123026767e+152	-2.3106012996827125e+132	-1.6867875730018388e+145

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	27
1	41	27
2	41	27

end0.0ms

sample726.0ms

Algorithm

intervals

Results

559.0ms

8000×

body

valid