Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify8.0ms

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: 37.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite24.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series302.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (* x x) (* y y)) (* z z))
49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
191.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (31.0ms)

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

prune331.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.5b

localize11.0ms

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 (/ 1 3.0)))
34.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

3.0ms	(+ (* x x) (* y y))
5.0ms	(+ (+ (* x x) (* y y)) (* z z))
13.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
38.0ms	(+ (+ (* x x) (* y y)) (* z z))
155.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
93.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	354	986
1	1482	945
2	5001	924

prune247.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.5b

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))
34.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite29.0ms

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:

6.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* x x) (* y y))
37.0ms	(+ (+ (* x x) (* y y)) (* z z))
230.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
96.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (32.0ms)

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

prune232.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.4b

localize4.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ (* -1 x) (sqrt 3.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-exp-log` `times-frac` `associate-/r*` `sqrt-prod` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`cbrt-undiv` `div-exp`
1×	`pow1` `frac-2neg` `mul-1-neg` `distribute-frac-neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

5.0ms

(/ (* -1 x) (sqrt 3.0))

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

(/ (* -1 x) (sqrt 3.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	132	140
1	693	121
2	4212	121
3	5001	121

prune72.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 16.4b

regimes521.0ms

Accuracy

61.4% (7.6b remaining)

Error of 25.9b against oracle of 18.3b and baseline of 38.1b

bsearch61.0ms

Steps

Iters	Range		Point
8	2.796236108609171e+125	1.4046107460541326e+130	6.392742446151673e+128
6	-2.038249239639625e+41	-4.492569743774758e+40	-2.009142108550562e+41

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	21
1	37	21

end0.0ms

sample424.0ms

Algorithm

intervals

Results

267.0ms

8000×

body

valid