Details

sample41.0ms

Algorithm

intervals

Results

29.0ms

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: 39.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite61.0ms

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:

2.0ms	(+ (* x x) (* y y))
11.0ms	(+ (+ (* x x) (* y y)) (* z z))
28.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series282.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (* x x) (* y y)) (* z z))
54.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
164.0ms	(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

prune242.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite68.0ms

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:

2.0ms	(+ (* x x) (* y y))
11.0ms	(+ (+ (* x x) (* y y)) (* z z))
39.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (* x x) (* y y)) (* z z))
160.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
95.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify43.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (34.0ms)

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

prune238.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.3b

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 3.0))
36.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite257.0ms

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:

2.0ms	(+ (* x x) (* y y))
12.0ms	(+ (+ (* x x) (* y y)) (* z z))
226.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
12.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* x x) (* y y))
35.0ms	(+ (+ (* x x) (* y y)) (* z z))
214.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
100.0ms	(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

prune263.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 15.5b

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))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(/ x (sqrt 3.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 4 (54.0ms)

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

prune75.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 15.5b

regimes634.0ms

Accuracy

43.3% (14.6b remaining)

Error of 27.4b against oracle of 12.8b and baseline of 38.5b

bsearch213.0ms

Steps

Iters	Range		Point
9	1.888478144065373e+152	1.9238923005045905e+158	2.3757984146179946e+152
11	-1.3495990944802807e-217	-1.4741522130286226e-248	-2.5746552440525236e-243
8	-1451612.104863074	-1078.7327260164275	-1182.041878556847
8	-2.574833517855131e+125	-3.0685301016191877e+121	-2.187041864145105e+125

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	33
1	50	33
2	54	33
3	54	33

end0.0ms

sample851.0ms

Algorithm

intervals

Results

664.0ms

8000×

body

valid