Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	7
1	27	7
2	33	7
3	34	7
4	34	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize13.0ms

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))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `sum-log` `log1p-expm1-u`
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 → 90

Calls

4 calls:

13.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
30.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series298.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
54.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
177.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	345	852
1	1445	759
2	5001	739

prune303.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.6b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

0.0ms	(fma y y (* z z))
3.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
2.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

series276.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(fma y y (* z z))
58.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
181.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	137	272
1	541	235
2	2831	235
3	5001	235

prune128.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.9b	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

49×	`sqrt-prod`
38×	`add-sqr-sqrt`
36×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
9×	`sqrt-div`
8×	`sqrt-pow1`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `pow1/2` `flip-+`
2×	`hypot-def` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sqrt-undiv` `frac-2neg` `pow-plus` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 122

Calls

4 calls:

23.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
14.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
17.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
23.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
104.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
237.0ms	(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	248	1565
1	762	1485
2	3773	1460
3	5001	1460

prune377.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.5b

localize4.0ms

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` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 41

Calls

1 calls:

3.0ms

(/ x (sqrt 3.0))

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

(/ x (sqrt 3.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (53.0ms)

Iter	Nodes	Cost
0	105	223
1	275	213
2	731	203
3	2029	203
4	5002	202

prune72.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 17.5b

regimes535.0ms

Accuracy

61.7% (7.5b remaining)

Error of 25.7b against oracle of 18.2b and baseline of 37.9b

bsearch70.0ms

Steps

Iters	Range		Point
10	7.491092794297452e+92	6.705329414328681e+109	6.601942283666501e+109
6	-1.6055413863283287e+120	-1.9275148810805934e+119	-4.241172532402712e+119

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	28	10
2	28	10

end0.0ms

sample445.0ms

Algorithm

intervals

Results

273.0ms

8000×

body

valid