Details

Time bar (total: 3.7s)

sample16.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×rem-sqrt-square div-inv associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 54
Calls
2 calls:
32.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series211.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
160.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify91.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0214630
1835578
23408576
35001574

prune165.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
29×sqrt-prod
16×associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt times-frac
9×sqrt-div
8×unswap-sqr
7×pow1
6×associate-*l*
4×add-exp-log add-cbrt-cube
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×frac-times associate-*l/ add-log-exp
1×rem-sqrt-square sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 64
Calls
2 calls:
40.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series268.0ms

Counts
2 → 6
Calls
2 calls:
167.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify77.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0235788
1772762
22635738
35001725

prune164.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.6b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.7b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
36×add-sqr-sqrt 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×add-log-exp
3×rem-sqrt-square flip3-+ pow1/2 flip-+
2×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 → 112
Calls
4 calls:
23.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
14.0ms
(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))))

series645.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
98.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
226.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

simplify86.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
02381481
17281407
236131383
350021383

prune313.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 16.5b

localize4.0ms

Local error

Found 1 expressions with local error:

0.3b
(* z (sqrt (/ 1 3.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
16×associate-*r* sqrt-prod
11×*-un-lft-identity times-frac
10×add-cube-cbrt
4×unswap-sqr
3×pow1 add-exp-log associate-*l* add-cbrt-cube
1×sqrt-div associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod div-inv add-log-exp
Counts
1 → 35
Calls
1 calls:
11.0ms
(* z (sqrt (/ 1 3.0)))

series43.0ms

Counts
1 → 3
Calls
1 calls:
43.0ms
(* z (sqrt (/ 1 3.0)))

simplify229.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 3 (24.0ms)

IterNodesCost
0133185
1443172
21117156
31916145
45001145

prune58.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 16.5b

regimes513.0ms

Accuracy

62.9% (7.3b remaining)

Error of 25.6b against oracle of 18.3b and baseline of 38.0b

bsearch70.0ms

Steps
ItersRangePoint
9
2.1628060713373462e+108
2.6911721134682347e+113
7.68757953447697e+110
7
-8.718926718946052e+135
-6.852890468496449e+133
-3.694047169561497e+135

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03314
13914
23914

end0.0ms

sample556.0ms

Algorithm
intervals
Results
344.0ms8000×body80valid