Details

Time bar (total: 4.3s)

sample32.0ms

Algorithm
intervals
Results
22.0ms256×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: 42.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
38.8b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite52.0ms

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:
3.0ms
(+ (* x x) (* y y))
32.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series239.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* x x) (* y y))
47.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
165.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify128.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (115.0ms)

IterNodesCost
0294707
11224644
24405642
35001640

prune226.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow y 2) (pow z 2))
0.3b
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
38.8b
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
8×pow1
7×add-sqr-sqrt distribute-lft-out
6×associate-*r*
5×add-exp-log add-cube-cbrt unpow-prod-down add-cbrt-cube add-log-exp
4×associate-*r/
3×flip3-+ associate-*l* flip-+
2×sqrt-pow1 sqrt-div pow-prod-down
1×+-commutative distribute-rgt-in distribute-lft-in pow1/2 prod-exp sum-log sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 51
Calls
3 calls:
9.0ms
(+ (pow y 2) (pow z 2))
111.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
28.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series239.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (pow y 2) (pow z 2))
52.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
160.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify39.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0260411
11384379
25002378

prune152.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.3b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
39.0b
(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))
23.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series342.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* x x) (* y y))
220.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify99.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
02941188
110831124
240831101
350011101

prune249.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.7b

localize4.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ z (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
(/ z (sqrt 3.0))

series58.0ms

Counts
1 → 3
Calls
1 calls:
58.0ms
(/ z (sqrt 3.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 4 (49.0ms)

IterNodesCost
0103217
1273207
2729197
32027197
45001196

prune73.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.7b

regimes924.0ms

Accuracy

43.6% (16.2b remaining)

Error of 28.5b against oracle of 12.3b and baseline of 41.0b

bsearch287.0ms

Steps
ItersRangePoint
5
1.3633964723283668e+110
4.321994932968824e+110
4.245734338350756e+110
5
1.3424345861994201e+79
2.881075092756815e+79
1.4079949245820615e+79
5
1.0128241126019152e-62
3.911469862670213e-62
3.6020310138858934e-62
9
-5.609608288906496e-172
-5.021689689751489e-179
-5.178390466828926e-174
9
-1.0385934880099485e-95
-1.3034355320647412e-101
-3.265579843763803e-100
11
-3.314665875535389e+27
-3.016982961048864
-2.110786827503938e+24
6
-1.4834030117593821e+122
-2.124845354426568e+121
-3.9555152073667915e+121

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06051
16251
26251

end0.0ms

sample895.0ms

Algorithm
intervals
Results
722.0ms8000×body80valid