Details

Time bar (total: 4.0s)

sample19.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347
done347

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite106.0ms

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×expm1-log1p-u rem-sqrt-square log1p-expm1-u 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 → 58
Calls
2 calls:
75.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
30.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series240.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
179.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify108.0ms

Counts
64 → 64
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0223655
1877586
23651577
35001577
done5001577

prune218.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.5b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log sqrt-div add-cbrt-cube
3×pow1
2×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
2 → 83
Calls
2 calls:
50.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
32.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series353.0ms

Counts
2 → 6
Calls
2 calls:
244.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
108.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify63.0ms

Counts
89 → 89
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02191150
16571087
224431063
350021063
done50021063

prune226.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (sqrt (+ (* x x) (* y y))) z)
0.4b
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
31.5b
(sqrt (+ (* x x) (* y y)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×times-frac
15×sqrt-prod
6×associate-/r*
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
2×hypot-udef sqrt-div
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp clear-num flip-+ hypot-def div-inv
Counts
3 → 70
Calls
3 calls:
0.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
9.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
8.0ms
(sqrt (+ (* x x) (* y y)))

series749.0ms

Counts
3 → 9
Calls
3 calls:
407.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
303.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
38.0ms
(sqrt (+ (* x x) (* y y)))

simplify115.0ms

Counts
79 → 79
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0214731
1558679
21420665
34000665
45001665
done5001665

prune243.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot (hypot x y) z)
0.4b
(/ (hypot (hypot x y) z) (sqrt 3.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
4×add-exp-log add-cbrt-cube
3×associate-/l*
2×pow1 expm1-log1p-u hypot-udef log1p-expm1-u add-log-exp
1×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
0.0ms
(hypot (hypot x y) z)
6.0ms
(/ (hypot (hypot x y) z) (sqrt 3.0))

series525.0ms

Counts
2 → 6
Calls
2 calls:
204.0ms
(hypot (hypot x y) z)
321.0ms
(/ (hypot (hypot x y) z) (sqrt 3.0))

simplify60.0ms

Counts
58 → 58
Iterations

Useful iterations: 4 (56.0ms)

IterNodesCost
0128397
1305374
2766363
32107363
45001362
done5001362

prune151.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes224.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0129
1129
done129

end0.0ms

sample470.0ms

Algorithm
intervals
Results
250.0ms8000×body80valid