Details

Time bar (total: 13.9s)

sample44.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify21.0ms

Counts
1 → 1
Iterations
IterNodes
done25
325
222
115
011

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize43.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y y) (+ (* x x) (* z z)))
0.1b
(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
35.9b
(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
8×add-log-exp
5×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* sum-log associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+r+ clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp
Counts
3 → 67
Calls
3 calls:
26.0ms
(+ (* y y) (+ (* x x) (* z z)))
53.0ms
(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
32.0ms
(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

series387.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ (* y y) (+ (* x x) (* z z)))
72.0ms
(/ (+ (* y y) (+ (* x x) (* z z))) 3.0)
261.0ms
(sqrt (/ (+ (* y y) (+ (* x x) (* z z))) 3.0))

simplify782.0ms

Counts
76 → 76
Iterations
IterNodes
done5001
21463
1296
0123

prune461.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* z z) (* y y))
0.0b
(+ (* x x) (+ (* z z) (* y y)))
0.3b
(* (sqrt (+ (* x x) (+ (* z z) (* y y)))) (sqrt (/ 1 3.0)))
35.9b
(sqrt (+ (* x x) (+ (* z z) (* y y))))

rewrite155.0ms

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-cbrt-cube associate-*l* add-exp-log
5×flip3-+ flip-+
4×sum-log
3×sqrt-pow1 pow1/2 pow-prod-down
2×frac-times +-commutative associate-*l/
1×rem-sqrt-square associate-+r+ sqrt-unprod prod-exp associate-*r/ *-commutative cbrt-unprod div-inv
Counts
4 → 88
Calls
4 calls:
6.0ms
(+ (* z z) (* y y))
16.0ms
(+ (* x x) (+ (* z z) (* y y)))
87.0ms
(* (sqrt (+ (* x x) (+ (* z z) (* y y)))) (sqrt (/ 1 3.0)))
44.0ms
(sqrt (+ (* x x) (+ (* z z) (* y y))))

series479.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ (* z z) (* y y))
55.0ms
(+ (* x x) (+ (* z z) (* y y)))
243.0ms
(* (sqrt (+ (* x x) (+ (* z z) (* y y)))) (sqrt (/ 1 3.0)))
134.0ms
(sqrt (+ (* x x) (+ (* z z) (* y y))))

simplify994.0ms

Counts
100 → 100
Iterations
IterNodes
done5001
21998
1392
0151

prune539.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.4b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×*-un-lft-identity add-cube-cbrt
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×associate-/r* add-exp-log associate-/l*
5×add-cbrt-cube
4×sqrt-pow1 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/l/
1×frac-times cbrt-undiv clear-num frac-2neg div-exp pow-prod-down associate-*l/ associate-*r/ div-inv
Counts
4 → 106
Calls
4 calls:
41.0ms
(/ (sqrt (+ (* x x) (+ (* z z) (* y y)))) (cbrt 3.0))
26.0ms
(sqrt (+ (* x x) (+ (* z z) (* y y))))
29.0ms
(sqrt (+ (* x x) (+ (* z z) (* y y))))
52.0ms
(sqrt (* (/ (sqrt (+ (* x x) (+ (* z z) (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (* x x) (+ (* z z) (* y y)))) (cbrt 3.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
349.0ms
(/ (sqrt (+ (* x x) (+ (* z z) (* y y)))) (cbrt 3.0))
147.0ms
(sqrt (+ (* x x) (+ (* z z) (* y y))))
147.0ms
(sqrt (+ (* x x) (+ (* z z) (* y y))))
493.0ms
(sqrt (* (/ (sqrt (+ (* x x) (+ (* z z) (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (* x x) (+ (* z z) (* y y)))) (cbrt 3.0))))

simplify2.0s

Counts
118 → 118
Iterations
IterNodes
done5001
34392
2856
1268
0145

prune825.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cbrt (+ (* x x) (+ (* z z) (* y y)))) 3.0)
0.3b
(* (fabs (cbrt (+ (* x x) (+ (* z z) (* y y))))) (sqrt (/ (cbrt (+ (* x x) (+ (* z z) (* y y)))) 3.0)))
37.0b
(cbrt (+ (* x x) (+ (* z z) (* y y))))
37.0b
(cbrt (+ (* x x) (+ (* z z) (* y y))))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
38×times-frac
36×*-un-lft-identity add-cube-cbrt
28×cbrt-prod
25×associate-*r* sqrt-prod
8×add-exp-log
7×add-cbrt-cube
6×pow1 cbrt-div associate-/l*
4×add-log-exp unswap-sqr
3×associate-/r* flip3-+ associate-*l* flip-+
2×pow1/3 div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-div div-exp pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 111
Calls
4 calls:
74.0ms
(/ (cbrt (+ (* x x) (+ (* z z) (* y y)))) 3.0)
118.0ms
(* (fabs (cbrt (+ (* x x) (+ (* z z) (* y y))))) (sqrt (/ (cbrt (+ (* x x) (+ (* z z) (* y y)))) 3.0)))
20.0ms
(cbrt (+ (* x x) (+ (* z z) (* y y))))
20.0ms
(cbrt (+ (* x x) (+ (* z z) (* y y))))

series816.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (cbrt (+ (* x x) (+ (* z z) (* y y)))) 3.0)
311.0ms
(* (fabs (cbrt (+ (* x x) (+ (* z z) (* y y))))) (sqrt (/ (cbrt (+ (* x x) (+ (* z z) (* y y)))) 3.0)))
153.0ms
(cbrt (+ (* x x) (+ (* z z) (* y y))))
172.0ms
(cbrt (+ (* x x) (+ (* z z) (* y y))))

simplify1.1s

Counts
123 → 123
Iterations
IterNodes
done5001
22000
1490
0222

prune1.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.4b

regimes872.0ms

Accuracy

37.6% (19.7b remaining)

Error of 26.0b against oracle of 6.3b and baseline of 37.8b

bsearch163.0ms

Steps
ItersRangePoint
2
1.742174409442309e+138
1.9984873672364886e+138
1.902370008063671e+138
6
3.2169827340741625e-158
3.8351514196249426e-157
3.2674790057421634e-158
8
1.1080663442396689e-198
2.711563690867585e-195
2.6739111412369096e-195
9
-4.43927391119578e+89
-1.1635566203916602e+84
-1.7173332726401035e+89

simplify7.0ms

Iterations
IterNodes
done44
244
141
032

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s8000×body80valid