Details

Time bar (total: 16.6s)

sample22.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify37.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite195.0ms

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:
8.0ms
(+ (* x x) (* y y))
122.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
62.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series364.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ (* x x) (* y y))
77.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
237.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.0s

Counts
74 → 74

prune325.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow x 2) (pow y 2))
0.1b
(/ (+ (+ (pow x 2) (pow y 2)) (* z z)) 3.0)
32.7b
(sqrt (/ (+ (+ (pow x 2) (pow y 2)) (* z z)) 3.0))

rewrite438.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt
13×sqrt-prod
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×associate-/r* associate-/l*
2×unpow-prod-down rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/ distribute-lft-out
1×cbrt-undiv +-commutative frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 67
Calls
3 calls:
33.0ms
(+ (pow x 2) (pow y 2))
275.0ms
(/ (+ (+ (pow x 2) (pow y 2)) (* z z)) 3.0)
127.0ms
(sqrt (/ (+ (+ (pow x 2) (pow y 2)) (* z z)) 3.0))

series382.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ (pow x 2) (pow y 2))
74.0ms
(/ (+ (+ (pow x 2) (pow y 2)) (* z z)) 3.0)
269.0ms
(sqrt (/ (+ (+ (pow x 2) (pow y 2)) (* z z)) 3.0))

simplify1.9s

Counts
76 → 76

prune278.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (/ 3.0 (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))))
32.6b
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
32.6b
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
32.7b
(sqrt (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (/ 3.0 (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))))))

rewrite946.0ms

Algorithm
rewrite-expression-head
Rules
532×times-frac
424×sqrt-prod
293×add-sqr-sqrt
274×add-cube-cbrt *-un-lft-identity
33×sqrt-div
28×associate-/r/
24×associate-/r*
16×flip3-+ flip-+
15×div-inv
9×add-exp-log rem-sqrt-square add-cbrt-cube
7×pow1
6×associate-/l*
4×add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×associate-/l/
1×frac-2neg clear-num
Counts
4 → 387
Calls
4 calls:
290.0ms
(/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (/ 3.0 (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))))
138.0ms
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
137.0ms
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
347.0ms
(sqrt (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (/ 3.0 (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))))))

series526.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (/ 3.0 (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))))
126.0ms
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
106.0ms
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
201.0ms
(sqrt (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (/ 3.0 (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))))))

simplify1.8s

Counts
399 → 399

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (cbrt 3.0))
32.6b
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
32.6b
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
32.7b
(sqrt (* (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (cbrt 3.0))))

rewrite668.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×sqrt-pow1 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 106
Calls
4 calls:
200.0ms
(/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (cbrt 3.0))
149.0ms
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
116.0ms
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
199.0ms
(sqrt (* (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (cbrt 3.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
246.0ms
(/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (cbrt 3.0))
131.0ms
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
165.0ms
(sqrt (+ (+ (pow x 2) (pow y 2)) (* z z)))
468.0ms
(sqrt (* (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (pow x 2) (pow y 2)) (* z z))) (cbrt 3.0))))

simplify869.0ms

Counts
118 → 118

prune594.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 16.2b

regimes198.0ms

Accuracy

63.7% (7.1b remaining)

Error of 25.6b against oracle of 18.5b and baseline of 38.1b

bsearch97.0ms

Steps
ItersRangePoint
10
2.8053186864578327e+135
2.73300969175321e+146
1.879788545217996e+136
4
-9.449645097479712e+129
-5.360575220071455e+129
-8.247629272160778e+129

simplify1.4s

end0.0ms

sample953.0ms

Algorithm
intervals
Results
612.0ms8000×body80valid