Details

Time bar (total: 16.0s)

sample27.0ms

Algorithm
intervals
Results
9.0ms273×body80valid

simplify57.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12111
23711
35911
48811
511111
done11111

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 2 expressions with local error:

3.5b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.0b
(* y (+ 1.0 (* z z)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
17.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
16.0ms
(* y (+ 1.0 (* z z)))

series118.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
58.0ms
(* y (+ 1.0 (* z z)))

simplify1.0s

Counts
76 → 76
Iterations

Useful iterations: 2 (298.0ms)

IterNodesCost
01561062
14391035
22200897
done5002897

prune216.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.4b
(/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
4.0b
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) y) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
555×times-frac
341×add-sqr-sqrt
272×add-cube-cbrt *-un-lft-identity
270×cbrt-prod
126×associate-*r*
102×add-exp-log
64×add-cbrt-cube
48×cbrt-undiv div-exp
40×associate-/l*
30×prod-exp cbrt-unprod
19×associate-*l*
18×unswap-sqr
13×div-inv
6×pow1
4×associate-/r/ add-log-exp
3×associate-/r*
2×flip3-+ pow1/3 flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 413
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
33.0ms
(/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
176.0ms
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) y) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

series963.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(cbrt x)
231.0ms
(cbrt x)
286.0ms
(/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
197.0ms
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) y) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

simplify1.1s

Counts
425 → 425
Iterations

Useful iterations: done (1.1s)

IterNodesCost
062111655
1228211161
done500110355

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.4b
(/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
1.7b
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (cbrt y)) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z))))
1.8b
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (* (cbrt y) (cbrt y))) (* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (cbrt y)) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))))

rewrite647.0ms

Algorithm
rewrite-expression-head
Rules
666×times-frac
465×add-sqr-sqrt
325×cbrt-prod
294×add-cube-cbrt *-un-lft-identity
138×add-exp-log
127×associate-*r*
94×add-cbrt-cube
64×associate-*l*
59×sqrt-prod
53×cbrt-undiv div-exp
52×prod-exp cbrt-unprod
42×unswap-sqr
40×associate-/l*
18×div-inv
11×pow1
6×frac-times associate-*r/
4×pow-prod-down associate-*l/ associate-/r/ add-log-exp
3×associate-/r*
2×flip3-+ *-commutative flip-+
1×frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 507
Calls
4 calls:
1.0ms
(cbrt x)
23.0ms
(/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
221.0ms
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (cbrt y)) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z))))
362.0ms
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (* (cbrt y) (cbrt y))) (* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (cbrt y)) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
249.0ms
(cbrt x)
278.0ms
(/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
272.0ms
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (cbrt y)) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z))))
220.0ms
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (* (cbrt y) (cbrt y))) (* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (cbrt y)) (/ (/ (cbrt 1.0) (cbrt x)) (+ 1.0 (* z z)))))

simplify1.3s

Counts
519 → 519
Iterations

Useful iterations: done (1.2s)

IterNodesCost
072218500
1258817052
done500015332

prune3.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.8b
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (* (cbrt y) (cbrt y))) (* (/ (/ (sqrt (/ (pow (cbrt 1.0) 2) (* (cbrt x) (cbrt x)))) (cbrt y)) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) (cbrt x)) (sqrt (+ 1.0 (* z z))))))
15.9b
(sqrt (+ 1.0 (* z z)))
15.9b
(sqrt (+ 1.0 (* z z)))

rewrite518.0ms

Algorithm
rewrite-expression-head
Rules
175×add-exp-log
128×add-cbrt-cube
74×cbrt-undiv div-exp
67×prod-exp cbrt-unprod
12×add-sqr-sqrt associate-*l*
11×pow1 sqrt-prod
10×add-cube-cbrt *-un-lft-identity
9×times-frac
5×frac-times associate-*r/
4×sqrt-div add-log-exp
3×cbrt-prod pow-prod-down associate-*l/
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ div-inv
1×pow1/3 associate-*r* *-commutative
Counts
4 → 131
Calls
4 calls:
1.0ms
(cbrt x)
499.0ms
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (* (cbrt y) (cbrt y))) (* (/ (/ (sqrt (/ (pow (cbrt 1.0) 2) (* (cbrt x) (cbrt x)))) (cbrt y)) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) (cbrt x)) (sqrt (+ 1.0 (* z z))))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series595.0ms

Counts
4 → 12
Calls
4 calls:
266.0ms
(cbrt x)
221.0ms
(* (/ (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x)))) (* (cbrt y) (cbrt y))) (* (/ (/ (sqrt (/ (pow (cbrt 1.0) 2) (* (cbrt x) (cbrt x)))) (cbrt y)) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) (cbrt x)) (sqrt (+ 1.0 (* z z))))))
51.0ms
(sqrt (+ 1.0 (* z z)))
57.0ms
(sqrt (+ 1.0 (* z z)))

simplify916.0ms

Counts
143 → 143
Iterations

Useful iterations: done (908.0ms)

IterNodesCost
02778407
19547386
done50005167

prune685.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

regimes462.0ms

Accuracy

0% (1.2b remaining)

Error of 6.3b against oracle of 5.1b and baseline of 6.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02653
12953
done2953

end0.0ms

sample1.0s

Algorithm
intervals
Results
594.0ms8634×body80valid