Details

Time bar (total: 6.2s)

sample20.0ms

Algorithm
intervals
Results
9.0ms277×body80valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215
done1215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize7.0ms

Local error

Found 2 expressions with local error:

4.2b
(* y (+ 1.0 (* z z)))
4.5b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite33.0ms

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:
15.0ms
(* y (+ 1.0 (* z z)))
15.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series116.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(* y (+ 1.0 (* z z)))
63.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify48.0ms

Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443
done5001443

prune153.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
6.6b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 frac-2neg clear-num associate-/r/ associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 264
Calls
2 calls:
10.0ms
(/ (/ 1.0 y) x)
26.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series81.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(/ (/ 1.0 y) x)
58.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify101.0ms

Counts
270 → 270
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
011322994
145722919
250022919
done50022919

prune688.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ 1.0 y))
1.3b
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
17.5b
(sqrt (+ 1.0 (* z z)))
17.5b
(sqrt (+ 1.0 (* z z)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
846×times-frac
408×add-sqr-sqrt
406×add-cube-cbrt *-un-lft-identity
286×cbrt-prod
165×sqrt-prod
52×associate-/l*
30×div-inv
9×add-exp-log
8×add-cbrt-cube
6×pow1 sqrt-div associate-/r*
4×add-log-exp
3×cbrt-undiv flip3-+ div-exp flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-div frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 439
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 y))
33.0ms
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(cbrt (/ 1.0 y))
180.0ms
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
48.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify133.0ms

Counts
451 → 451
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
015297159
147866956
250026916
done50026916

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
2.0b
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
5.2b
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
606×times-frac
385×add-sqr-sqrt
283×add-cube-cbrt *-un-lft-identity
149×sqrt-prod
140×cbrt-prod
126×associate-*r*
63×add-exp-log
52×add-cbrt-cube
40×associate-/l*
34×associate-*l*
30×cbrt-undiv div-exp
24×unswap-sqr
15×prod-exp cbrt-unprod
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 → 422
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
22.0ms
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
141.0ms
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(cbrt x)
173.0ms
(cbrt x)
213.0ms
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
190.0ms
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

simplify85.0ms

Counts
434 → 434
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
018656625
150016273
done50016273

prune1.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.8b

regimes162.0ms

Accuracy

0% (1.2b remaining)

Error of 6.1b against oracle of 4.9b and baseline of 6.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01617
11617
done1617

end0.0ms

sample447.0ms

Algorithm
intervals
Results
217.0ms8627×body80valid