Details

Time bar (total: 13.1s)

sample20.0ms

Algorithm
intervals
Results
10.0ms272×body80valid

simplify83.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12111
23711
35811
48711
511111
done11111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize16.0ms

Local error

Found 2 expressions with local error:

3.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
6.0b
(* y (+ 1.0 (* z z)))

rewrite75.0ms

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:
32.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
30.0ms
(* y (+ 1.0 (* z z)))

series145.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
64.0ms
(* y (+ 1.0 (* z z)))

simplify1.7s

Counts
76 → 76
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01561062
13951035
21321887
done5000885

prune243.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 2 expressions with local error:

3.9b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
4.2b
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
299×times-frac
199×add-sqr-sqrt
152×add-cube-cbrt *-un-lft-identity
79×sqrt-prod
72×associate-*r*
28×add-exp-log add-cbrt-cube
22×associate-*l* associate-/l*
12×cbrt-undiv div-exp unswap-sqr
10×div-inv
6×prod-exp cbrt-unprod
4×pow1 associate-/r/
3×associate-/r*
2×flip3-+ flip-+ add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
2 → 238
Calls
2 calls:
120.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
50.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

series419.0ms

Counts
2 → 6
Calls
2 calls:
274.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
145.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

simplify2.1s

Counts
244 → 244
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03635187
110584711
235404441
done50004401

prune922.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
3.4b
(* (/ (sqrt 1.0) y) (/ (/ (fabs (cbrt 1.0)) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z)))))
17.3b
(sqrt (+ 1.0 (* z z)))
17.3b
(sqrt (+ 1.0 (* z z)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
106×times-frac
101×add-sqr-sqrt
48×associate-*r*
47×add-cube-cbrt *-un-lft-identity sqrt-prod
36×add-exp-log
32×add-cbrt-cube
22×associate-*l*
15×unswap-sqr
14×cbrt-undiv div-exp
10×prod-exp cbrt-unprod
8×pow1 div-inv
6×sqrt-div
4×add-log-exp
3×cbrt-prod flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 154
Calls
4 calls:
1.0ms
(cbrt x)
108.0ms
(* (/ (sqrt 1.0) y) (/ (/ (fabs (cbrt 1.0)) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

series745.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(cbrt x)
366.0ms
(* (/ (sqrt 1.0) y) (/ (/ (fabs (cbrt 1.0)) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z)))))
46.0ms
(sqrt (+ 1.0 (* z z)))
72.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.9s

Counts
166 → 166
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02953781
18543528
232173016
done50003005

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.7b

localize17.0ms

Local error

Found 2 expressions with local error:

0.7b
(/ 1.0 (* x y))
7.5b
(/ (/ 1.0 (* x y)) (+ 1.0 (* z z)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
10×associate-/l*
7×cbrt-undiv div-exp
6×div-inv
4×associate-/r*
2×pow1 frac-2neg prod-exp clear-num associate-/r/ cbrt-unprod add-log-exp
1×flip3-+ flip-+ associate-/l/
Counts
2 → 71
Calls
2 calls:
15.0ms
(/ 1.0 (* x y))
37.0ms
(/ (/ 1.0 (* x y)) (+ 1.0 (* z z)))

series132.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(/ 1.0 (* x y))
108.0ms
(/ (/ 1.0 (* x y)) (+ 1.0 (* z z)))

simplify1.3s

Counts
77 → 77
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01401176
13491141
211391023
done50001021

prune242.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.7b

regimes347.0ms

Accuracy

0% (1.3b remaining)

Error of 6.0b against oracle of 4.7b and baseline of 6.0b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11315
done1315

end0.0ms

sample1.2s

Algorithm
intervals
Results
556.0ms8613×body80valid