Details

Time bar (total: 13.6s)

sample16.0ms

Algorithm
intervals
Results
7.0ms274×body80valid

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
12111
23611
35611
48211
510011
done10011

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize7.0ms

Local error

Found 2 expressions with local error:

3.7b
(* y (+ 1.0 (* z z)))
5.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite18.0ms

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:
7.0ms
(* y (+ 1.0 (* z z)))
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series120.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(* y (+ 1.0 (* z z)))
62.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify604.0ms

Counts
76 → 76
Iterations

Useful iterations: 2 (172.0ms)

IterNodesCost
01561062
14081035
21620887
done5001887

prune184.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize9.0ms

Local error

Found 2 expressions with local error:

2.4b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
3.4b
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

rewrite86.0ms

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:
59.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
11.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

series295.0ms

Counts
2 → 6
Calls
2 calls:
177.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
118.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

simplify1.4s

Counts
244 → 244
Iterations

Useful iterations: 2 (576.0ms)

IterNodesCost
03635187
111154741
240144441
done50014441

prune811.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize7.0ms

Local error

Found 2 expressions with local error:

2.4b
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
3.4b
(/ (/ 1.0 x) (+ 1.0 (* z z)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
230×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
58×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
10×associate-/r/
9×cbrt-undiv div-exp
6×associate-/r*
5×flip3-+ flip-+
2×pow1 frac-2neg clear-num associate-/l/ add-log-exp
Counts
2 → 272
Calls
2 calls:
21.0ms
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
8.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

series125.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
57.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

simplify1.6s

Counts
278 → 278
Iterations

Useful iterations: 2 (800.0ms)

IterNodesCost
05126378
112426051
245845887
done50005887

prune773.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z))))
2.4b
(* (/ (sqrt 1.0) y) (/ (/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite589.0ms

Algorithm
rewrite-expression-head
Rules
2676×times-frac
1395×add-sqr-sqrt
1347×sqrt-prod
1171×add-cube-cbrt *-un-lft-identity
834×associate-*r*
52×div-inv
45×unswap-sqr
41×add-exp-log add-cbrt-cube
22×associate-*l* associate-/l*
20×sqrt-div
19×cbrt-undiv div-exp
16×associate-/r/
10×flip3-+ flip-+
8×pow1 prod-exp cbrt-unprod
6×associate-/r*
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1136
Calls
4 calls:
12.0ms
(/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z))))
436.0ms
(* (/ (sqrt 1.0) y) (/ (/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z))))
169.0ms
(* (/ (sqrt 1.0) y) (/ (/ (/ (sqrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
45.0ms
(sqrt (+ 1.0 (* z z)))
51.0ms
(sqrt (+ 1.0 (* z z)))

simplify3.8s

Counts
1148 → 1148
Iterations

Useful iterations: 1 (3.3s)

IterNodesCost
0140833233
1487627728
done500027728

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

regimes205.0ms

Accuracy

0% (1.6b remaining)

Error of 6.4b against oracle of 4.7b and baseline of 6.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01323
11623
done1623

end0.0ms

sample409.0ms

Algorithm
intervals
Results
239.0ms8683×body80valid