Details

Time bar (total: 10.8s)

sample26.0ms

Algorithm
intervals
Results
11.0ms279×body80valid

simplify92.0ms

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: 5.1b

localize9.0ms

Local error

Found 2 expressions with local error:

2.6b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.1b
(* y (+ 1.0 (* z z)))

rewrite74.0ms

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:
42.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
26.0ms
(* y (+ 1.0 (* z z)))

series173.0ms

Counts
2 → 6
Calls
2 calls:
91.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
82.0ms
(* y (+ 1.0 (* z z)))

simplify1.2s

Counts
76 → 76
Iterations

Useful iterations: 2 (493.0ms)

IterNodesCost
01561062
14391035
22200897
done5002897

prune269.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize28.0ms

Local error

Found 2 expressions with local error:

2.4b
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))
3.2b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))

rewrite188.0ms

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:
36.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))
124.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))

series418.0ms

Counts
2 → 6
Calls
2 calls:
151.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))
267.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))

simplify660.0ms

Counts
244 → 244
Iterations

Useful iterations: done (648.0ms)

IterNodesCost
03635187
112154879
done50014645

prune857.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.7b
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
4.0b
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

rewrite288.0ms

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)
2.0ms
(cbrt x)
38.0ms
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
210.0ms
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

series1.1s

Counts
4 → 12
Calls
4 calls:
248.0ms
(cbrt x)
236.0ms
(cbrt x)
366.0ms
(/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z)))
249.0ms
(* (/ (/ (sqrt 1.0) (* (cbrt x) (cbrt x))) y) (/ (/ (sqrt 1.0) (cbrt x)) (+ 1.0 (* z z))))

simplify932.0ms

Counts
434 → 434
Iterations

Useful iterations: done (917.0ms)

IterNodesCost
057611136
1200410511
done50019996

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ 1.0 (* x (* y (+ 1.0 (* z z)))))
2.4b
(* x (* y (+ 1.0 (* z z))))
4.1b
(* y (+ 1.0 (* z z)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
10×pow1 add-sqr-sqrt associate-*r/
8×add-cube-cbrt *-un-lft-identity
7×prod-exp cbrt-unprod
6×associate-*l*
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down
3×cbrt-undiv flip3-+ times-frac div-exp flip-+ associate-/l* add-log-exp
2×associate-/r/ *-commutative
1×frac-2neg clear-num associate-/r* div-inv unswap-sqr
Counts
3 → 71
Calls
3 calls:
29.0ms
(/ 1.0 (* x (* y (+ 1.0 (* z z)))))
25.0ms
(* x (* y (+ 1.0 (* z z))))
17.0ms
(* y (+ 1.0 (* z z)))

series193.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(/ 1.0 (* x (* y (+ 1.0 (* z z)))))
72.0ms
(* x (* y (+ 1.0 (* z z))))
55.0ms
(* y (+ 1.0 (* z z)))

simplify948.0ms

Counts
80 → 80
Iterations

Useful iterations: done (945.0ms)

IterNodesCost
01241034
13651010
22134836
done5000824

prune183.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.6b

regimes328.0ms

Accuracy

2.7% (1.4b remaining)

Error of 6.4b against oracle of 5.0b and baseline of 6.4b

bsearch8.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01832
12232
done2232

end0.0ms

sample1.1s

Algorithm
intervals
Results
795.0ms8626×body80valid