Details

Time bar (total: 17.9s)

sample34.0ms

Algorithm
intervals
Results
15.0ms270×body80valid

simplify88.0ms

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: 6.4b

localize9.0ms

Local error

Found 2 expressions with local error:

3.4b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.4b
(* y (+ 1.0 (* z z)))

rewrite42.0ms

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:
22.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
18.0ms
(* y (+ 1.0 (* z z)))

series166.0ms

Counts
2 → 6
Calls
2 calls:
89.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
77.0ms
(* y (+ 1.0 (* z z)))

simplify1.4s

Counts
76 → 76
Iterations

Useful iterations: 2 (331.0ms)

IterNodesCost
01561062
14391035
22200897
done5002897

prune243.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize10.0ms

Local error

Found 2 expressions with local error:

2.7b
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
3.4b
(/ (/ 1.0 x) (+ 1.0 (* z z)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
116×add-sqr-sqrt
89×*-un-lft-identity
86×add-cube-cbrt
46×add-exp-log
45×associate-*r*
28×add-cbrt-cube
21×div-exp
13×associate-*l* associate-/l*
12×cbrt-undiv prod-exp
10×div-inv
9×unswap-sqr
6×cbrt-unprod
4×pow1 associate-/r/
3×rec-exp 1-exp 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 → 169
Calls
2 calls:
67.0ms
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
21.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

series160.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
90.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

simplify663.0ms

Counts
175 → 175
Iterations

Useful iterations: done (653.0ms)

IterNodesCost
03063281
110233108
done50002716

prune597.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

localize18.0ms

Local error

Found 2 expressions with local error:

2.7b
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
3.4b
(/ (/ 1.0 x) (+ 1.0 (* z z)))

rewrite111.0ms

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:
54.0ms
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
30.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

series201.0ms

Counts
2 → 6
Calls
2 calls:
84.0ms
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
116.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

simplify724.0ms

Counts
278 → 278
Iterations

Useful iterations: done (711.0ms)

IterNodesCost
05126378
113606051
done50005919

prune950.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1.0 x) (sqrt (+ 1.0 (* z z))))
2.7b
(/ (/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))) y)
15.7b
(sqrt (+ 1.0 (* z z)))
15.7b
(sqrt (+ 1.0 (* z z)))

rewrite657.0ms

Algorithm
rewrite-expression-head
Rules
6855×times-frac
2928×add-sqr-sqrt
2926×add-cube-cbrt *-un-lft-identity
1992×sqrt-prod
523×associate-/l*
181×div-inv
62×sqrt-div
58×associate-/r/
31×flip3-+ flip-+
23×add-exp-log add-cbrt-cube
13×cbrt-undiv div-exp
9×associate-/r*
6×pow1
4×add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 2206
Calls
4 calls:
23.0ms
(/ (/ 1.0 x) (sqrt (+ 1.0 (* z z))))
226.0ms
(/ (/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))) y)
6.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (/ 1.0 x) (sqrt (+ 1.0 (* z z))))
76.0ms
(/ (/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))) y)
57.0ms
(sqrt (+ 1.0 (* z z)))
46.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.8s

Counts
2218 → 2218
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0278988288
done500081469

prune8.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.9b

regimes292.0ms

Accuracy

0% (1.6b remaining)

Error of 6.7b against oracle of 5.0b and baseline of 6.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11219
done1219

end0.0ms

sample872.0ms

Algorithm
intervals
Results
526.0ms8610×body80valid