Details

Time bar (total: 12.2s)

sample37.0ms

Algorithm
intervals
Results
16.0ms275×body80valid

simplify110.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12111
23711
35911
48811
511111
done11111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 2 expressions with local error:

3.3b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.1b
(* y (+ 1.0 (* z z)))

rewrite67.0ms

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:
41.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
19.0ms
(* y (+ 1.0 (* z z)))

series162.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
79.0ms
(* y (+ 1.0 (* z z)))

simplify1.2s

Counts
76 → 76
Iterations

Useful iterations: 2 (406.0ms)

IterNodesCost
01561062
14391035
22200897
done5002897

prune357.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize30.0ms

Local error

Found 2 expressions with local error:

2.9b
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
3.5b
(/ (/ 1.0 x) (+ 1.0 (* z z)))

rewrite85.0ms

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:
57.0ms
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
19.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

series169.0ms

Counts
2 → 6
Calls
2 calls:
97.0ms
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
72.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

simplify569.0ms

Counts
175 → 175
Iterations

Useful iterations: done (563.0ms)

IterNodesCost
03063281
110233108
done50002716

prune786.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize24.0ms

Local error

Found 2 expressions with local error:

2.9b
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
3.5b
(/ (/ 1.0 x) (+ 1.0 (* z z)))

rewrite94.0ms

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:
39.0ms
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
36.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

series159.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
77.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

simplify859.0ms

Counts
278 → 278
Iterations

Useful iterations: done (844.0ms)

IterNodesCost
05126378
113606051
done50005919

prune2.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.3b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
28×sqrt-div
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
16×associate-*r/
14×flip3-+ flip-+
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
8×frac-times associate-/r/
6×associate-*r*
4×associate-*l/ add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 117
Calls
4 calls:
56.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
61.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
97.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
81.0ms
(sqrt (+ 1.0 (* z z)))
77.0ms
(sqrt (+ 1.0 (* z z)))

simplify2.0s

Counts
129 → 129
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02172776
16282060
235261804
done50001728

prune629.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.2b

regimes731.0ms

Accuracy

0% (1.3b remaining)

Error of 6.5b against oracle of 5.2b and baseline of 6.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
01419
11813
22011
done2011

end0.0ms

sample1.0s

Algorithm
intervals
Results
577.0ms8626×body80valid