Details

Time bar (total: 5.7s)

sample17.0ms

Algorithm
intervals
Results
8.0ms279×body80valid

simplify47.0ms

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: 6.0b

localize7.0ms

Local error

Found 2 expressions with local error:

3.5b
(* y (+ 1.0 (* z z)))
4.3b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite17.0ms

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))))

series114.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(* y (+ 1.0 (* z z)))
60.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify572.0ms

Counts
76 → 76
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
01561062
14081035
21361887
done5000887

prune178.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
4.3b
(/ (/ 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)))

rewrite51.0ms

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:
20.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
21.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
59.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
42.0ms
(sqrt (+ 1.0 (* z z)))
46.0ms
(sqrt (+ 1.0 (* z z)))

simplify871.0ms

Counts
129 → 129
Iterations

Useful iterations: 2 (391.0ms)

IterNodesCost
02172776
16082060
223891728
done50001728

prune335.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 1.0 (* x (* y (+ (* z z) 1.0))))
3.5b
(* y (+ (* z z) 1.0))
4.1b
(* x (* y (+ (* z z) 1.0)))

rewrite40.0ms

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:
13.0ms
(/ 1.0 (* x (* y (+ (* z z) 1.0))))
11.0ms
(* y (+ (* z z) 1.0))
14.0ms
(* x (* y (+ (* z z) 1.0)))

series179.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(/ 1.0 (* x (* y (+ (* z z) 1.0))))
57.0ms
(* y (+ (* z z) 1.0))
66.0ms
(* x (* y (+ (* z z) 1.0)))

simplify536.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
01241034
13391010
21292820
done5000820

prune170.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize17.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (/ 1.0 x) (* (* y (* (sqrt (sqrt (+ 1.0 (* z z)))) (sqrt (sqrt (+ 1.0 (* z z)))))) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
36×add-exp-log add-cbrt-cube
32×associate-*r/
31×times-frac
30×flip3-+ flip-+
28×frac-times
26×associate-/r/
24×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
14×associate-*l/
13×associate-/l*
12×cbrt-undiv div-exp prod-exp cbrt-unprod
9×sqrt-prod
7×pow1
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 125
Calls
4 calls:
129.0ms
(/ (/ 1.0 x) (* (* y (* (sqrt (sqrt (+ 1.0 (* z z)))) (sqrt (sqrt (+ 1.0 (* z z)))))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ (/ 1.0 x) (* (* y (* (sqrt (sqrt (+ 1.0 (* z z)))) (sqrt (sqrt (+ 1.0 (* z z)))))) (sqrt (+ 1.0 (* z z)))))
43.0ms
(sqrt (+ 1.0 (* z z)))
48.0ms
(sqrt (+ 1.0 (* z z)))
43.0ms
(sqrt (+ 1.0 (* z z)))

simplify901.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (392.0ms)

IterNodesCost
02703867
17562470
228952100
done50012100

prune421.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

regimes248.0ms

Accuracy

0% (1.6b remaining)

Error of 6.2b against oracle of 4.7b and baseline of 6.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11111
done1111

end0.0ms

sample427.0ms

Algorithm
intervals
Results
248.0ms8608×body80valid