Details

Time bar (total: 20.1s)

sample41.0ms

Algorithm
intervals
Results
18.0ms272×body80valid

simplify126.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12111
23711
35811
48711
511111
done11111

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize9.0ms

Local error

Found 2 expressions with local error:

3.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.0b
(* y (+ 1.0 (* z z)))

rewrite48.0ms

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:
17.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
27.0ms
(* y (+ 1.0 (* z z)))

series173.0ms

Counts
2 → 6
Calls
2 calls:
74.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
99.0ms
(* y (+ 1.0 (* z z)))

simplify1.6s

Counts
76 → 76
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01561062
13951035
21321887
done5000885

prune299.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.2b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
18.9b
(sqrt (+ 1.0 (* z z)))
18.9b
(sqrt (+ 1.0 (* z z)))

rewrite161.0ms

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:
60.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
77.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
77.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
66.0ms
(sqrt (+ 1.0 (* z z)))
50.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.2s

Counts
129 → 129
Iterations

Useful iterations: 2 (438.0ms)

IterNodesCost
02172776
15832060
221911728
done50001728

prune464.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
1.0b
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
18.9b
(sqrt (+ 1.0 (* z z)))
18.9b
(sqrt (+ 1.0 (* z z)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
148×times-frac
103×add-sqr-sqrt
84×associate-*r*
81×*-un-lft-identity
79×add-cube-cbrt
69×add-exp-log
48×sqrt-prod
45×add-cbrt-cube
30×div-exp
21×prod-exp
17×cbrt-undiv
13×cbrt-unprod
10×sqrt-div
9×associate-*l* div-inv
8×pow1
7×unswap-sqr
6×associate-/r/
5×flip3-+ associate-*r/ flip-+
4×add-log-exp
3×rec-exp 1-exp associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num associate-/r* *-commutative
Counts
4 → 189
Calls
4 calls:
12.0ms
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
109.0ms
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
6.0ms
(sqrt (+ 1.0 (* z z)))
8.0ms
(sqrt (+ 1.0 (* z z)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
99.0ms
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
59.0ms
(sqrt (+ 1.0 (* z z)))
44.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.7s

Counts
201 → 201
Iterations

Useful iterations: 2 (771.0ms)

IterNodesCost
03454726
110094053
232493303
done50003303

prune586.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (sqrt (+ 1.0 (* z z))))
2.6b
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
18.9b
(sqrt (+ 1.0 (* z z)))
18.9b
(sqrt (+ 1.0 (* z z)))

rewrite910.0ms

Algorithm
rewrite-expression-head
Rules
6852×times-frac
2927×add-sqr-sqrt
2925×add-cube-cbrt *-un-lft-identity
1752×sqrt-prod
340×associate-/l*
184×div-inv
56×sqrt-div
52×associate-/r/
28×flip3-+ flip-+
27×add-exp-log add-cbrt-cube
16×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 → 2205
Calls
4 calls:
172.0ms
(/ (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (sqrt (+ 1.0 (* z z))))
56.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
5.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (sqrt (+ 1.0 (* z z))))
134.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
57.0ms
(sqrt (+ 1.0 (* z z)))
61.0ms
(sqrt (+ 1.0 (* z z)))

simplify1.6s

Counts
2217 → 2217
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0259090314
done500083334

prune8.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

regimes239.0ms

Accuracy

0% (1.1b remaining)

Error of 6.2b against oracle of 5.2b and baseline of 6.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
12039
done2039

end0.0ms

sample903.0ms

Algorithm
intervals
Results
529.0ms8619×body80valid