Details

Time bar (total: 14.9s)

sample40.0ms

Algorithm
intervals
Results
18.0ms278×body80valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
12111
23711
35811
48711
511111
done11111

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 2 expressions with local error:

3.5b
(* y (+ 1.0 (* z z)))
3.9b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite58.0ms

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:
31.0ms
(* y (+ 1.0 (* z z)))
23.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series134.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(* y (+ 1.0 (* z z)))
74.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify1.4s

Counts
76 → 76
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01561062
13951035
21322887
done5000885

prune245.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize12.0ms

Local error

Found 2 expressions with local error:

2.1b
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
4.1b
(/ (/ 1 x) (+ 1.0 (* z z)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
114×add-sqr-sqrt
88×*-un-lft-identity
86×add-cube-cbrt
46×add-exp-log
45×associate-*r*
28×add-cbrt-cube
23×div-exp
13×associate-*l* associate-/l*
12×cbrt-undiv
10×prod-exp div-inv
8×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 → 168
Calls
2 calls:
58.0ms
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
18.0ms
(/ (/ 1 x) (+ 1.0 (* z z)))

series440.0ms

Counts
2 → 6
Calls
2 calls:
366.0ms
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
74.0ms
(/ (/ 1 x) (+ 1.0 (* z z)))

simplify1.7s

Counts
174 → 174
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02923239
18272887
222612562
done50002544

prune539.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z))))
0.8b
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z)))))
12.8b
(sqrt (+ 1.0 (* z z)))
12.8b
(sqrt (+ 1.0 (* z z)))

rewrite395.0ms

Algorithm
rewrite-expression-head
Rules
754×times-frac
541×add-sqr-sqrt
345×*-un-lft-identity
335×add-cube-cbrt
218×sqrt-prod
138×associate-*r*
137×cbrt-prod
84×associate-*l*
45×add-exp-log unswap-sqr
41×add-cbrt-cube
22×div-inv associate-/l*
21×cbrt-undiv div-exp
10×sqrt-div
9×prod-exp cbrt-unprod
8×pow1
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 504
Calls
4 calls:
35.0ms
(/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z))))
280.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z)))))
8.0ms
(sqrt (+ 1.0 (* z z)))
8.0ms
(sqrt (+ 1.0 (* z z)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z))))
76.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z)))))
48.0ms
(sqrt (+ 1.0 (* z z)))
49.0ms
(sqrt (+ 1.0 (* z z)))

simplify2.5s

Counts
516 → 516
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
062714026
1188911801
2466410815
done500110815

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (* (fabs (cbrt (+ 1.0 (* z z)))) (sqrt (cbrt (+ 1.0 (* z z)))))))
12.8b
(sqrt (+ 1.0 (* z z)))
13.3b
(cbrt (+ 1.0 (* z z)))
13.3b
(cbrt (+ 1.0 (* z z)))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
107×add-sqr-sqrt
90×add-cube-cbrt *-un-lft-identity
84×associate-*l*
73×add-exp-log
67×add-cbrt-cube
44×sqrt-prod
33×cbrt-undiv div-exp
28×associate-*r*
21×prod-exp cbrt-unprod
15×cbrt-prod
9×div-inv
7×pow1
6×cbrt-div sqrt-div
5×flip3-+ flip-+ unswap-sqr
4×associate-/r/ add-log-exp
3×associate-*r/
2×pow1/3
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative
Counts
4 → 200
Calls
4 calls:
189.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (* (fabs (cbrt (+ 1.0 (* z z)))) (sqrt (cbrt (+ 1.0 (* z z)))))))
8.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(cbrt (+ 1.0 (* z z)))
5.0ms
(cbrt (+ 1.0 (* z z)))

series825.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (* (fabs (cbrt (+ 1.0 (* z z)))) (sqrt (cbrt (+ 1.0 (* z z)))))))
57.0ms
(sqrt (+ 1.0 (* z z)))
216.0ms
(cbrt (+ 1.0 (* z z)))
215.0ms
(cbrt (+ 1.0 (* z z)))

simplify2.3s

Counts
212 → 212
Iterations

Useful iterations: done (2.3s)

IterNodesCost
04317024
112506384
248045471
done50005465

prune996.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.8b

regimes308.0ms

Accuracy

0% (1.1b remaining)

Error of 6.1b against oracle of 5.1b and baseline of 6.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01422
11821
done1821

end0.0ms

sample925.0ms

Algorithm
intervals
Results
537.0ms8610×body80valid