Details

Time bar (total: 16.6s)

sample19.0ms

Algorithm
intervals
Results
9.0ms271×body80valid

simplify89.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09204
121204
237204
359204
488204
5112204
6117204
done117204

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

localize11.0ms

Local error

Found 2 expressions with local error:

4.3b
(* y (+ 1.0 (* z z)))
5.8b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
16×add-cbrt-cube add-exp-log
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 clear-num associate-/r* frac-2neg distribute-lft-in pow-prod-down *-commutative unswap-sqr associate-/l/
Counts
2 → 70
Calls
2 calls:
13.0ms
(* y (+ 1.0 (* z z)))
17.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series136.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(* y (+ 1.0 (* z z)))
70.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify1.3s

Counts
76 → 76
Iterations

Useful iterations: done (1.3s)

IterNodesCost
015621902
143619572
2217819210
done500219050

prune452.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize22.0ms

Local error

Found 2 expressions with local error:

3.9b
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
5.3b
(/ (/ 1 x) (+ 1.0 (* z z)))

rewrite110.0ms

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 associate-/r* 1-exp
2×flip3-+ flip-+ add-log-exp
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
2 → 168
Calls
2 calls:
71.0ms
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
27.0ms
(/ (/ 1 x) (+ 1.0 (* z z)))

series171.0ms

Counts
2 → 6
Calls
2 calls:
81.0ms
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
89.0ms
(/ (/ 1 x) (+ 1.0 (* z z)))

simplify855.0ms

Counts
174 → 174
Iterations

Useful iterations: done (837.0ms)

IterNodesCost
029269272
193958154
done500155503

prune917.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (/ 1.0 y) (/ (/ (sqrt 1) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z))))) (/ (/ (sqrt 1) (cbrt x)) (sqrt (+ 1.0 (* z z)))))
1.9b
(* (/ 1.0 y) (/ (/ (sqrt 1) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z)))))
15.7b
(sqrt (+ 1.0 (* z z)))
15.7b
(sqrt (+ 1.0 (* z z)))

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
598×times-frac
342×add-sqr-sqrt
312×associate-*r*
298×sqrt-prod
287×*-un-lft-identity
283×add-cube-cbrt
189×add-exp-log
164×add-cbrt-cube
108×cbrt-prod
83×cbrt-undiv div-exp
67×prod-exp cbrt-unprod
18×unswap-sqr
15×div-inv
14×associate-*l*
13×pow1
8×sqrt-div
6×frac-times associate-*l/
4×flip3-+ pow-prod-down associate-*r/ associate-/r/ flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
Counts
4 → 473
Calls
4 calls:
249.0ms
(* (* (/ 1.0 y) (/ (/ (sqrt 1) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z))))) (/ (/ (sqrt 1) (cbrt x)) (sqrt (+ 1.0 (* z z)))))
106.0ms
(* (/ 1.0 y) (/ (/ (sqrt 1) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z)))))
4.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (* (/ 1.0 y) (/ (/ (sqrt 1) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z))))) (/ (/ (sqrt 1) (cbrt x)) (sqrt (+ 1.0 (* z z)))))
238.0ms
(* (/ 1.0 y) (/ (/ (sqrt 1) (* (cbrt x) (cbrt x))) (sqrt (+ 1.0 (* z z)))))
59.0ms
(sqrt (+ 1.0 (* z z)))
78.0ms
(sqrt (+ 1.0 (* z z)))

simplify3.2s

Counts
485 → 485
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0764327455
12999261223
done5000246938

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
3.9b
(* (/ 1.0 y) (* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z))))))
15.7b
(sqrt (+ 1.0 (* z z)))
15.7b
(sqrt (+ 1.0 (* z z)))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
264×add-exp-log
237×times-frac
221×add-sqr-sqrt
123×div-exp
119×*-un-lft-identity
102×prod-exp
95×add-cube-cbrt
90×add-cbrt-cube
85×associate-*r*
83×sqrt-prod
37×associate-*l*
35×unswap-sqr
34×cbrt-undiv
32×cbrt-unprod
27×rec-exp 1-exp
13×pow1
9×div-inv
8×sqrt-div
6×frac-times associate-*r/
4×flip3-+ pow-prod-down associate-*l/ associate-/r/ flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
Counts
4 → 298
Calls
4 calls:
99.0ms
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
137.0ms
(* (/ 1.0 y) (* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z))))))
9.0ms
(sqrt (+ 1.0 (* z z)))
4.0ms
(sqrt (+ 1.0 (* z z)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
96.0ms
(* (/ 1.0 y) (* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z))))))
46.0ms
(sqrt (+ 1.0 (* z z)))
79.0ms
(sqrt (+ 1.0 (* z z)))

simplify2.2s

Counts
310 → 310
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0453151798
11675125040
done5000113990

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.8b

regimes741.0ms

Accuracy

0% (0.9b remaining)

Error of 5.8b against oracle of 4.9b and baseline of 5.8b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
018565
123525
done23525

end0.0ms

sample696.0ms

Algorithm
intervals
Results
449.0ms8599×body80valid