Details

Time bar (total: 35.1s)

sample186.0ms

Algorithm
intervals
Results
94.0ms843×body80nan
25.0ms287×body80valid

simplify9.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01320
12720
27220
318820
441720
577220
6149620
7249020
8340220
9472420
done500020

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.1b
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
26×*-un-lft-identity times-frac
24×add-cube-cbrt associate-*l*
13×add-exp-log add-cbrt-cube
11×pow1
8×associate-*r/ sqrt-prod
6×flip3-- sqrt-div associate-*r* flip--
4×frac-times associate-/r* associate-/r/ add-log-exp
3×flip3-+ pow-prod-down associate-*l/ prod-exp cbrt-unprod flip-+ associate-/l* unswap-sqr
2×cbrt-undiv sqrt-pow1 div-exp *-commutative div-inv difference-of-squares
1×distribute-rgt-in frac-2neg distribute-lft-in pow1/2 clear-num distribute-lft-out--
Counts
4 → 114
Calls
4 calls:
68.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
12.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
69.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
25.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series723.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
108.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
228.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
211.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.9s

Counts
126 → 126
Iterations

Useful iterations: 2 (706.0ms)

IterNodesCost
03032615
18232480
229602274
done50022274

prune459.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.1b
(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

rewrite391.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×times-frac
25×*-un-lft-identity
23×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*l*
14×pow1
9×associate-*r*
8×associate-*r/ sqrt-prod
7×prod-exp cbrt-unprod
6×sqrt-div
5×flip3-- pow-prod-down associate-*l/ flip--
4×associate-/r* associate-/r/ add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×distribute-rgt-in frac-times sub-neg distribute-lft-in sqrt-pow1 *-commutative div-inv difference-of-squares unswap-sqr
1×frac-2neg pow1/2 clear-num distribute-lft-out--
Counts
4 → 115
Calls
4 calls:
12.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
88.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
17.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
269.0ms
(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

series763.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
228.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
199.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
247.0ms
(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

simplify1.8s

Counts
127 → 127
Iterations

Useful iterations: 2 (676.0ms)

IterNodesCost
02982467
17872371
227392113
done50002113

prune493.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
0.3b
(/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
0.4b
(/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
7.1b
(* (* (/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand) (- a (/ 1.0 3.0)))

rewrite976.0ms

Algorithm
rewrite-expression-head
Rules
725×times-frac
525×sqrt-prod
372×add-sqr-sqrt
345×*-un-lft-identity
343×add-cube-cbrt
196×associate-*l*
72×sqrt-div
38×associate-*r/
36×associate-/r/
34×add-exp-log add-cbrt-cube
30×associate-/l*
20×flip3-- flip--
18×div-inv
14×associate-/r*
11×pow1
10×cbrt-undiv div-exp prod-exp cbrt-unprod
9×associate-*r*
7×unswap-sqr
5×associate-*l/
4×pow-prod-down add-log-exp
2×distribute-rgt-in frac-times sub-neg frac-2neg distribute-lft-in clear-num *-commutative difference-of-squares
1×associate-/l/ distribute-lft-out--
Counts
4 → 540
Calls
4 calls:
291.0ms
(* (/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
32.0ms
(/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
84.0ms
(/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
496.0ms
(* (* (/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand) (- a (/ 1.0 3.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
288.0ms
(* (/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
309.0ms
(/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
155.0ms
(/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
252.0ms
(* (* (/ (/ 1.0 (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) (sqrt (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand) (- a (/ 1.0 3.0)))

simplify3.0s

Counts
552 → 552
Iterations

Useful iterations: 2 (1.8s)

IterNodesCost
072118349
1185716115
2496814848
done500014848

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))))
0.2b
(* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b
(/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0))))
0.3b
(* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
183×add-sqr-sqrt
175×sqrt-prod
162×times-frac
125×*-un-lft-identity
106×associate-*l*
97×add-cube-cbrt
34×add-exp-log add-cbrt-cube
28×difference-of-squares
14×distribute-lft-out--
13×pow1 prod-exp cbrt-unprod
9×associate-/r*
7×cbrt-undiv div-exp associate-*r*
6×associate-*l/ associate-/l* unswap-sqr
5×frac-times flip3-- pow-prod-down flip--
4×sqrt-div associate-/r/ add-log-exp
3×flip3-+ associate-*r/ *-commutative flip-+ div-inv
1×distribute-rgt-in sqrt-undiv frac-2neg distribute-lft-in clear-num
Counts
4 → 263
Calls
4 calls:
76.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))))
72.0ms
(* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
26.0ms
(/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0))))
95.0ms
(* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))

series1.4s

Counts
4 → 12
Calls
4 calls:
381.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))))
358.0ms
(* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
138.0ms
(/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0))))
565.0ms
(* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))

simplify3.4s

Counts
275 → 275
Iterations

Useful iterations: done (3.4s)

IterNodesCost
04365863
111705477
247464811
done50014787

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01426
11926
done1926

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.7s26709×body80nan
885.0ms9112×body80valid