Details

Time bar (total: 19.9s)

sample63.0ms

Algorithm
intervals
Results
28.0ms813×body80nan
10.0ms289×body80valid

simplify5.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01320
12720
27020
317220
435220
566720
6110220
7185220
8393320
done500020

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)))))

rewrite85.0ms

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:
27.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
6.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
38.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series574.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
82.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
200.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
159.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.3s

Counts
126 → 126
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03032615
18222480
229762274
done50012268

prune381.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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)))))
8.6b
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×times-frac
25×*-un-lft-identity
24×associate-*l*
23×add-cube-cbrt
20×add-exp-log add-cbrt-cube
14×pow1
8×sqrt-prod
7×associate-*r/ prod-exp cbrt-unprod
6×sqrt-div associate-*l/
5×flip3-- pow-prod-down flip--
4×associate-*r* associate-/r* associate-/r/ add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×frac-times sqrt-pow1 *-commutative div-inv difference-of-squares unswap-sqr
1×frac-2neg pow1/2 clear-num distribute-lft-out--
Counts
4 → 111
Calls
4 calls:
7.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
37.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
106.0ms
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series600.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
206.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
148.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
168.0ms
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify983.0ms

Counts
123 → 123
Iterations

Useful iterations: done (979.0ms)

IterNodesCost
02912353
17542261
225742003
done50001995

prune369.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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))
8.6b
(* (- a (/ 1.0 3.0)) (* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
180×add-sqr-sqrt
175×sqrt-prod
162×times-frac
124×*-un-lft-identity
106×associate-*l*
96×add-cube-cbrt
61×add-exp-log add-cbrt-cube
29×prod-exp cbrt-unprod
28×difference-of-squares
20×pow1
15×associate-*l/
14×distribute-lft-out--
12×cbrt-undiv div-exp
10×frac-times pow-prod-down
9×associate-/r*
7×associate-*r/
6×flip3-- flip-- associate-/l*
5×associate-*r* unswap-sqr
4×sqrt-div associate-/r/ add-log-exp
3×*-commutative div-inv
1×sqrt-undiv frac-2neg clear-num
Counts
4 → 275
Calls
4 calls:
43.0ms
(* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
16.0ms
(/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0))))
55.0ms
(* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))
154.0ms
(* (- a (/ 1.0 3.0)) (* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)))

series1.0s

Counts
4 → 12
Calls
4 calls:
221.0ms
(* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
110.0ms
(/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0))))
361.0ms
(* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))
323.0ms
(* (- a (/ 1.0 3.0)) (* (/ (sqrt 1.0) (sqrt 9.0)) (* (/ (sqrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)))

simplify1.8s

Counts
287 → 287
Iterations

Useful iterations: 2 (928.0ms)

IterNodesCost
04426167
111775766
247314900
done50004900

prune829.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- a (/ 1.0 3.0)))
0.3b
(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
0.4b
(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
8.4b
(* (sqrt (- a (/ 1.0 3.0))) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
322×times-frac
246×add-sqr-sqrt
206×sqrt-prod
157×*-un-lft-identity
109×add-cube-cbrt
97×associate-*r*
48×difference-of-squares
47×add-exp-log add-cbrt-cube
34×sqrt-div
24×distribute-lft-out--
21×div-inv
18×frac-times associate-*l*
17×flip3-- flip--
16×prod-exp cbrt-unprod
15×cbrt-undiv div-exp
12×pow1
10×associate-*l/ associate-/l*
9×associate-*r/ associate-/r*
6×unswap-sqr
4×pow-prod-down associate-/r/ add-log-exp
2×*-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 326
Calls
4 calls:
12.0ms
(sqrt (- a (/ 1.0 3.0)))
19.0ms
(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
98.0ms
(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
89.0ms
(* (sqrt (- a (/ 1.0 3.0))) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

series574.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(sqrt (- a (/ 1.0 3.0)))
257.0ms
(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
201.0ms
(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
74.0ms
(* (sqrt (- a (/ 1.0 3.0))) (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))))

simplify2.0s

Counts
338 → 338
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
04638760
112607853
247667291
done50007291

prune932.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes88.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01635
12135
done2135

end0.0ms

sample1.7s

Algorithm
intervals
Results
843.0ms27100×body80nan
312.0ms9178×body80valid