Details

Time bar (total: 28.2s)

sample126.0ms

Algorithm
intervals
Results
55.0ms857×body80nan
21.0ms291×body80valid

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
01320
12720
27619
320819
455319
5115019
6249119
done500019

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

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

rewrite269.0ms

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×expm1-log1p-u frac-times associate-/r* associate-/r/ log1p-expm1-u 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 → 122
Calls
4 calls:
76.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
66.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
25.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
98.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)

series687.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
101.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
213.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
215.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)

simplify2.6s

Counts
134 → 134
Iterations

Useful iterations: done (2.6s)

IterNodesCost
03112723
18942576
246832374
done50002373

prune611.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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)))))
0.3b
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
6.4b
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite501.0ms

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×expm1-log1p-u associate-*r* associate-/r* associate-/r/ log1p-expm1-u 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 → 119
Calls
4 calls:
45.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
18.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
84.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
349.0ms
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series760.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
221.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
243.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
198.0ms
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify2.5s

Counts
131 → 131
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02992457
18022356
236942115
done50002110

prune638.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- a (/ 1.0 3.0)))
0.3b
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
0.4b
(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
6.4b
(* (- a (/ 1.0 3.0)) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite589.0ms

Algorithm
rewrite-expression-head
Rules
795×times-frac
605×add-sqr-sqrt
452×sqrt-prod
439×*-un-lft-identity
345×add-cube-cbrt
210×associate-*l*
94×difference-of-squares
47×distribute-lft-out--
32×add-exp-log add-cbrt-cube
22×associate-/l*
21×div-inv
12×pow1
10×prod-exp cbrt-unprod
9×cbrt-undiv div-exp associate-/r*
7×unswap-sqr
6×sqrt-div associate-*l/
5×flip3-- flip--
4×expm1-log1p-u associate-*r* pow-prod-down associate-/r/ log1p-expm1-u add-log-exp
2×frac-times *-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num associate-/l/
Counts
4 → 532
Calls
4 calls:
33.0ms
(sqrt (- a (/ 1.0 3.0)))
232.0ms
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
53.0ms
(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
202.0ms
(* (- a (/ 1.0 3.0)) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand))

series985.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (- a (/ 1.0 3.0)))
341.0ms
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
292.0ms
(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
292.0ms
(* (- a (/ 1.0 3.0)) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand))

simplify1.0s

Counts
544 → 544
Iterations

Useful iterations: done (998.0ms)

IterNodesCost
063311459
1169810761
done500010463

prune2.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b
(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
0.4b
(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
6.3b
(* (sqrt (- a (/ 1.0 3.0))) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
795×times-frac
606×add-sqr-sqrt
458×sqrt-prod
441×*-un-lft-identity
347×add-cube-cbrt
222×associate-*l*
94×difference-of-squares
52×add-exp-log add-cbrt-cube
47×distribute-lft-out--
32×sqrt-div
23×associate-*l/
22×prod-exp cbrt-unprod associate-/l*
21×div-inv
20×pow1
18×frac-times
16×flip3-- flip--
12×cbrt-undiv div-exp
10×pow-prod-down
9×associate-*r/ associate-/r*
7×unswap-sqr
5×associate-*r*
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×*-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 565
Calls
4 calls:
205.0ms
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
556.0ms
(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
37.0ms
(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
215.0ms
(* (sqrt (- a (/ 1.0 3.0))) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand))

series1.0s

Counts
4 → 12
Calls
4 calls:
323.0ms
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
307.0ms
(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
276.0ms
(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))
106.0ms
(* (sqrt (- a (/ 1.0 3.0))) (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand))

simplify1.1s

Counts
577 → 577
Iterations

Useful iterations: done (1.1s)

IterNodesCost
065413342
1175512227
done500111709

prune2.5s

Pruning

4 alts after pruning (2 fresh and 2 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

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
11926
done1926

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.5s26826×body80nan
855.0ms9081×body80valid