Details

Time bar (total: 13.0s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089
1119
2149
done149

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.3b

localize8.0ms

Local error

Found 1 expressions with local error:

9.3b
(/ (+ x y) (- 1.0 (/ y z)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
29×times-frac
13×add-cube-cbrt
10×difference-of-squares
7×distribute-lft-out
6×associate-/r*
5×distribute-lft-out--
4×associate-/l*
3×add-exp-log add-cbrt-cube
2×associate-/r/ associate-/l/
1×pow1 cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv add-log-exp
Counts
1 → 50
Calls
1 calls:
48.0ms
(/ (+ x y) (- 1.0 (/ y z)))

series83.0ms

Counts
1 → 3
Calls
1 calls:
82.0ms
(/ (+ x y) (- 1.0 (/ y z)))

simplify1.3s

Counts
53 → 53
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
095835
1209812
2679776
33135776
done5000776

prune136.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (* (cbrt (+ x y)) (cbrt (+ x y))) (* (cbrt (- 1.0 (/ y z))) (cbrt (- 1.0 (/ y z)))))
9.6b
(cbrt (- 1.0 (/ y z)))
9.6b
(cbrt (- 1.0 (/ y z)))
9.6b
(cbrt (- 1.0 (/ y z)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-div
22×add-sqr-sqrt
18×cbrt-prod
16×add-exp-log
13×*-un-lft-identity
9×flip3-- flip--
8×frac-times associate-/r/ add-cbrt-cube associate-/l/
7×add-cube-cbrt
6×flip3-+ flip-+ difference-of-squares
4×pow1 cbrt-undiv times-frac associate-*r/ div-exp associate-*l/ prod-exp cbrt-unprod add-log-exp
3×pow1/3 distribute-lft-out--
1×frac-2neg clear-num associate-/r* div-inv associate-/l*
Counts
4 → 85
Calls
4 calls:
52.0ms
(/ (* (cbrt (+ x y)) (cbrt (+ x y))) (* (cbrt (- 1.0 (/ y z))) (cbrt (- 1.0 (/ y z)))))
9.0ms
(cbrt (- 1.0 (/ y z)))
19.0ms
(cbrt (- 1.0 (/ y z)))
13.0ms
(cbrt (- 1.0 (/ y z)))

series1.7s

Counts
4 → 12
Calls
4 calls:
466.0ms
(/ (* (cbrt (+ x y)) (cbrt (+ x y))) (* (cbrt (- 1.0 (/ y z))) (cbrt (- 1.0 (/ y z)))))
392.0ms
(cbrt (- 1.0 (/ y z)))
378.0ms
(cbrt (- 1.0 (/ y z)))
420.0ms
(cbrt (- 1.0 (/ y z)))

simplify806.0ms

Counts
97 → 97
Iterations

Useful iterations: done (803.0ms)

IterNodesCost
01831891
14751802
213621582
done50001527

prune482.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ y z) (/ y z))
3.2b
(/ (+ x y) (- (pow 1.0 3) (pow (/ y z) 3)))
3.8b
(+ (* (/ y z) (/ y z)) (* 1.0 (/ y z)))
23.5b
(* (/ (+ x y) (- (pow 1.0 3) (pow (/ y z) 3))) (+ (* 1.0 1.0) (+ (* (/ y z) (/ y z)) (* 1.0 (/ y z)))))

rewrite560.0ms

Algorithm
rewrite-expression-head
Rules
541×add-sqr-sqrt
377×times-frac
334×*-un-lft-identity
216×difference-of-squares
162×unpow-prod-down cube-prod
151×associate-*l*
110×add-cube-cbrt
90×sqr-pow
67×distribute-lft-out
45×distribute-lft-out--
33×associate-/r*
23×add-exp-log add-cbrt-cube
16×associate-*r*
13×pow1 swap-sqr
9×difference-cubes
7×associate-*r/
6×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv add-log-exp unswap-sqr
4×frac-times flip3-+ associate-/r/ flip-+ associate-/l*
3×associate-*l/ frac-add
2×flip3-- pow-prod-down *-commutative flip-- associate-/l/
1×+-commutative pow2 distribute-rgt-in distribute-rgt-out frac-2neg distribute-lft-in pow-plus clear-num sum-log pow-sqr pow-prod-up
Counts
4 → 430
Calls
4 calls:
24.0ms
(* (/ y z) (/ y z))
90.0ms
(/ (+ x y) (- (pow 1.0 3) (pow (/ y z) 3)))
16.0ms
(+ (* (/ y z) (/ y z)) (* 1.0 (/ y z)))
398.0ms
(* (/ (+ x y) (- (pow 1.0 3) (pow (/ y z) 3))) (+ (* 1.0 1.0) (+ (* (/ y z) (/ y z)) (* 1.0 (/ y z)))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (/ y z) (/ y z))
120.0ms
(/ (+ x y) (- (pow 1.0 3) (pow (/ y z) 3)))
46.0ms
(+ (* (/ y z) (/ y z)) (* 1.0 (/ y z)))
159.0ms
(* (/ (+ x y) (- (pow 1.0 3) (pow (/ y z) 3))) (+ (* 1.0 1.0) (+ (* (/ y z) (/ y z)) (* 1.0 (/ y z)))))

simplify810.0ms

Counts
442 → 442
Iterations

Useful iterations: done (790.0ms)

IterNodesCost
043911881
1159210524
done500010230

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z))))
0.1b
(/ (/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z)))) (- (sqrt 1.0) (sqrt (/ y z))))
10.6b
(sqrt (/ y z))
10.6b
(sqrt (/ y z))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
628×*-un-lft-identity
620×times-frac
560×add-sqr-sqrt
375×sqrt-prod
176×add-cube-cbrt
172×distribute-lft-out
162×difference-of-squares
54×distribute-lft-out--
30×associate-/l*
28×associate-/r/
16×associate-/r* div-inv
14×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv rem-sqrt-square div-exp add-log-exp
3×associate-/l/
2×frac-2neg sqrt-pow1 pow1/2 sqrt-div clear-num
1×flip3-- flip--
Counts
4 → 435
Calls
4 calls:
70.0ms
(/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z))))
129.0ms
(/ (/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z)))) (- (sqrt 1.0) (sqrt (/ y z))))
4.0ms
(sqrt (/ y z))
4.0ms
(sqrt (/ y z))

series906.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z))))
572.0ms
(/ (/ (+ x y) (+ (sqrt 1.0) (sqrt (/ y z)))) (- (sqrt 1.0) (sqrt (/ y z))))
60.0ms
(sqrt (/ y z))
61.0ms
(sqrt (/ y z))

simplify2.2s

Counts
447 → 447
Iterations

Useful iterations: done (2.1s)

IterNodesCost
038514453
195012971
2471412797
done500112793

prune960.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 6.9b

regimes140.0ms

Accuracy

67% (0.7b remaining)

Error of 6.4b against oracle of 5.7b and baseline of 7.7b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02263
12755
done2755

end0.0ms

sample765.0ms

Algorithm
intervals
Results
406.0ms7999×body80valid
0.0ms1×body320valid