Details

Time bar (total: 9.0s)

sample21.0ms

Algorithm
intervals
Results
7.0ms67×body1280valid
3.0ms130×body80valid
2.0ms32×body640valid
1.0ms20×body320valid
0.0ms7×body160valid

simplify20.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036
done3036

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
1.6b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
10.0ms
(/ x (+ x 1.0))
25.0ms
(/ (+ x 1.0) (- x 1.0))
87.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series194.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
38.0ms
(/ (+ x 1.0) (- x 1.0))
122.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0392760
11379726
25001716
done5001716

prune205.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
0.0b
(pow (/ x (+ x 1.0)) 3)
1.6b
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1102×*-un-lft-identity
735×times-frac
560×add-sqr-sqrt
344×unpow-prod-down cube-prod
273×distribute-lft-out--
188×difference-of-squares
176×distribute-lft-out
124×add-cube-cbrt
77×associate-/l*
62×sqr-pow
31×associate-/r/
27×frac-add
16×frac-times associate-*r/
12×add-exp-log add-cbrt-cube
10×associate-*l/
9×flip3-+ flip-+
6×pow1 cube-div pow-unpow add-log-exp
5×difference-cubes div-inv
4×flip3-- pow-exp flip-- rem-cube-cbrt
3×cbrt-undiv div-exp associate-/r* associate-/l/
2×cube-mult pow-to-exp pow-pow unpow3 frac-sub
1×sub-neg frac-2neg diff-log div-sub clear-num
Counts
4 → 565
Calls
4 calls:
20.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
771.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
13.0ms
(pow (/ x (+ x 1.0)) 3)
250.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series955.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
552.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
54.0ms
(pow (/ x (+ x 1.0)) 3)
292.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify171.0ms

Counts
577 → 577
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0167717474
1500217231
done500217231

prune752.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (/ x (+ x 1.0)) 3) (log (exp (pow (/ (+ x 1.0) (- x 1.0)) 3)))) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
0.0b
(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b
(pow (/ x (+ x 1.0)) 3)
1.6b
(- (pow (/ x (+ x 1.0)) 3) (log (exp (pow (/ (+ x 1.0) (- x 1.0)) 3))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
140×add-sqr-sqrt
122×*-un-lft-identity
107×times-frac
59×add-cube-cbrt
54×unpow-prod-down cube-prod
38×difference-of-squares
31×associate-/r/
27×frac-add
18×distribute-lft-out--
16×frac-times associate-*r/ distribute-lft-out
12×add-exp-log add-cbrt-cube
11×pow1 associate-/l*
10×associate-*l/
9×flip3-+ flip-+
7×sqr-pow
6×pow-unpow
5×log-pow div-inv add-log-exp
4×flip3-- pow-exp flip-- rem-cube-cbrt
3×cbrt-undiv log-prod div-exp associate-/r* associate--r+
2×cube-div cube-mult pow-to-exp pow-pow unpow3 associate-/l/
1×sub-neg frac-2neg diff-log div-sub clear-num
Counts
4 → 236
Calls
4 calls:
1.1s
(/ (- (pow (/ x (+ x 1.0)) 3) (log (exp (pow (/ (+ x 1.0) (- x 1.0)) 3)))) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
20.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
14.0ms
(pow (/ x (+ x 1.0)) 3)
392.0ms
(- (pow (/ x (+ x 1.0)) 3) (log (exp (pow (/ (+ x 1.0) (- x 1.0)) 3))))

series944.0ms

Counts
4 → 12
Calls
4 calls:
548.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (log (exp (pow (/ (+ x 1.0) (- x 1.0)) 3)))) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
60.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
52.0ms
(pow (/ x (+ x 1.0)) 3)
284.0ms
(- (pow (/ x (+ x 1.0)) 3) (log (exp (pow (/ (+ x 1.0) (- x 1.0)) 3))))

simplify72.0ms

Counts
248 → 248
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014505161
150014892
done50014892

prune594.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.2b
(/ 3.0 (pow x 3))
0.5b
(/ (- 1.0) (pow x 2))
8.4b
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite843.0ms

Algorithm
rewrite-expression-head
Rules
143×times-frac
120×add-sqr-sqrt
105×*-un-lft-identity
78×add-cube-cbrt
48×unpow-prod-down
29×distribute-rgt-neg-in
27×distribute-lft-neg-in
20×associate-/r*
18×sqr-pow
15×difference-of-squares
14×add-exp-log
13×cube-prod associate-/l* unpow2
11×add-log-exp
10×distribute-lft-out--
9×neg-mul-1
8×add-cbrt-cube
6×div-exp
5×frac-sub
4×pow1 cube-mult diff-log unpow3
3×sub-neg flip3-- flip--
2×cbrt-undiv associate--l- neg-sub0 pow-to-exp frac-2neg div-sub pow-exp associate--l+ clear-num div-inv
1×distribute-frac-neg
Counts
4 → 234
Calls
4 calls:
99.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
8.0ms
(/ 3.0 (pow x 3))
11.0ms
(/ (- 1.0) (pow x 2))
715.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series182.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
36.0ms
(/ 3.0 (pow x 3))
40.0ms
(/ (- 1.0) (pow x 2))
38.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify100.0ms

Counts
246 → 246
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07381754
134481596
250011578
done50011578

prune417.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch93.0ms

Steps
ItersRangePoint
9
7.055123656280252
892369.0132880388
10925.369890187123
10
-1.8070707071506563e+17
-0.15939393977811658
-8688.23846861602

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04235
14235
done4235

end0.0ms

sample555.0ms

Algorithm
intervals
Results
180.0ms1769×body1280valid
100.0ms4076×body80valid
97.0ms1250×body640valid
36.0ms615×body320valid
15.0ms290×body160valid