Details

Time bar (total: 9.1s)

sample23.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
7.0ms275×body80nan

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
12114
23814
35714
47514
59614
610414
done10414

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b
(* 6.0 (- x 1.0))
0.1b
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×*-un-lft-identity
8×add-log-exp
7×add-cube-cbrt
5×pow1 associate-*r*
4×associate-*r/
3×times-frac associate-*l* associate-/r* sum-log
2×cbrt-undiv distribute-rgt-in sub-neg flip3-- distribute-lft-in flip3-+ div-exp prod-exp associate-/r/ flip-- cbrt-unprod flip-+ associate-/l/
1×+-commutative associate-+l+ frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 64
Calls
3 calls:
13.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
11.0ms
(* 6.0 (- x 1.0))
20.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series160.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
40.0ms
(* 6.0 (- x 1.0))
81.0ms
(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify579.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (125.0ms)

IterNodesCost
0133982
1377955
21390811
done5000811

prune144.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b
(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
0.0b
(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
103×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×associate-/r/
10×add-exp-log add-cbrt-cube
8×add-log-exp
6×div-inv associate-/l*
5×flip3-- flip--
4×cbrt-undiv div-exp
3×pow1 sum-log
2×frac-2neg flip3-+ clear-num flip-+ associate-/l/
1×+-commutative associate-+l+
Counts
3 → 154
Calls
3 calls:
15.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
35.0ms
(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
23.0ms
(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

series196.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (+ x 1.0) (* 4.0 (sqrt x)))
76.0ms
(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
83.0ms
(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

simplify922.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (259.0ms)

IterNodesCost
02643901
16413749
225273557
done50003557

prune374.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))))
0.0b
(/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))
0.0b
(/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0))))
0.0b
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

rewrite388.0ms

Algorithm
rewrite-expression-head
Rules
875×times-frac
803×add-sqr-sqrt
612×*-un-lft-identity
579×sqrt-prod
364×add-cube-cbrt
196×difference-of-squares
185×associate-*r*
98×distribute-lft-out--
75×associate-/r*
36×associate-*l*
34×add-exp-log add-cbrt-cube
26×distribute-lft-out
22×associate-/r/
14×cbrt-undiv div-exp associate-/l*
12×div-inv unswap-sqr
8×flip3-- flip--
6×pow1 sqrt-div prod-exp cbrt-unprod
4×flip3-+ flip-+ associate-/l/ add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 657
Calls
4 calls:
233.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))))
35.0ms
(/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))
36.0ms
(/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0))))
34.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
453.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))))
522.0ms
(/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))
316.0ms
(/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0))))
242.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

simplify780.0ms

Counts
669 → 669
Iterations

Useful iterations: done (746.0ms)

IterNodesCost
066523651
1193421627
done500021126

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
5.8b
(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
7.0b
(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
13.7b
(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
48×frac-add
45×pow1
42×frac-times
41×flip3-+ flip-+
32×associate-*r/
30×add-exp-log add-cbrt-cube
25×flip3-- flip--
18×pow-prod-down
15×*-un-lft-identity
13×associate-*l/ prod-exp cbrt-unprod
12×associate-*l*
11×add-sqr-sqrt
10×times-frac
9×add-cube-cbrt add-log-exp
5×associate-/r*
4×cbrt-undiv div-exp associate-*r* associate-/r/ pow-sqr pow-prod-up
3×sum-cubes distribute-lft-out
2×distribute-rgt-in associate-+l+ associate-+r+ distribute-lft-in pow-plus sum-log *-commutative div-inv associate-/l/
1×+-commutative pow2 associate-+r- sub-neg frac-2neg diff-log swap-sqr clear-num associate-/l* unswap-sqr
Counts
4 → 165
Calls
4 calls:
15.0ms
(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
51.0ms
(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
47.0ms
(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
296.0ms
(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
92.0ms
(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
83.0ms
(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
189.0ms
(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

simplify443.0ms

Counts
177 → 177
Iterations

Useful iterations: done (434.0ms)

IterNodesCost
035010839
113478543
done50008342

prune642.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
01633
12133
done2133

end0.0ms

sample606.0ms

Algorithm
intervals
Results
230.0ms8000×body80valid
199.0ms7968×body80nan