Details

Time bar (total: 55.1s)

sample45.0ms

Algorithm
intervals
Results
16.0ms65×body640valid
12.0ms136×body80valid
6.0ms37×body320valid
2.0ms18×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize21.0ms

Local error

Found 3 expressions with local error:

1.9b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
72×add-sqr-sqrt
69×times-frac
32×add-cube-cbrt
27×distribute-lft-out--
17×difference-of-squares
11×associate-/r* add-exp-log
10×distribute-lft-out
7×add-cbrt-cube
6×associate-/r/ div-inv associate-/l*
5×pow1 add-log-exp
4×difference-of-sqr-1 div-exp
3×insert-posit16 flip--
2×cbrt-undiv rec-exp clear-num frac-2neg flip3-- 1-exp flip-+ pow-flip inv-pow
1×sub-neg flip3-+ diff-log frac-sub
Counts
3 → 128
Calls
3 calls:
Slowest
68.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
13.0ms
(/ 1 (- x 1))
8.0ms
(/ 1 (+ x 1))

series132.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
84.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
24.0ms
(/ 1 (- x 1))
23.0ms
(/ 1 (+ x 1))

simplify6.1s

Counts
153 → 137
Calls
153 calls:
Slowest
488.0ms
(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
426.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
406.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
309.0ms
(+ (/ 1 (pow x 3)) (+ (/ 1 (pow x 2)) (/ 1 x)))
293.0ms
(+ (/ 1 (pow x 3)) (+ (/ 1 (pow x 2)) (/ 1 x)))

prune957.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize19.0ms

Local error

Found 2 expressions with local error:

1.0b
(/ -2 (* (+ x 1) (- x 1)))
0.0b
(* (+ x 1) (- x 1))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×frac-times associate-/r/
7×associate-*r*
6×flip3-+ flip3-- add-cube-cbrt flip-+ flip--
4×pow1 associate-*l* associate-*l/ associate-*r/
3×times-frac associate-/l*
2×distribute-rgt-in cbrt-undiv sub-neg distribute-lft-in div-exp prod-exp cbrt-unprod insert-posit16 add-log-exp difference-of-squares
1×clear-num associate-/r* frac-2neg difference-of-sqr-1 pow-prod-down *-commutative div-inv distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
2 → 66
Calls
2 calls:
Slowest
38.0ms
(* (+ x 1) (- x 1))
13.0ms
(/ -2 (* (+ x 1) (- x 1)))

series172.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
120.0ms
(* (+ x 1) (- x 1))
52.0ms
(/ -2 (* (+ x 1) (- x 1)))

simplify7.6s

Counts
57 → 72
Calls
57 calls:
Slowest
1.0s
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
603.0ms
(* (+ (pow x 3) (pow 1 3)) (- (* x x) (* 1 1)))
584.0ms
(* (+ (pow x 3) (pow 1 3)) (- (pow x 3) (pow 1 3)))
518.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (+ x 1))
496.0ms
(* (- (* x x) (* 1 1)) (- (* x x) (* 1 1)))

prune518.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (/ -2 (+ x 1)) (- x 1))
0.0b
(/ -2 (+ x 1))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
207×*-un-lft-identity
170×add-sqr-sqrt
94×add-cube-cbrt
38×difference-of-squares
28×distribute-lft-out
21×associate-/l*
20×associate-/r/
19×difference-of-sqr-1 distribute-lft-out--
11×associate-/r*
10×div-inv
9×flip3-+ add-cbrt-cube add-exp-log flip-+
4×cbrt-undiv div-exp
2×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×flip3-- flip-- associate-/l/
Counts
2 → 203
Calls
2 calls:
Slowest
17.0ms
(/ (/ -2 (+ x 1)) (- x 1))
10.0ms
(/ -2 (+ x 1))

series83.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
56.0ms
(/ (/ -2 (+ x 1)) (- x 1))
27.0ms
(/ -2 (+ x 1))

simplify27.4s

Counts
321 → 209
Calls
321 calls:
Slowest
578.0ms
(/ (* (* (/ -2 (+ x 1)) (/ -2 (+ x 1))) (/ -2 (+ x 1))) (* (* (- x 1) (- x 1)) (- x 1)))
470.0ms
(/ (/ -2 (- (* x x) (* 1 1))) (+ (sqrt x) 1))
455.0ms
(/ (/ -2 (+ (pow x 3) (pow 1 3))) (sqrt (- x 1)))
446.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
431.0ms
(/ (/ -2 (- (* x x) (* 1 1))) (+ (sqrt x) 1))

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1))
0.3b
(cbrt (- x 1))
0.3b
(cbrt (- x 1))
0.3b
(* (cbrt (- x 1)) (cbrt (- x 1)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
61×cbrt-prod
55×add-sqr-sqrt
44×*-un-lft-identity
18×cbrt-div
16×difference-of-squares
15×add-cube-cbrt
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-- pow1/3 difference-of-sqr-1 flip-- distribute-lft-out--
6×add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 119
Calls
4 calls:
Slowest
33.0ms
(* (cbrt (- x 1)) (cbrt (- x 1)))
5.0ms
(cbrt (- x 1))
3.0ms
(cbrt (- x 1))
3.0ms
(cbrt (- x 1))

series257.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(* (cbrt (- x 1)) (cbrt (- x 1)))
68.0ms
(cbrt (- x 1))
63.0ms
(cbrt (- x 1))
55.0ms
(cbrt (- x 1))

simplify6.9s

Counts
119 → 131
Calls
119 calls:
Slowest
453.0ms
(* (cbrt (+ (* x x) (+ (* 1 1) (* x 1)))) (cbrt (+ x 1)))
400.0ms
(- (* (pow (* x -1) 1/3) (cbrt -1)) (+ (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ -1 (pow x 2)) 1/3) (cbrt -1)))))
367.0ms
(- (* (pow (* x -1) 1/3) (cbrt -1)) (+ (* 1/9 (* (pow (/ -1 (pow x 5)) 1/3) (cbrt -1))) (* 1/3 (* (pow (/ -1 (pow x 2)) 1/3) (cbrt -1)))))
337.0ms
(* (cbrt (- (pow x 3) (pow 1 3))) (cbrt (- (* x x) (* 1 1))))
336.0ms
(* (cbrt (- (pow x 3) (pow 1 3))) (cbrt (- (pow x 3) (pow 1 3))))

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
817.0ms1938×body640valid
428.0ms4200×body80valid
336.0ms1231×body320valid
104.0ms631×body160valid