Details

Time bar (total: 41.6s)

sample112.0ms

Algorithm
intervals
Results
49.0ms136×body80valid
24.0ms50×body1280valid
18.0ms45×body640valid
5.0ms8×body160valid
5.0ms17×body320valid

simplify67.0ms

Calls
1 calls:
Slowest
67.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize26.0ms

Local error

Found 3 expressions with local error:

2.3b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
60×times-frac
57×add-sqr-sqrt
25×add-cube-cbrt
20×distribute-lft-out
18×distribute-lft-out--
14×difference-of-squares
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×difference-of-sqr-1 add-log-exp
4×associate-/r/
3×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ div-inv flip-- associate-/l/
1×sub-neg diff-log frac-sub
Calls
3 calls:
Slowest
71.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
17.0ms
(/ (+ x 1) (- x 1))
10.0ms
(/ x (+ x 1))

series183.0ms

Calls
3 calls:
Slowest
112.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
41.0ms
(/ (+ x 1) (- x 1))
30.0ms
(/ x (+ x 1))

simplify4.6s

Calls
142 calls:
Slowest
370.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
306.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
262.0ms
(/ (* (* x x) x) (* (* (+ x 1) (+ x 1)) (+ x 1)))
227.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
218.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune930.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (/ x (+ x 1)) (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1)))))
0.0b
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
0.0b
(* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1))))
0.0b
(cbrt (/ (+ x 1) (- x 1)))

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
391×*-un-lft-identity
294×cbrt-prod
257×add-sqr-sqrt
251×times-frac
93×add-cube-cbrt
75×swap-sqr
74×associate-*r*
72×distribute-lft-out
68×difference-of-squares
40×difference-of-sqr-1 distribute-lft-out--
38×associate-*l*
30×pow1
29×cbrt-div
16×pow1/3
12×associate-/r/ unswap-sqr
11×frac-times associate-*l/ add-exp-log pow-prod-up
7×pow-plus flip3-- pow-prod-down associate-*r/ frac-sub flip--
6×div-inv add-log-exp
5×add-cbrt-cube pow-sqr
4×prod-exp cbrt-unprod insert-posit16
3×pow2
2×*-commutative
1×sub-neg diff-log pow3
Calls
4 calls:
Slowest
112.0ms
(* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1))))
80.0ms
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
62.0ms
(- (/ x (+ x 1)) (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1)))))
11.0ms
(cbrt (/ (+ x 1) (- x 1)))

series410.0ms

Calls
4 calls:
Slowest
128.0ms
(- (/ x (+ x 1)) (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1)))))
124.0ms
(cbrt (/ (+ x 1) (- x 1)))
113.0ms
(* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1))))
45.0ms
(* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1))))

simplify14.7s

Calls
398 calls:
Slowest
507.0ms
(+ (* 2/9 (* (/ (cbrt -1) (pow x 2)) (pow -1 1/3))) (+ (* 2/3 (* (/ (cbrt -1) x) (pow -1 1/3))) (* (cbrt -1) (pow -1 1/3))))
467.0ms
(- (* x (* (* (cbrt (- x 1)) (cbrt (- x 1))) (cbrt (- x 1)))) (* (+ x 1) (* (* (cbrt (+ x 1)) (cbrt (+ x 1))) (cbrt (+ x 1)))))
396.0ms
(* (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))) (/ (+ x 1) (- x 1)))
386.0ms
(- (* x (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (+ x 1) (* (* (cbrt (+ x 1)) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (+ x 1)))))
366.0ms
(/ (exp (/ x (+ x 1))) (exp (* (* (cbrt (/ (+ x 1) (- x 1))) (cbrt (/ (+ x 1) (- x 1)))) (cbrt (/ (+ x 1) (- x 1))))))

prune3.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

6.7b
(- (* x (/ 1 (+ x 1))) (/ (+ x 1) (- x 1)))
0.1b
(* x (/ 1 (+ x 1)))
0.0b
(/ 1 (+ x 1))
0.0b
(/ (+ x 1) (- x 1))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
62×add-sqr-sqrt
54×times-frac
35×add-cube-cbrt
19×add-exp-log
18×associate-*r*
15×distribute-lft-out
13×add-cbrt-cube
11×associate-/r*
10×difference-of-squares
7×pow1 associate-/l*
6×associate-/r/ add-log-exp
5×difference-of-sqr-1 div-exp distribute-lft-out--
4×prod-exp insert-posit16
3×cbrt-undiv flip3-+ associate-*l* flip-+ div-inv unswap-sqr
2×rec-exp clear-num frac-2neg flip3-- 1-exp associate-*r/ un-div-inv frac-sub cbrt-unprod flip-- associate-/l/
1×sub-neg diff-log pow-prod-down *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
33.0ms
(/ (+ x 1) (- x 1))
33.0ms
(* x (/ 1 (+ x 1)))
25.0ms
(- (* x (/ 1 (+ x 1))) (/ (+ x 1) (- x 1)))
16.0ms
(/ 1 (+ x 1))

series195.0ms

Calls
4 calls:
Slowest
107.0ms
(- (* x (/ 1 (+ x 1))) (/ (+ x 1) (- x 1)))
40.0ms
(* x (/ 1 (+ x 1)))
28.0ms
(/ (+ x 1) (- x 1))
20.0ms
(/ 1 (+ x 1))

simplify6.8s

Calls
159 calls:
Slowest
512.0ms
(* (* (* x x) x) (/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1))))
428.0ms
(* (* (* x x) x) (* (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (/ 1 (+ x 1))))
420.0ms
(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
402.0ms
(- (* (* x 1) (- x 1)) (* (+ x 1) (+ x 1)))
366.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

19.8b
(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
15×*-un-lft-identity
14×cbrt-prod times-frac
8×difference-of-squares
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out--
Calls
4 calls:
Slowest
56.0ms
(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))
3.0ms
(cbrt (+ x 1))
2.0ms
(cbrt (+ x 1))
2.0ms
(cbrt (+ x 1))

series243.0ms

Calls
4 calls:
Slowest
107.0ms
(- (/ x (+ x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1)))))
50.0ms
(cbrt (+ x 1))
46.0ms
(cbrt (+ x 1))
40.0ms
(cbrt (+ x 1))

simplify4.9s

Calls
50 calls:
Slowest
448.0ms
(* (+ x 1) (/ (- x 1) (cbrt (+ x 1))))
344.0ms
(- (* x (/ (- x 1) (cbrt (+ x 1)))) (* (+ x 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))))
275.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
268.0ms
(/ (exp (/ x (+ x 1))) (exp (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ (- x 1) (cbrt (+ x 1))))))
237.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune687.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.2b

bsearch169.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s1642×body1280valid
442.0ms1285×body640valid
401.0ms4119×body80valid
233.0ms616×body320valid
53.0ms338×body160valid