Details

Time bar (total: 3.9m)

sample74.0ms

Algorithm
intervals
Results
37.0ms40×body640valid
17.0ms54×body1280valid
7.0ms130×body80valid
3.0ms20×body320valid
1.0ms12×body160valid

simplify67.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize25.0ms

Local error

Found 3 expressions with local error:

3.7b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite166.0ms

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
Counts
3 → 117
Calls
3 calls:
Slowest
110.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
35.0ms
(/ (+ x 1) (- x 1))
18.0ms
(/ x (+ x 1))

series162.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
100.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
36.0ms
(/ x (+ x 1))
26.0ms
(/ (+ x 1) (- x 1))

simplify4.6s

Counts
142 → 126
Calls
142 calls:
Slowest
428.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
270.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
231.0ms
(/ (* (* x x) x) (* (* (+ x 1) (+ x 1)) (+ x 1)))
228.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
207.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 2)) 1)))

prune956.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

7.1b
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))
0.1b
(* (+ x 1) (/ 1 (- x 1)))
0.0b
(/ 1 (- x 1))
0.0b
(/ x (+ x 1))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
69×*-un-lft-identity
56×times-frac
37×add-cube-cbrt
27×associate-*r*
19×add-exp-log
14×difference-of-squares
13×add-cbrt-cube
11×associate-/r*
7×pow1 difference-of-sqr-1 distribute-lft-out--
6×associate-/r/ frac-sub associate-/l* add-log-exp
5×flip3-+ div-exp flip-+ distribute-lft-out
4×frac-times associate-*l* associate-*l/ prod-exp insert-posit16
3×cbrt-undiv flip3-- div-inv flip-- unswap-sqr
2×rec-exp clear-num frac-2neg 1-exp associate-*r/ un-div-inv cbrt-unprod
1×sub-neg diff-log pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 159
Calls
4 calls:
Slowest
65.0ms
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))
57.0ms
(* (+ x 1) (/ 1 (- x 1)))
17.0ms
(/ 1 (- x 1))
10.0ms
(/ x (+ x 1))

series207.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))
41.0ms
(/ x (+ x 1))
30.0ms
(* (+ x 1) (/ 1 (- x 1)))
17.0ms
(/ 1 (- x 1))

simplify10.0s

Counts
166 → 171
Calls
166 calls:
Slowest
697.0ms
(/ (* (* 1 1) 1) (* (* (- x 1) (- x 1)) (- x 1)))
559.0ms
(* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (/ 1 (- x 1)) (/ 1 (- x 1))) (/ 1 (- x 1))))
519.0ms
(* (- (* x x) (* 1 1)) (/ 1 (- x 1)))
472.0ms
(* (+ x 1) (* (+ (* x x) (- (* 1 1) (* x 1))) (- x 1)))
380.0ms
(* (+ (pow x 3) (pow 1 3)) (/ 1 (- x 1)))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

7.1b
(- (/ x (+ x 1)) (cbrt (* (* (* (+ x 1) (/ 1 (- x 1))) (* (+ x 1) (/ 1 (- x 1)))) (* (+ x 1) (/ 1 (- x 1))))))
0.1b
(* (+ x 1) (/ 1 (- x 1)))
0.1b
(* (+ x 1) (/ 1 (- x 1)))
0.1b
(* (+ x 1) (/ 1 (- x 1)))

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
840×frac-times
390×associate-*l/
342×cbrt-div frac-sub
300×flip3-+ flip-+
198×associate-*r/
150×un-div-inv
102×add-sqr-sqrt
81×associate-*r*
78×*-un-lft-identity
70×times-frac
40×add-cube-cbrt
31×add-exp-log
20×difference-of-squares
19×add-cbrt-cube
12×associate-*l* prod-exp
10×pow1 distribute-lft-out--
9×difference-of-sqr-1 unswap-sqr
6×div-exp associate-/r/ cbrt-unprod add-log-exp
4×flip3-- insert-posit16 flip--
3×cbrt-undiv rec-exp 1-exp pow-prod-down *-commutative div-inv distribute-lft-out
1×sub-neg diff-log
Counts
4 → 526
Calls
4 calls:
Slowest
133.0ms
(- (/ x (+ x 1)) (cbrt (* (* (* (+ x 1) (/ 1 (- x 1))) (* (+ x 1) (/ 1 (- x 1)))) (* (+ x 1) (/ 1 (- x 1))))))
53.0ms
(* (+ x 1) (/ 1 (- x 1)))
40.0ms
(* (+ x 1) (/ 1 (- x 1)))
35.0ms
(* (+ x 1) (/ 1 (- x 1)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(- (/ x (+ x 1)) (cbrt (* (* (* (+ x 1) (/ 1 (- x 1))) (* (+ x 1) (/ 1 (- x 1)))) (* (+ x 1) (/ 1 (- x 1))))))
38.0ms
(* (+ x 1) (/ 1 (- x 1)))
28.0ms
(* (+ x 1) (/ 1 (- x 1)))
24.0ms
(* (+ x 1) (/ 1 (- x 1)))

simplify3.5m

Counts
852 → 538
Calls
852 calls:
Slowest
1.0s
(- (* x (cbrt (* (* (- x 1) (- x 1)) (- x 1)))) (* (+ x 1) (cbrt (* (* (* (+ x 1) (/ 1 (- x 1))) (* (- (* x x) (* 1 1)) 1)) (* (- (* x x) (* 1 1)) (/ 1 (- x 1)))))))
963.0ms
(* (+ x 1) (cbrt (* (* (- x 1) (* (+ (* x x) (- (* 1 1) (* x 1))) (- x 1))) (- x 1))))
831.0ms
(- (* x (cbrt (* (- x 1) (* (- x 1) (- x 1))))) (* (+ x 1) (cbrt (* (* (* (+ x 1) 1) (* (+ x 1) (/ 1 (- x 1)))) (* (- (* x x) (* 1 1)) 1)))))
801.0ms
(- (* x (cbrt (* (* (- x 1) (* (- x 1) (- x 1))) (- x 1)))) (* (+ x 1) (cbrt (* (* (* (- (* x x) (* 1 1)) (/ 1 (- x 1))) (* (- (* x x) (* 1 1)) 1)) (* (- (* x x) (* 1 1)) (/ 1 (- x 1)))))))
795.0ms
(- (* x (cbrt (* (* (+ (* x x) (- (* 1 1) (* x 1))) (* (+ (* x x) (- (* 1 1) (* x 1))) (- x 1))) (+ (* x x) (- (* 1 1) (* x 1)))))) (* (+ x 1) (cbrt (* (* (* (+ (pow x 3) (pow 1 3)) (/ 1 (- x 1))) (* (+ (pow x 3) (pow 1 3)) 1)) (* (+ (pow x 3) (pow 1 3)) (/ 1 (- x 1)))))))

prune4.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ x 3) x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity
4×associate-*l*
3×pow1 add-cbrt-cube associate-*r* add-exp-log add-cube-cbrt
2×associate-*l/
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ insert-posit16 distribute-lft-out add-log-exp unswap-sqr
Counts
1 → 22
Calls
1 calls:
Slowest
15.0ms
(* (+ x 3) x)

series50.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
50.0ms
(* (+ x 3) x)

simplify803.0ms

Counts
14 → 25
Calls
14 calls:
Slowest
363.0ms
(* (* (* (+ x 3) (+ x 3)) (+ x 3)) (* (* x x) x))
199.0ms
(* (- (* x x) (* 3 3)) x)
146.0ms
(* (+ (pow x 3) (pow 3 3)) x)
21.0ms
(+ (* 3 x) (pow x 2))
18.0ms
(+ (* 3 x) (pow x 2))

prune112.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.6b

bsearch125.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
589.0ms1732×body1280valid
308.0ms1239×body640valid
274.0ms4072×body80valid
124.0ms646×body320valid
56.0ms311×body160valid