Details

Time bar (total: 33.8s)

sample55.0ms

Algorithm
intervals
Results
20.0ms51×body1280valid
11.0ms144×body80valid
10.0ms31×body640valid
4.0ms19×body320valid
2.0ms11×body160valid

simplify55.0ms

Calls
1 calls:
Slowest
55.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize13.0ms

Local error

Found 3 expressions with local error:

2.5b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt
10×times-frac
6×associate-/r*
5×add-cbrt-cube add-exp-log add-log-exp
4×associate-/r/
3×pow1 insert-posit16 associate-/l*
2×clear-num frac-2neg flip3-+ flip3-- flip-+ div-inv flip-- difference-of-squares associate-/l/
1×cbrt-undiv sub-neg diff-log div-exp frac-sub distribute-lft-out--
Calls
3 calls:
Slowest
8.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
5.0ms
(/ (+ x 1) (- x 1))
1.0ms
(/ x (+ x 1))

series65.0ms

Calls
3 calls:
Slowest
39.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
14.0ms
(/ (+ x 1) (- x 1))
12.0ms
(/ x (+ x 1))

simplify2.4s

Calls
51 calls:
Slowest
386.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
287.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
207.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
199.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
156.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 2)) 1)))

prune570.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
0.1b
(pow (/ (+ x 1) (- x 1)) 3)
0.0b
(* (/ x (+ x 1)) (/ x (+ x 1)))
0.0b
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
44×*-un-lft-identity
42×times-frac
34×add-cube-cbrt
30×unpow-prod-down cube-prod
21×add-cbrt-cube associate-*r* associate-*l* add-exp-log
15×pow1 difference-of-squares
12×associate-/r/
6×div-inv add-log-exp
5×cbrt-undiv flip3-- div-exp prod-exp cbrt-unprod flip-- distribute-lft-out--
4×insert-posit16
3×cube-div
2×pow2 frac-times flip3-+ pow-plus pow-prod-down associate-*l/ pow-exp associate-*r/ *-commutative pow-prod-up flip-+ rem-cube-cbrt
1×cube-mult pow-to-exp difference-cubes sub-neg pow-pow diff-log unpow3 frac-sub
Calls
4 calls:
Slowest
24.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
18.0ms
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
9.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))
6.0ms
(pow (/ (+ x 1) (- x 1)) 3)

series145.0ms

Calls
4 calls:
Slowest
87.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
22.0ms
(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
19.0ms
(pow (/ (+ x 1) (- x 1)) 3)
18.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))

simplify20.8s

Calls
157 calls:
Slowest
535.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (sqrt (- x 1))) 3)
532.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (sqrt (- x 1))) 3)
521.0ms
(+ (sqrt (pow (/ x (+ x 1)) 3)) (pow (sqrt (/ (+ x 1) (- x 1))) 3))
494.0ms
(+ (sqrt (pow (/ x (+ x 1)) 3)) (sqrt (pow (/ (+ x 1) (- x 1)) 3)))
491.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (- x 1)) (cbrt (- x 1)))) 3)

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))
0.0b
(/ 1 (/ (- x 1) (+ x 1)))
0.0b
(/ x (+ x 1))
0.0b
(/ (- x 1) (+ x 1))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×associate-/r*
20×add-cube-cbrt
18×times-frac
9×add-exp-log
7×associate-/r/
6×add-cbrt-cube add-log-exp
5×pow1 div-inv
4×insert-posit16
3×clear-num frac-2neg flip3-+ flip-+ associate-/l*
2×rec-exp flip3-- div-exp flip-- distribute-lft-out-- associate-/l/
1×cbrt-undiv sub-neg diff-log div-sub frac-sub pow-flip inv-pow difference-of-squares
Calls
4 calls:
Slowest
12.0ms
(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))
3.0ms
(/ (- x 1) (+ x 1))
3.0ms
(/ 1 (/ (- x 1) (+ x 1)))
1.0ms
(/ x (+ x 1))

series65.0ms

Calls
4 calls:
Slowest
34.0ms
(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))
11.0ms
(/ 1 (/ (- x 1) (+ x 1)))
10.0ms
(/ (- x 1) (+ x 1))
10.0ms
(/ x (+ x 1))

simplify3.9s

Calls
71 calls:
Slowest
329.0ms
(/ (* (* (- x 1) (- x 1)) (- x 1)) (* (* (+ x 1) (+ x 1)) (+ x 1)))
278.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
258.0ms
(- (* x (/ (- x 1) (+ x 1))) (* (+ x 1) 1))
223.0ms
(/ (exp (/ x (+ x 1))) (exp (/ 1 (/ (- x 1) (+ x 1)))))
181.0ms
(* (+ x 1) (/ (- x 1) (+ x 1)))

prune724.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (+ x 3))
0.0b
(+ 1 (* x (+ x 3)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
2×distribute-rgt-in pow1 associate-+r+ distribute-lft-in flip3-+ add-cbrt-cube associate-*r/ add-exp-log flip-+ insert-posit16 add-log-exp
1×+-commutative *-commutative
Calls
2 calls:
Slowest
1.0ms
(* x (+ x 3))
1.0ms
(+ 1 (* x (+ x 3)))

series27.0ms

Calls
2 calls:
Slowest
19.0ms
(* x (+ x 3))
8.0ms
(+ 1 (* x (+ x 3)))

simplify270.0ms

Calls
15 calls:
Slowest
70.0ms
(+ (* x x) (- (* 3 3) (* x 3)))
47.0ms
(+ (* 3 x) (+ (pow x 2) 1))
30.0ms
(+ (* 3 x) (+ (pow x 2) 1))
26.0ms
(+ (* 3 x) (+ (pow x 2) 1))
23.0ms
(+ (* 3 x) (pow x 2))

prune247.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch178.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
755.0ms1191×body640valid
755.0ms1732×body1280valid
388.0ms4102×body80valid
196.0ms650×body320valid
46.0ms325×body160valid