Details

Time bar (total: 1.2m)

sample48.0ms

Algorithm
intervals
Results
17.0ms56×body1280valid
9.0ms40×body640valid
8.0ms128×body80valid
4.0ms21×body320valid
1.0ms11×body160valid

simplify82.0ms

Calls
1 calls:
Slowest
82.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize16.0ms

Local error

Found 3 expressions with local error:

3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite23.0ms

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
14.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
7.0ms
(/ (+ x 1) (- x 1))
1.0ms
(/ x (+ x 1))

series206.0ms

Calls
3 calls:
Slowest
127.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
40.0ms
(/ (+ x 1) (- x 1))
39.0ms
(/ x (+ x 1))

simplify2.6s

Calls
51 calls:
Slowest
365.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
259.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
225.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
206.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 2)) 1)))
197.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune635.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
0.0b
(pow (/ x (+ x 1)) 3)
0.0b
(pow (/ (+ x 1) (- x 1)) 3)
0.0b
(* (/ x (+ x 1)) (/ x (+ x 1)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
36×unpow-prod-down cube-prod
32×*-un-lft-identity
24×times-frac
22×add-cube-cbrt
15×difference-of-squares
12×associate-/r/
11×pow1
10×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* div-inv add-log-exp
5×distribute-lft-out--
4×cube-div flip3-+ flip-+ insert-posit16
3×flip3-- pow-exp flip-- rem-cube-cbrt
2×cube-mult pow-to-exp pow-pow unpow3
1×pow2 frac-times difference-cubes cbrt-undiv sub-neg pow-plus diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up frac-sub cbrt-unprod
Calls
4 calls:
Slowest
31.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
9.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))
6.0ms
(pow (/ (+ x 1) (- x 1)) 3)
3.0ms
(pow (/ x (+ x 1)) 3)

series378.0ms

Calls
4 calls:
Slowest
254.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
43.0ms
(pow (/ (+ x 1) (- x 1)) 3)
42.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))
38.0ms
(pow (/ x (+ x 1)) 3)

simplify19.3s

Calls
128 calls:
Slowest
655.0ms
(pow (/ (sqrt (+ x 1)) (* (cbrt (- x 1)) (cbrt (- x 1)))) 3)
558.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (- x 1)) (cbrt (- x 1)))) 3)
544.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (sqrt (- x 1))) 3)
525.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (- x 1)) (cbrt (- x 1)))) 3)
506.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (sqrt (- x 1))) 3)

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
3.5b
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
0.0b
(pow (/ x (+ x 1)) 3)
0.0b
(pow (/ (+ x 1) (- x 1)) 3)

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
51×unpow-prod-down cube-prod
42×*-un-lft-identity
30×times-frac difference-of-squares
25×log-pow
24×exp-prod
22×add-cube-cbrt
10×distribute-lft-out--
8×add-cbrt-cube add-exp-log associate-/r/
7×pow1
6×add-log-exp
5×log-prod
4×cube-div insert-posit16 div-inv
3×flip3-- pow-exp flip-- rem-cube-cbrt
2×cube-mult pow-to-exp difference-cubes sub-neg pow-pow flip3-+ unpow3 exp-sum flip-+
1×cbrt-undiv log-div exp-diff diff-log div-exp rem-log-exp frac-sub
Calls
4 calls:
Slowest
51.0ms
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
27.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
6.0ms
(pow (/ (+ x 1) (- x 1)) 3)
3.0ms
(pow (/ x (+ x 1)) 3)

series635.0ms

Calls
4 calls:
Slowest
274.0ms
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
263.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
52.0ms
(pow (/ x (+ x 1)) 3)
46.0ms
(pow (/ (+ x 1) (- x 1)) 3)

simplify25.4s

Calls
139 calls:
Slowest
728.0ms
(pow (/ (+ x 1) (- (pow x 3) (pow 1 3))) 3)
495.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (sqrt (- x 1))) 3)
482.0ms
(+ (sqrt (pow (/ x (+ x 1)) 3)) (pow (sqrt (/ (+ x 1) (- x 1))) 3))
478.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (sqrt (- x 1))) 3)
471.0ms
(pow (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) (* (cbrt (- x 1)) (cbrt (- x 1)))) 3)

prune1.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (pow (cbrt (/ x (+ x 1))) 3)) (pow (/ (+ x 1) (- x 1)) 3))
0.4b
(pow (cbrt (/ x (+ x 1))) 3)
0.3b
(cbrt (/ x (+ x 1)))
0.0b
(* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (pow (cbrt (/ x (+ x 1))) 3))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-prod
23×associate-*r*
18×unpow-prod-down cube-prod add-exp-log
16×cube-div
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×frac-times cbrt-div associate-*l/ associate-/r/
9×add-cbrt-cube prod-exp
7×frac-sub
6×associate-*r/ add-log-exp
5×pow1 flip3-+ flip-+ div-inv
4×insert-posit16
3×pow-to-exp pow-exp cbrt-unprod
2×cube-mult pow-pow pow1/3 unpow3
1×sub-neg flip3-- diff-log associate-*l* *-commutative flip-- rem-cube-cbrt
Calls
4 calls:
Slowest
26.0ms
(* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (pow (cbrt (/ x (+ x 1))) 3))
18.0ms
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (pow (cbrt (/ x (+ x 1))) 3)) (pow (/ (+ x 1) (- x 1)) 3))
2.0ms
(pow (cbrt (/ x (+ x 1))) 3)
1.0ms
(cbrt (/ x (+ x 1)))

series611.0ms

Calls
4 calls:
Slowest
311.0ms
(- (* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (pow (cbrt (/ x (+ x 1))) 3)) (pow (/ (+ x 1) (- x 1)) 3))
136.0ms
(pow (cbrt (/ x (+ x 1))) 3)
101.0ms
(cbrt (/ x (+ x 1)))
63.0ms
(* (* (/ x (+ 1 x)) (/ x (+ 1 x))) (pow (cbrt (/ x (+ x 1))) 3))

simplify11.3s

Calls
98 calls:
Slowest
701.0ms
(* (* (+ 1 x) (pow (cbrt (+ x 1)) 3)) (pow (- x 1) 3))
580.0ms
(* (* (+ 1 x) (pow (cbrt (+ x 1)) 3)) (pow (- x 1) 3))
470.0ms
(+ (+ (log (/ x (+ 1 x))) (log (/ x (+ 1 x)))) (log (pow (cbrt (/ x (+ x 1))) 3)))
441.0ms
(* (* x (/ x (+ 1 x))) (pow (cbrt (/ x (+ x 1))) 3))
423.0ms
(* (* (+ 1 x) (+ 1 x)) (pow (- x 1) 3))

prune1.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.4b

bsearch156.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
704.0ms4089×body80valid
638.0ms1669×body1280valid
462.0ms1321×body640valid
213.0ms627×body320valid
104.0ms294×body160valid