Details

Time bar (total: 4.6m)

sample73.0ms

Algorithm
intervals
Results
27.0ms56×body1280valid
15.0ms40×body640valid
13.0ms128×body80valid
6.0ms21×body320valid
2.0ms11×body160valid

simplify54.0ms

Calls
1 calls:
Slowest
54.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize18.0ms

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))

rewrite80.0ms

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
51.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
20.0ms
(/ (+ x 1) (- x 1))
7.0ms
(/ x (+ x 1))

series183.0ms

Calls
3 calls:
Slowest
125.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
32.0ms
(/ x (+ x 1))
25.0ms
(/ (+ x 1) (- x 1))

simplify4.7s

Calls
142 calls:
Slowest
663.0ms
(/ (* (* x x) x) (* (* (+ x 1) (+ x 1)) (+ x 1)))
349.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
333.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
202.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
179.0ms
(- (+ x (pow x 3)) (pow x 2))

prune929.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

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)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
374×*-un-lft-identity
232×times-frac
210×add-sqr-sqrt
112×unpow-prod-down cube-prod
82×add-cube-cbrt
70×distribute-lft-out
61×distribute-lft-out--
52×difference-of-squares
24×swap-sqr
22×add-cbrt-cube add-exp-log
18×associate-*r* associate-*l*
16×associate-/r/
14×sqr-pow
13×pow1
8×difference-of-sqr-1 div-inv
6×cbrt-undiv pow-unpow flip3-+ div-exp flip-+ add-log-exp
4×cube-div pow-exp prod-exp cbrt-unprod insert-posit16 rem-cube-cbrt unswap-sqr
3×flip3-- flip--
2×cube-mult pow-to-exp pow-pow unpow3
1×pow2 frac-times difference-cubes sub-neg pow-plus diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up frac-sub
Calls
4 calls:
Slowest
99.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
26.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))
13.0ms
(pow (/ (+ x 1) (- x 1)) 3)
7.0ms
(pow (/ x (+ x 1)) 3)

series381.0ms

Calls
4 calls:
Slowest
263.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
47.0ms
(pow (/ x (+ x 1)) 3)
38.0ms
(pow (/ (+ x 1) (- x 1)) 3)
33.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))

simplify1.1m

Calls
390 calls:
Slowest
753.0ms
(pow (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) 3)
680.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
498.0ms
(pow (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) 3)
491.0ms
(pow (/ (* (cbrt x) (cbrt x)) 1) 3)
491.0ms
(pow (/ (* (cbrt x) (cbrt x)) 1) 3)

prune3.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

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)

rewrite489.0ms

Algorithm
rewrite-expression-head
Rules
484×*-un-lft-identity
256×times-frac
248×add-sqr-sqrt
172×unpow-prod-down cube-prod
114×distribute-lft-out--
88×difference-of-squares
84×distribute-lft-out
78×log-pow
77×exp-prod
48×add-cube-cbrt
26×sqr-pow
10×add-cbrt-cube add-exp-log
8×difference-of-sqr-1 associate-/r/
7×pow1
6×pow-unpow add-log-exp
5×log-prod
4×cube-div pow-exp insert-posit16 div-inv rem-cube-cbrt
3×flip3-- flip--
2×cube-mult pow-to-exp difference-cubes cbrt-undiv sub-neg pow-pow flip3-+ unpow3 div-exp exp-sum flip-+
1×log-div exp-diff diff-log rem-log-exp frac-sub
Calls
4 calls:
Slowest
319.0ms
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
139.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
11.0ms
(pow (/ (+ x 1) (- x 1)) 3)
7.0ms
(pow (/ x (+ x 1)) 3)

series600.0ms

Calls
4 calls:
Slowest
270.0ms
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
247.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
42.0ms
(pow (/ (+ x 1) (- x 1)) 3)
41.0ms
(pow (/ x (+ x 1)) 3)

simplify1.4m

Calls
366 calls:
Slowest
772.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
675.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
656.0ms
(- (pow (sqrt (/ x (+ x 1))) 3) (pow (sqrt (/ (+ x 1) (- x 1))) 3))
499.0ms
(pow (/ (* (cbrt x) (cbrt x)) 1) 3)
487.0ms
(pow (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) 3)

prune4.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
754×*-un-lft-identity
352×times-frac
346×add-sqr-sqrt
240×unpow-prod-down cube-prod
212×distribute-lft-out--
160×log-pow
156×sqrt-pow1
154×exp-prod
144×difference-of-squares
128×distribute-lft-out
48×sqr-pow
16×log-prod
10×add-cube-cbrt sqrt-prod
8×pow1 add-log-exp
6×add-exp-log
4×cube-div difference-cubes sub-neg add-cbrt-cube exp-sum insert-posit16
2×log-div flip3-- pow1/2 exp-diff sqrt-div diff-log rem-log-exp frac-sub flip--
Calls
4 calls:
Slowest
371.0ms
(log (sqrt (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3)))))
363.0ms
(log (sqrt (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3)))))
142.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
120.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))

series1.3s

Calls
4 calls:
Slowest
414.0ms
(log (sqrt (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3)))))
355.0ms
(log (sqrt (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3)))))
256.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
253.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))

simplify1.7m

Calls
488 calls:
Slowest
732.0ms
(+ (pow (sqrt (/ x (+ x 1))) 3) (pow (/ (sqrt (+ x 1)) (sqrt (- x 1))) 3))
671.0ms
(+ (pow (/ (sqrt x) (sqrt (+ x 1))) 3) (pow (sqrt (/ (+ x 1) (- x 1))) 3))
642.0ms
(/ (- (pow (/ (sqrt x) (sqrt (+ x 1))) 3) (pow (sqrt (/ (+ x 1) (- x 1))) 3)) 2)
566.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
502.0ms
(+ (pow (sqrt (/ x (+ x 1))) 3) (pow (/ (sqrt (+ x 1)) (sqrt (- x 1))) 3))

prune4.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.4b

bsearch187.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
977.0ms1669×body1280valid
411.0ms1321×body640valid
330.0ms4089×body80valid
137.0ms627×body320valid
37.0ms294×body160valid