Details

Time bar (total: 5.0m)

sample81.0ms

Algorithm
intervals
Results
18.0ms51×body1280valid
14.0ms44×body640valid
10.0ms137×body80valid
3.0ms16×body320valid
1.0ms8×body160valid

simplify34.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
34.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize27.0ms

Local error

Found 3 expressions with local error:

2.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite116.0ms

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
89.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
18.0ms
(/ (+ x 1) (- x 1))
7.0ms
(/ x (+ x 1))

series207.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
130.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
40.0ms
(/ (+ x 1) (- x 1))
37.0ms
(/ x (+ x 1))

simplify4.5s

Counts
142 → 126
Calls
142 calls:
Slowest
404.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- x 1) (- x 1)) (- x 1)))
290.0ms
(- (* x (- x 1)) (* (+ x 1) (+ x 1)))
266.0ms
(/ (* (* x x) x) (* (* (+ x 1) (+ x 1)) (+ x 1)))
239.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
227.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune924.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize78.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (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 1) (- x 1)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
348×*-un-lft-identity
212×times-frac
210×add-sqr-sqrt
112×unpow-prod-down cube-prod
66×add-cube-cbrt
65×distribute-lft-out--
62×distribute-lft-out
60×difference-of-squares
34×associate-*r*
22×add-cbrt-cube add-exp-log
18×associate-*l*
14×sqr-pow
12×difference-of-sqr-1 associate-/r/
8×pow1
6×cbrt-undiv pow-unpow div-exp div-inv add-log-exp
4×cube-div flip3-- pow-exp prod-exp cbrt-unprod insert-posit16 flip-- rem-cube-cbrt unswap-sqr
3×flip3-+ flip-+
2×cube-mult pow-to-exp pow-pow unpow3
1×frac-times difference-cubes sub-neg diff-log pow-prod-down associate-*l/ associate-*r/ *-commutative frac-sub
Counts
4 → 311
Calls
4 calls:
Slowest
139.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
68.0ms
(* (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
20.0ms
(pow (/ (+ x 1) (- x 1)) 3)
7.0ms
(pow (/ x (+ x 1)) 3)

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
247.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
52.0ms
(pow (/ (+ x 1) (- x 1)) 3)
35.0ms
(* (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
31.0ms
(pow (/ x (+ x 1)) 3)

simplify1.1m

Counts
353 → 323
Calls
353 calls:
Slowest
777.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
680.0ms
(pow (/ (sqrt (+ x 1)) (sqrt (- x 1))) 3)
620.0ms
(- (pow (sqrt (/ x (+ x 1))) 3) (pow (/ (+ x 1) (- x 1)) (/ 3 2)))
542.0ms
(+ (- (log x) (log (+ x 1))) (- (log (+ x 1)) (log (- x 1))))
510.0ms
(+ (log (/ x (+ x 1))) (log (/ (+ x 1) (- x 1))))

prune3.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize90.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
2.1b
(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)

rewrite500.0ms

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
Counts
4 → 327
Calls
4 calls:
Slowest
339.0ms
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
104.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
24.0ms
(pow (/ (+ x 1) (- x 1)) 3)
15.0ms
(pow (/ x (+ x 1)) 3)

series611.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
242.0ms
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
54.0ms
(pow (/ (+ x 1) (- x 1)) 3)
46.0ms
(pow (/ x (+ x 1)) 3)

simplify1.4m

Counts
366 → 339
Calls
366 calls:
Slowest
778.0ms
(+ (pow (sqrt (/ x (+ x 1))) 3) (pow (sqrt (/ (+ x 1) (- x 1))) 3))
756.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
747.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
720.0ms
(pow (/ (+ x 1) (- (* x x) (* 1 1))) 3)
492.0ms
(pow (/ (sqrt (+ x 1)) (+ (sqrt x) 1)) 3)

prune4.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
2.1b
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
2.1b
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
2.1b
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))

rewrite792.0ms

Algorithm
rewrite-expression-head
Rules
750×*-un-lft-identity
352×times-frac
342×add-sqr-sqrt
240×unpow-prod-down cube-prod
212×distribute-lft-out--
144×difference-of-squares
128×distribute-lft-out
78×log-pow
77×exp-prod
48×sqr-pow
10×add-log-exp
6×cube-div add-cube-cbrt
5×pow1 log-prod
4×difference-cubes sub-neg add-cbrt-cube add-exp-log insert-posit16
3×flip3-- diff-log frac-sub flip--
2×exp-sum
1×log-div exp-diff rem-log-exp
Counts
4 → 357
Calls
4 calls:
Slowest
406.0ms
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
144.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
113.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
104.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
297.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
267.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
264.0ms
(log (exp (- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))))
254.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))

simplify2.1m

Counts
546 → 369
Calls
546 calls:
Slowest
823.0ms
(+ (pow (sqrt (/ x (+ x 1))) 3) (pow (/ (sqrt (+ x 1)) (sqrt (- x 1))) 3))
799.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
768.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))
661.0ms
(- (sqrt (pow (/ x (+ x 1)) 3)) (pow (/ (+ x 1) (- x 1)) (/ 3 2)))
640.0ms
(- (pow (/ x (+ x 1)) 3) (pow (/ (+ x 1) (- x 1)) 3))

prune5.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes89.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.7b

bsearch206.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s1700×body1280valid
486.0ms1316×body640valid
377.0ms4047×body80valid
143.0ms610×body320valid
50.0ms327×body160valid