Details

Time bar (total: 52.8s)

sample170.0ms

Algorithm
intervals
Results
75.0ms68×body1280valid
36.0ms53×body640valid
22.0ms24×body2560valid
14.0ms32×body320valid
7.0ms62×body80valid
5.0ms17×body160valid

simplify13.0ms

Calls
1 calls:
Slowest
13.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize28.0ms

Local error

Found 3 expressions with local error:

14.5b
(sqrt (+ (* x x) 1))
4.0b
(log (+ x (sqrt (+ (* x x) 1))))
0.4b
(+ x (sqrt (+ (* x x) 1)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt sqrt-prod add-log-exp
4×log-prod add-exp-log distribute-lft-out
3×flip3-+ add-cbrt-cube flip-+ insert-posit16
2×log-div sqrt-div
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp associate-*l* log-pow
Calls
3 calls:
Slowest
39.0ms
(+ x (sqrt (+ (* x x) 1)))
39.0ms
(log (+ x (sqrt (+ (* x x) 1))))
17.0ms
(sqrt (+ (* x x) 1))

series276.0ms

Calls
3 calls:
Slowest
168.0ms
(log (+ x (sqrt (+ (* x x) 1))))
64.0ms
(+ x (sqrt (+ (* x x) 1)))
44.0ms
(sqrt (+ (* x x) 1))

simplify4.0s

Calls
27 calls:
Slowest
478.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
475.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
462.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
381.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
369.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))

prune520.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

17.7b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.2b
(* (* x x) -1/6)
0.1b
(* (* (* x x) -1/6) x)
0.0b
(* (pow x 5) 3/40)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
88×associate-*l*
67×add-sqr-sqrt
49×*-un-lft-identity
29×unswap-sqr
23×add-exp-log
21×add-cube-cbrt
20×pow1 add-cbrt-cube
18×associate-*r* distribute-lft-out
12×prod-exp
10×pow-prod-down cbrt-unprod
9×swap-sqr *-commutative add-log-exp
4×unpow-prod-down insert-posit16
3×sum-log
2×+-commutative associate-+l+ sqr-pow
1×pow-to-exp flip3-+ pow-exp flip-+
Calls
4 calls:
Slowest
1.2s
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
97.0ms
(* (* (* x x) -1/6) x)
22.0ms
(* (* x x) -1/6)
11.0ms
(* (pow x 5) 3/40)

series224.0ms

Calls
4 calls:
Slowest
73.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
67.0ms
(* (pow x 5) 3/40)
44.0ms
(* (* x x) -1/6)
39.0ms
(* (* (* x x) -1/6) x)

simplify11.5s

Calls
118 calls:
Slowest
933.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
647.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
633.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
622.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
605.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

10.2b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
0.3b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
132×add-sqr-sqrt
90×associate-*l*
86×*-un-lft-identity
84×times-frac
72×add-cube-cbrt
35×unswap-sqr
34×associate-/r*
30×associate-*r*
24×pow1
20×swap-sqr
19×add-exp-log
18×add-cbrt-cube frac-add
16×*-commutative
11×flip3-+ flip-+
9×distribute-lft-out associate-/l* add-log-exp
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod
4×insert-posit16
3×cbrt-undiv clear-num sum-log frac-2neg div-exp pow-prod-down
2×pow2 +-commutative log-div associate-+l+ pow3 pow-sqr
1×rem-log-exp log-pow div-inv
Calls
4 calls:
Slowest
883.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
543.0ms
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))
41.0ms
(* (* x x) x)
27.0ms
(/ -1/8 (* (* x x) x))

series271.0ms

Calls
4 calls:
Slowest
123.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
62.0ms
(/ -1/8 (* (* x x) x))
46.0ms
(+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))
39.0ms
(* (* x x) x)

simplify25.8s

Calls
297 calls:
Slowest
618.0ms
(* (+ (* (/ -1/8 (* (* x x) x)) (/ -1/8 (* (* x x) x))) (- (* x x) (* (/ -1/8 (* (* x x) x)) x))) (- x))
610.0ms
(* (+ (* (/ -1/8 (* (* x x) x)) (/ -1/8 (* (* x x) x))) (- (* x x) (* (/ -1/8 (* (* x x) x)) x))) (/ x 1/2))
574.0ms
(* (+ (* (/ -1/8 (* (* x x) x)) (/ -1/8 (* (* x x) x))) (- (* x x) (* (/ -1/8 (* (* x x) x)) x))) (/ x 1/2))
568.0ms
(+ (* (- (* (/ -1/8 (* (* x x) x)) (/ -1/8 (* (* x x) x))) (* x x)) (/ x 1/2)) (* (- (/ -1/8 (* (* x x) x)) x) 1))
554.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))

prune2.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

19.9b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
12.6b
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.3b
(/ 1/16 (pow x 5))
0.1b
(/ (/ 1/8 x) x)

rewrite2.8s

Algorithm
rewrite-expression-head
Rules
24001×associate-/l*
19025×*-un-lft-identity
19023×add-sqr-sqrt
19003×add-cube-cbrt
18070×frac-sub
18018×frac-add
17855×associate-/r*
17658×times-frac
9037×log-div
8667×associate-/l/
4184×unpow-prod-down
4097×clear-num frac-2neg
1396×sqr-pow
1176×div-inv
26×flip3-+ flip-+
15×add-exp-log
11×add-cbrt-cube
10×log-prod
9×add-log-exp
8×difference-of-squares
6×div-exp distribute-lft-out--
5×pow1
4×cbrt-undiv insert-posit16 distribute-lft-out
2×flip3-- diff-log associate--l+ flip--
1×pow-to-exp +-commutative sum-log sub-neg rem-log-exp pow-exp log-pow
Calls
4 calls:
Slowest
382.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
293.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
16.0ms
(/ (/ 1/8 x) x)
11.0ms
(/ 1/16 (pow x 5))

series295.0ms

Calls
4 calls:
Slowest
135.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
66.0ms
(/ 1/16 (pow x 5))
64.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
29.0ms
(/ (/ 1/8 x) x)