Details

sample162.0ms

Algorithm

intervals

Results

82.0ms	81×	body	1280	valid
29.0ms	45×	body	640	valid
18.0ms	21×	body	2560	valid
12.0ms	30×	body	320	valid
7.0ms	66×	body	80	valid
3.0ms	13×	body	160	valid

simplify34.0ms

Calls

1 calls:

Slowest

34.0ms

(log (+ x (sqrt (+ (* x x) 1))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize12.0ms

Local error

Found 4 expressions with local error:

14.3b	(sqrt (+ (* x x) 1))
2.4b	(log (+ x (sqrt (+ (* x x) 1))))
1.0b	(+ x (sqrt (+ (* x x) 1)))
0.0b	(+ (* x x) 1)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `distribute-lft-out`
5×	`add-exp-log` `sqrt-prod`
4×	`log-prod` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16`
2×	`+-commutative` `log-div` `sum-log` `sqrt-div` `associate-l`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Calls

4 calls:

Slowest

52.0ms	(+ x (sqrt (+ (* x x) 1)))
36.0ms	(log (+ x (sqrt (+ (* x x) 1))))
21.0ms	(sqrt (+ (* x x) 1))
15.0ms	(+ (* x x) 1)

series308.0ms

Calls

4 calls:

Slowest

151.0ms	(log (+ x (sqrt (+ (* x x) 1))))
57.0ms	(+ x (sqrt (+ (* x x) 1)))
52.0ms	(sqrt (+ (* x x) 1))
48.0ms	(+ (* x x) 1)

simplify4.4s

Calls

33 calls:

Slowest

561.0ms	(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
501.0ms	(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
499.0ms	(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
403.0ms	(sqrt (+ (pow (* x x) 3) (pow 1 3)))
382.0ms	(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))

prune682.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

18.7b	(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.2b	(* (* x x) -1/6)
0.1b	(* (* (* x x) -1/6) x)
0.1b	(* (pow x 5) 3/40)

rewrite1.2s

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

1.1s	(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
99.0ms	(* (* (* x x) -1/6) x)
38.0ms	(* (* x x) -1/6)
21.0ms	(* (pow x 5) 3/40)

series246.0ms

Calls

4 calls:

Slowest

79.0ms	(* (pow x 5) 3/40)
71.0ms	(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
56.0ms	(* (* (* x x) -1/6) x)
40.0ms	(* (* x x) -1/6)

simplify11.1s

Calls

118 calls:

Slowest

662.0ms	(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
649.0ms	(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
619.0ms	(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
615.0ms	(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
604.0ms	(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

18.6b	(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
12.2b	(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.2b	(/ (/ 1/8 x) x)
0.1b	(/ (/ (/ 1/8 x) x) x)

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

24057×	`associate-/l*`
19203×	`*-un-lft-identity`
19201×	`add-sqr-sqrt`
19181×	`add-cube-cbrt`
18070×	`frac-sub`
18039×	`times-frac`
18018×	`frac-add`
17857×	`associate-/r*`
9037×	`log-div`
8704×	`associate-/l/`
4172×	`unpow-prod-down`
4099×	`clear-num` `frac-2neg`
1392×	`sqr-pow`
1193×	`div-inv`
26×	`flip3-+` `flip-+`
19×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`log-prod`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
8×	`difference-of-squares`
6×	`distribute-lft-out--`
5×	`pow1`
4×	`insert-posit16` `distribute-lft-out`
2×	`flip3--` `diff-log` `associate--l+` `flip--`
1×	`+-commutative` `sum-log` `sub-neg` `rem-log-exp` `log-pow`

Calls

4 calls:

Slowest

352.0ms	(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
291.0ms	(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
29.0ms	(/ (/ (/ 1/8 x) x) x)
8.0ms	(/ (/ 1/8 x) x)

series325.0ms

Calls

4 calls:

Slowest

130.0ms	(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
84.0ms	(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
71.0ms	(/ (/ (/ 1/8 x) x) x)
39.0ms	(/ (/ 1/8 x) x)