Details

sample488.0ms

Algorithm

intervals

Results

260.0ms	92×	body	2560	valid
101.0ms	76×	body	1280	valid
51.0ms	16×	body	160	valid
41.0ms	52×	body	640	valid
11.0ms	256×	pre	80	true
10.0ms	19×	body	320	valid
0.0ms	1×	body	80	valid

simplify31.0ms

Calls

1 calls:

Slowest

31.0ms

(- (/ 1 x) (/ 1 (tan x)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize22.0ms

Local error

Found 2 expressions with local error:

3.9b	(- (/ 1 x) (/ 1 (tan x)))
0.0b	(/ 1 (tan x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
72×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
57×	`associate-/r` `associate-/l`
48×	`add-cube-cbrt`
27×	`times-frac`
19×	`clear-num` `frac-2neg`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
5×	`div-inv`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1`
2×	`div-exp` `insert-posit16`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `pow-flip` `flip--` `inv-pow`

Calls

2 calls:

Slowest

41.0ms	(- (/ 1 x) (/ 1 (tan x)))
6.0ms	(/ 1 (tan x))

series120.0ms

Calls

2 calls:

Slowest

80.0ms	(- (/ 1 x) (/ 1 (tan x)))
40.0ms	(/ 1 (tan x))

simplify13.2s

Calls

225 calls:

Slowest

647.0ms	(- (* (- 1) (cbrt (tan x))) (* (- x) (/ 1 (* (cbrt (tan x)) (cbrt (tan x))))))
464.0ms	(- (* (/ 1 (* (cbrt x) (cbrt x))) (cbrt (tan x))) (* (cbrt x) (/ 1 (* (cbrt (tan x)) (cbrt (tan x))))))
417.0ms	(- (* 1 (cbrt (tan x))) (* x (/ 1 (* (cbrt (tan x)) (cbrt (tan x))))))
406.0ms	(- (* (/ 1 (sqrt x)) (cbrt (tan x))) (* (sqrt x) (/ 1 (* (cbrt (tan x)) (cbrt (tan x))))))
387.0ms	(- (* (/ 1 (sqrt x)) (- (tan x))) (* (sqrt x) (- 1)))

prune1.1s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (+ 1/3 (* 1/45 (* x x))))
0.2b	(* 1/45 (* x x))
0.1b	(* (pow x 5) 2/945)
0.0b	(+ 1/3 (* 1/45 (* x x)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
26×	`associate-r`
23×	`*-un-lft-identity`
18×	`associate-l`
16×	`add-exp-log`
15×	`add-cube-cbrt`
13×	`pow1` `add-cbrt-cube`
11×	`unswap-sqr`
7×	`prod-exp`
6×	`add-log-exp`
5×	`pow-prod-down` `*-commutative` `cbrt-unprod`
4×	`unpow-prod-down` `swap-sqr` `insert-posit16` `distribute-lft-out`
3×	`+-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `sum-log` `pow-exp`

Calls

4 calls:

Slowest

139.0ms	(* x (+ 1/3 (* 1/45 (* x x))))
34.0ms	(* 1/45 (* x x))
24.0ms	(+ 1/3 (* 1/45 (* x x)))
12.0ms	(* (pow x 5) 2/945)

series308.0ms

Calls

4 calls:

Slowest

130.0ms	(* x (+ 1/3 (* 1/45 (* x x))))
79.0ms	(+ 1/3 (* 1/45 (* x x)))
65.0ms	(* (pow x 5) 2/945)
35.0ms	(* 1/45 (* x x))

simplify3.7s

Calls

82 calls:

Slowest

492.0ms	(+ (* 1/3 1/3) (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 (* 1/45 (* x x)))))
283.0ms	(* (exp 1/3) (exp (* 1/45 (* x x))))
263.0ms	(* (* (* x x) x) (* (* (+ 1/3 (* 1/45 (* x x))) (+ 1/3 (* 1/45 (* x x)))) (+ 1/3 (* 1/45 (* x x)))))
221.0ms	(* (* (* 1/45 1/45) 1/45) (* (* (* x x) x) (* (* x x) x)))
220.0ms	(* (* (* 1/45 1/45) 1/45) (* (* (* x x) (* x x)) (* x x)))

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
0.4b	(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))
0.2b	(* (* 1/45 (* x x)) (* 1/45 (* x x)))
0.2b	(* 1/45 (* x x))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

19442×	`add-sqr-sqrt`
10863×	`unswap-sqr`
4793×	`difference-of-squares`
3484×	`associate-r`
2937×	`times-frac`
2775×	`swap-sqr`
2055×	`*-commutative`
1788×	`*-un-lft-identity`
666×	`distribute-lft-out--`
538×	`associate-l`
344×	`add-cube-cbrt`
267×	`associate-/l*`
125×	`pow1`
70×	`pow-prod-down`
52×	`add-cbrt-cube` `add-exp-log`
32×	`prod-exp` `cbrt-unprod`
11×	`associate-/r*`
9×	`pow-sqr` `pow-prod-up`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`pow-plus` `flip3--` `flip--`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `div-exp` `associate-/r/` `associate-/l/`
1×	`pow2` `clear-num` `frac-2neg` `div-inv`

Calls

4 calls:

Slowest

1.5s	(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
627.0ms	(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))
166.0ms	(* (* 1/45 (* x x)) (* 1/45 (* x x)))
31.0ms	(* 1/45 (* x x))

series655.0ms

Calls

4 calls:

Slowest

321.0ms	(/ (* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x))))) (- 1/3 (* 1/45 (* x x))))
240.0ms	(* x (- (* 1/3 1/3) (* (* 1/45 (* x x)) (* 1/45 (* x x)))))
60.0ms	(* (* 1/45 (* x x)) (* 1/45 (* x x)))
34.0ms	(* 1/45 (* x x))