Details

sample482.0ms

Algorithm

intervals

Results

182.0ms	52×	body	1280	valid
67.0ms	146×	body	80	valid
46.0ms	18×	body	320	valid
38.0ms	30×	body	640	valid
7.0ms	10×	body	160	valid

simplify137.0ms

Calls

1 calls:

Slowest

136.0ms

(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(- 1 (* (tan x) (tan x)))
0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

161×	`*-un-lft-identity`
143×	`add-sqr-sqrt`
75×	`times-frac`
70×	`difference-of-squares`
34×	`add-cube-cbrt`
32×	`distribute-lft-out`
29×	`associate-l`
20×	`swap-sqr`
18×	`pow1`
16×	`*-commutative` `unswap-sqr`
15×	`associate-/l*`
14×	`distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot`
6×	`associate-r` `add-log-exp`
5×	`associate-/r*`
4×	`insert-posit16`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up` `cbrt-unprod` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Calls

4 calls:

Slowest

51.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
30.0ms	(* (tan x) (tan x))
19.0ms	(- 1 (* (tan x) (tan x)))
16.0ms	(* (tan x) (tan x))

series249.0ms

Calls

4 calls:

Slowest

115.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
47.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))
41.0ms	(- 1 (* (tan x) (tan x)))

simplify12.0s

Calls

259 calls:

Slowest

606.0ms	(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
595.0ms	(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
504.0ms	(/ (* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x)))) (* (* (+ 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (+ 1 (* (tan x) (tan x)))))
434.0ms	(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
273.0ms	(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

11.6b	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
0.3b	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
0.2b	(* (* (tan x) (tan x)) (tan x))
0.2b	(* (* (tan x) (tan x)) (tan x))

rewrite746.0ms

Algorithm

rewrite-expression-head

Rules

612×	`pow1`
505×	`add-sqr-sqrt`
408×	`tan-quot`
321×	`pow-prod-up`
310×	`unswap-sqr`
284×	`associate-l`
268×	`frac-times`
215×	`pow-plus`
184×	`associate-*l/`
164×	`swap-sqr`
143×	`cbrt-prod`
116×	`associate-r` `associate-*r/`
110×	`*-commutative`
104×	`pow-prod-down`
97×	`*-un-lft-identity` `pow-sqr`
73×	`add-cube-cbrt`
68×	`pow3`
63×	`cbrt-div`
61×	`pow2`
50×	`add-cbrt-cube` `add-exp-log`
33×	`prod-exp` `cbrt-unprod`
4×	`rem-cbrt-cube` `insert-posit16` `add-log-exp`
1×	`pow1/3`

Calls

4 calls:

Slowest

323.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
293.0ms	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
53.0ms	(* (* (tan x) (tan x)) (tan x))
50.0ms	(* (* (tan x) (tan x)) (tan x))

series231.0ms

Calls

4 calls:

Slowest

71.0ms	(* (* (tan x) (tan x)) (tan x))
60.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
52.0ms	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
49.0ms	(* (* (tan x) (tan x)) (tan x))

simplify1.2m

Calls

1037 calls:

Slowest

1.5s	(* (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))))
1.1s	(* (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))))
1.1s	(* (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))))
1.0s	(* (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))) (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (tan x) (tan x)) (tan x))))
758.0ms	(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (tan x) (tan x)) (tan x)))

prune7.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

14.1b	(sqrt (* (tan x) (tan x)))
14.1b	(sqrt (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
34×	`pow1`
30×	`sqrt-prod`
22×	`*-un-lft-identity` `add-cube-cbrt`
16×	`tan-quot`
14×	`swap-sqr`
12×	`sqrt-pow1` `associate-r` `associate-l`
10×	`rem-sqrt-square`
8×	`add-cbrt-cube` `add-exp-log`
6×	`sqrt-div` `*-commutative` `unswap-sqr`
4×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
2×	`pow1/2` `prod-exp` `cbrt-unprod`

Calls

4 calls:

Slowest

28.0ms	(sqrt (* (tan x) (tan x)))
27.0ms	(* (tan x) (tan x))
22.0ms	(sqrt (* (tan x) (tan x)))
13.0ms	(* (tan x) (tan x))

series182.0ms

Calls

4 calls:

Slowest

56.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))
43.0ms	(sqrt (* (tan x) (tan x)))
26.0ms	(sqrt (* (tan x) (tan x)))

simplify2.4s

Calls

120 calls:

Slowest

290.0ms	(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))
238.0ms	(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))
212.0ms	(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
195.0ms	(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
176.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

11.6b	(cbrt (cbrt (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))))))
5.0b	(cbrt (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))))
0.3b	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
0.3b	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))

rewrite4.3m

Algorithm

rewrite-expression-head

Rules

4718976×	`tan-quot`
4194564×	`frac-times`
2096300×	`associate-*l/`
1906471×	`add-sqr-sqrt`
1838686×	`unswap-sqr`
1424492×	`associate-*r/`
786429×	`cbrt-div`
271857×	`cbrt-prod`
258012×	`swap-sqr`
185488×	`*-commutative`
4228×	`associate-r`
4084×	`associate-l`
1319×	`*-un-lft-identity`
1144×	`pow1`
618×	`pow-prod-up`
608×	`pow-prod-down`
592×	`pow3`
406×	`pow-plus`
359×	`add-cube-cbrt`
186×	`pow-sqr`
114×	`pow2`
100×	`rem-cbrt-cube`
76×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
40×	`cube-unmult`
4×	`insert-posit16` `add-log-exp`
2×	`pow1/3`

Calls

4 calls:

Slowest

33.9s	(cbrt (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))))
12.5s	(cbrt (cbrt (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))))))
410.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
311.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))

series386.0ms

Calls

4 calls:

Slowest

111.0ms	(cbrt (cbrt (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))))))
102.0ms	(cbrt (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))))
87.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
76.0ms	(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))