Details

Time bar (total: 1.7m)

sample404.0ms

Algorithm
intervals
Results
145.0ms44×body1280valid
66.0ms143×body80valid
42.0ms43×body640valid
10.0ms15×body320valid
4.0ms11×body160valid

simplify106.0ms

Calls
1 calls:
Slowest
105.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune467.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.2b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
192×*-un-lft-identity
180×add-sqr-sqrt
75×times-frac
70×difference-of-squares
65×add-cube-cbrt
45×prod-diff
38×associate-*l*
32×distribute-lft-out
29×swap-sqr
19×*-commutative unswap-sqr
18×pow1
15×associate-*r* associate-/l*
14×distribute-lft-out--
10×add-cbrt-cube add-exp-log
8×tan-quot
6×add-log-exp
5×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-neg
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
112.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
30.0ms
(* (tan x) (tan x))
28.0ms
(- 1 (* (tan x) (tan x)))
17.0ms
(* (tan x) (tan x))

series246.0ms

Calls
4 calls:
Slowest
105.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
54.0ms
(* (tan x) (tan x))
51.0ms
(- 1 (* (tan x) (tan x)))
35.0ms
(* (tan x) (tan x))

simplify21.0s

Calls
351 calls:
Slowest
537.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
506.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
387.0ms
(fma (sqrt 1) (sqrt 1) (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))
355.0ms
(fma 1 1 (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))
336.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.2b
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
658×*-un-lft-identity
551×add-sqr-sqrt
543×times-frac
220×difference-of-squares
211×add-cube-cbrt
124×distribute-lft-out
99×associate-*l*
96×associate-/r*
59×swap-sqr
49×*-commutative unswap-sqr
45×prod-diff
44×distribute-lft-out--
33×associate-/r/
19×pow1 add-exp-log
15×associate-*r*
13×add-cbrt-cube
11×associate-/l*
8×tan-quot
7×div-exp
6×add-log-exp
5×flip3-- div-inv flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u remove-double-div
3×cbrt-undiv clear-num fma-neg
2×pow2 frac-times rec-exp frac-2neg pow-plus 1-exp pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr pow-prod-up cbrt-unprod associate-/l/
1×sub-neg flip3-+ diff-log flip-+ pow-flip inv-pow
Calls
4 calls:
Slowest
144.0ms
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
27.0ms
(* (tan x) (tan x))
22.0ms
(* (tan x) (tan x))
14.0ms
(- 1 (* (tan x) (tan x)))

series246.0ms

Calls
4 calls:
Slowest
86.0ms
(/ 1 (/ (+ 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))))
57.0ms
(* (tan x) (tan x))
56.0ms
(* (tan x) (tan x))
47.0ms
(- 1 (* (tan x) (tan x)))

simplify1.2m

Calls
782 calls:
Slowest
613.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
553.0ms
(* (- 1 (* (tan x) (tan x))) (+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))))
455.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ 1 (+ 1 (* (sqrt (tan x)) (sqrt (tan x))))))
450.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
402.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (+ 1 (* (tan x) (tan x)))) (cbrt (+ 1 (* (tan x) (tan x))))) (+ 1 (* (sqrt (tan x)) (sqrt (tan x))))))

prune4.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite462.0ms

Algorithm
rewrite-expression-head
Rules
4287×*-un-lft-identity
2879×times-frac
2034×add-sqr-sqrt
1739×add-cube-cbrt
1701×prod-diff
1238×distribute-lft-out
987×associate-*l*
360×swap-sqr
357×associate-*r*
286×frac-sub
243×associate-/l*
213×associate-/r*
210×associate-/r/
122×*-commutative unswap-sqr
110×div-inv
105×flip3-+ flip-+
56×tan-quot
39×frac-2neg
37×clear-num
33×associate-/l/
25×pow1
24×distribute-lft-out--
21×fma-neg
19×sub-div
18×difference-of-squares
14×frac-times associate-*l/ associate-*r/
10×add-cbrt-cube add-exp-log
7×distribute-rgt-out--
6×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow2 pow-plus pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod
1×sub-neg flip3-- diff-log flip--
Calls
4 calls:
Slowest
282.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
23.0ms
(* (tan x) (tan x))
16.0ms
(* (tan x) (tan x))
13.0ms
(* (tan x) (tan x))

series279.0ms

Calls
4 calls:
Slowest
167.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
40.0ms
(* (tan x) (tan x))
38.0ms
(* (tan x) (tan x))
34.0ms
(* (tan x) (tan x))