Details

Time bar (total: 6.2m)

sample268.0ms

Algorithm
intervals
Results
55.0ms44×body1280valid
39.0ms43×body640valid
27.0ms138×body80valid
12.0ms19×body320valid
5.0ms12×body160valid

simplify112.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
111.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
24×add-cube-cbrt
18×pow1
15×times-frac
10×add-cbrt-cube add-exp-log difference-of-squares
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg prod-diff
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
4 → 128
Calls
4 calls:
Slowest
29.0ms
(* (tan x) (tan x))
25.0ms
(* (tan x) (tan x))
25.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
10.0ms
(- 1 (* (tan x) (tan x)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
70.0ms
(* (tan x) (tan x))
36.0ms
(- 1 (* (tan x) (tan x)))
34.0ms
(* (tan x) (tan x))

simplify6.0s

Counts
119 → 140
Calls
119 calls:
Slowest
612.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
540.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
362.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
325.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
317.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
62×*-un-lft-identity
37×times-frac
34×add-cube-cbrt
22×associate-*r*
16×difference-of-squares
11×add-cbrt-cube add-exp-log
9×prod-diff
8×distribute-lft-out-- add-log-exp
6×pow1 associate-/l*
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×associate-/r* fma-def flip3-+ fma-neg flip-+
2×frac-times cbrt-undiv flip3-- div-exp associate-*l/ prod-exp cbrt-unprod div-inv flip-- distribute-lft-out unswap-sqr associate-/l/
1×+-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub pow-prod-down associate-*r/ *-commutative
Counts
4 → 142
Calls
4 calls:
Slowest
57.0ms
(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
17.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
6.0ms
(+ (tan x) 1)
5.0ms
(- 1 (tan x))

series283.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
71.0ms
(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
24.0ms
(+ (tan x) 1)
22.0ms
(- 1 (tan x))

simplify9.4s

Counts
130 → 154
Calls
130 calls:
Slowest
670.0ms
(* (+ (* (tan x) (tan x)) (- (* 1 1) (* (tan x) 1))) (fma (tan x) (tan x) 1))
663.0ms
(* (- (* (tan x) (tan x)) (* 1 1)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))
410.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
400.0ms
(* (+ (pow (tan x) 3) (pow 1 3)) (- 1 (tan x)))
388.0ms
(- 1 (+ x (* 1/3 (pow x 3))))

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (tan x) (tan x) -1)
0.2b
(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))
0.2b
(/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))
0.2b
(/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
1709×times-frac
1174×add-sqr-sqrt
1096×*-un-lft-identity
598×add-cube-cbrt
332×difference-of-squares
166×distribute-lft-out--
83×associate-/l*
78×difference-of-sqr-1
69×associate-/r/
39×div-inv
37×associate-/r*
30×flip3-- flip--
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef associate-/l/
Counts
4 → 817
Calls
4 calls:
Slowest
29.0ms
(/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))
21.0ms
(/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
9.0ms
(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))
0.0ms
(fma (tan x) (tan x) -1)

series559.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
245.0ms
(/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))
160.0ms
(/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x))))
80.0ms
(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))
74.0ms
(fma (tan x) (tan x) -1)

simplify5.7m

Counts
1405 → 829
Calls
1405 calls:
Slowest
1.1s
(/ (/ (sqrt (fma (tan x) (tan x) -1)) (/ 1 (+ (sqrt 1) (sqrt (tan x))))) (+ (sqrt (tan x)) (sqrt 1)))
969.0ms
(/ (/ (sqrt (fma (tan x) (tan x) -1)) (/ (sqrt (fma (tan x) (tan x) 1)) (+ 1 (sqrt (tan x))))) (+ (sqrt (tan x)) (sqrt 1)))
934.0ms
(/ (/ (sqrt (fma (tan x) (tan x) -1)) (/ (sqrt (fma (tan x) (tan x) 1)) (+ 1 (sqrt (tan x))))) (+ (sqrt (tan x)) 1))
932.0ms
(/ (/ (fma (tan x) (tan x) -1) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x))))) (- (tan x) 1))
932.0ms
(/ (/ (sqrt (fma (tan x) (tan x) -1)) (/ (sqrt (fma (tan x) (tan x) 1)) (+ 1 (sqrt (tan x))))) (+ (sqrt (tan x)) 1))

prune10.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (tan x) (tan x) -1)
0.4b
(log (exp (/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))))
0.2b
(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))
0.2b
(/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
2986×times-frac
2034×add-sqr-sqrt
1879×*-un-lft-identity
997×add-cube-cbrt
588×difference-of-squares
546×log-pow
545×exp-prod
294×distribute-lft-out--
155×difference-of-sqr-1
111×associate-/r/
80×associate-/l*
63×div-inv
48×flip3-- flip--
15×add-cbrt-cube add-exp-log
13×associate-/r*
7×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×log-prod
2×clear-num frac-2neg
1×rem-log-exp fma-udef associate-/l/
Counts
4 → 1260
Calls
4 calls:
Slowest
71.0ms
(log (exp (/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))))
33.0ms
(/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))
9.0ms
(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))
0.0ms
(fma (tan x) (tan x) -1)

series756.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))
296.0ms
(log (exp (/ (/ (fma (tan x) (tan x) -1) (/ (fma (tan x) (tan x) 1) (- 1 (tan x)))) (- (tan x) 1))))
77.0ms
(/ (fma (tan x) (tan x) 1) (- 1 (tan x)))
75.0ms
(fma (tan x) (tan x) -1)