Details

Time bar (total: 1.3m)

sample381.0ms

Algorithm
intervals
Results
208.0ms52×body1280valid
36.0ms30×body640valid
34.0ms146×body80valid
17.0ms18×body320valid
6.0ms10×body160valid

simplify121.0ms

Calls
1 calls:
Slowest
120.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

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))))

rewrite177.0ms

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
74.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
37.0ms
(* (tan x) (tan x))
30.0ms
(* (tan x) (tan x))
30.0ms
(- 1 (* (tan x) (tan x)))

series251.0ms

Calls
4 calls:
Slowest
129.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
45.0ms
(* (tan x) (tan x))
42.0ms
(* (tan x) (tan x))
35.0ms
(- 1 (* (tan x) (tan x)))

simplify21.7s

Calls
351 calls:
Slowest
548.0ms
(fma 1 1 (- (* (cbrt (tan x)) (* (tan x) (* (cbrt (tan x)) (cbrt (tan x)))))))
544.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
510.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
449.0ms
(fma 1 1 (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))
398.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.2b
(- 1 (* (tan x) (tan x)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
52×*-un-lft-identity
45×prod-diff
43×add-cube-cbrt
18×pow1
17×swap-sqr
16×associate-*l*
15×associate-*r*
10×difference-of-squares
8×add-cbrt-cube tan-quot add-exp-log
7×*-commutative unswap-sqr
6×add-log-exp
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u
3×fma-neg
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr pow-prod-up cbrt-unprod distribute-lft-out--
1×log1p-udef sub-neg flip3-- diff-log log1p-expm1 flip--
Calls
4 calls:
Slowest
33.0ms
(* (tan x) (tan x))
15.0ms
(- 1 (* (tan x) (tan x)))
13.0ms
(* (tan x) (tan x))
1.0ms
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))

series413.0ms

Calls
4 calls:
Slowest
282.0ms
(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
51.0ms
(- 1 (* (tan x) (tan x)))
44.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))

simplify13.6s

Calls
178 calls:
Slowest
529.0ms
(log (- (+ (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)) 1) (/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)))))
472.0ms
(log (- (+ (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)) 1) (/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)))))
418.0ms
(fma 1 1 (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))
412.0ms
(fma (sqrt 1) (sqrt 1) (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))
345.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.2b
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
0.2b
(- 1 (* (tan x) (tan x)))
0.1b
(/ (sin x) (cos x))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
150×add-sqr-sqrt
125×*-un-lft-identity
115×add-cube-cbrt
82×frac-times
64×associate-/l*
63×associate-/r*
49×times-frac
45×prod-diff
27×swap-sqr
26×associate-*l*
25×associate-*r*
22×clear-num
21×frac-2neg
20×add-cbrt-cube add-exp-log
18×pow1
10×associate-*l/ associate-*r/ difference-of-squares unswap-sqr
7×*-commutative
6×add-log-exp
5×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u
3×fma-neg
2×pow2 pow-plus pow-prod-down pow-sqr un-div-inv pow-prod-up distribute-lft-out--
1×quot-tan sub-neg flip3-- diff-log flip--
Calls
4 calls:
Slowest
26.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
26.0ms
(* (tan x) (tan x))
14.0ms
(- 1 (* (tan x) (tan x)))
13.0ms
(/ (sin x) (cos x))

series166.0ms

Calls
4 calls:
Slowest
50.0ms
(* (tan x) (tan x))
50.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
46.0ms
(- 1 (* (tan x) (tan x)))
20.0ms
(/ (sin x) (cos x))

simplify22.3s

Calls
432 calls:
Slowest
889.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (cos x)) (cbrt (cos x)))))
462.0ms
(fma (sqrt 1) (sqrt 1) (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))
400.0ms
(fma 1 1 (- (* (* (cbrt (tan x)) (cbrt (tan x))) (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x)))))))
363.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x)))
323.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))

prune3.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

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))

rewrite89.0ms

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 expm1-log1p-u frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
2×pow1/2 prod-exp cbrt-unprod
Calls
4 calls:
Slowest
26.0ms
(* (tan x) (tan x))
24.0ms
(sqrt (* (tan x) (tan x)))
24.0ms
(sqrt (* (tan x) (tan x)))
13.0ms
(* (tan x) (tan x))

series153.0ms

Calls
4 calls:
Slowest
50.0ms
(* (tan x) (tan x))
38.0ms
(* (tan x) (tan x))
36.0ms
(sqrt (* (tan x) (tan x)))
29.0ms
(sqrt (* (tan x) (tan x)))

simplify2.6s

Calls
120 calls:
Slowest
331.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))
304.0ms
(+ x (+ (* 1/3 (pow x 3)) (* 2/15 (pow x 5))))
297.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
290.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
149.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes305.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.2s1538×body1280valid
1.6s1322×body640valid
897.0ms631×body320valid
793.0ms4196×body80valid
156.0ms313×body160valid