Details

Time bar (total: 49.8s)

sample675.0ms

Algorithm
intervals
Results
103.0ms51×body640valid
68.0ms42×body1280valid
36.0ms138×body80valid
12.0ms15×body320valid
6.0ms10×body160valid

simplify71.0ms

Calls
1 calls:
Slowest
70.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (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))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
27×*-un-lft-identity
22×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×insert-posit16
3×associate-/r*
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
Calls
4 calls:
Slowest
40.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
28.0ms
(* (tan x) (tan x))
24.0ms
(* (tan x) (tan x))
10.0ms
(- 1 (* (tan x) (tan x)))

series275.0ms

Calls
4 calls:
Slowest
99.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
73.0ms
(* (tan x) (tan x))
57.0ms
(* (tan x) (tan x))
45.0ms
(- 1 (* (tan x) (tan x)))

simplify6.3s

Calls
111 calls:
Slowest
634.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
568.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
565.0ms
(/ (* (* (- 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)))))
488.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
365.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
9×frac-times associate-*r*
8×associate-/l/
7×flip3-+ flip3-- associate-*l* flip-+ flip--
6×add-log-exp
5×associate-*l/ associate-*r/
4×tan-quot insert-posit16 difference-of-squares
3×associate-/r* sub-neg times-frac swap-sqr prod-exp cbrt-unprod
2×distribute-rgt-in cbrt-undiv distribute-lft-in div-exp pow-prod-down associate-/r/ *-commutative distribute-lft-out-- unswap-sqr
1×pow2 clear-num frac-2neg pow-plus diff-log pow-sqr pow-prod-up div-inv distribute-lft-out associate-/l*
Calls
4 calls:
Slowest
43.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
20.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
14.0ms
(* (tan x) (tan x))
4.0ms
(- 1 (tan x))

series278.0ms

Calls
4 calls:
Slowest
141.0ms
(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
64.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
39.0ms
(* (tan x) (tan x))
34.0ms
(- 1 (tan x))

simplify12.4s

Calls
96 calls:
Slowest
844.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
827.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
635.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
531.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
496.0ms
(* (+ 1 (tan x)) (- (pow 1 3) (pow (tan x) 3)))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
9×frac-times associate-*l*
8×associate-/l/
7×flip3-+ flip3-- associate-*r* flip-+ flip--
6×add-log-exp
5×associate-*l/ associate-*r/
4×tan-quot insert-posit16 difference-of-squares
3×associate-/r* times-frac swap-sqr prod-exp cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down associate-/r/ *-commutative distribute-lft-out-- unswap-sqr
1×pow2 distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in pow-plus diff-log pow-sqr pow-prod-up div-inv distribute-lft-out associate-/l*
Calls
4 calls:
Slowest
39.0ms
(/ (* (- 1 (tan x)) (+ 1 (tan x))) (+ 1 (* (tan x) (tan x))))
32.0ms
(* (- 1 (tan x)) (+ 1 (tan x)))
24.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (tan x))

series299.0ms

Calls
4 calls:
Slowest
159.0ms
(/ (* (- 1 (tan x)) (+ 1 (tan x))) (+ 1 (* (tan x) (tan x))))
80.0ms
(* (- 1 (tan x)) (+ 1 (tan x)))
37.0ms
(* (tan x) (tan x))
22.0ms
(- 1 (tan x))

simplify12.1s

Calls
94 calls:
Slowest
899.0ms
(* (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))) (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))))
869.0ms
(- (log (* (- 1 (tan x)) (+ 1 (tan x)))) (log (+ 1 (* (tan x) (tan x)))))
621.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
525.0ms
(* (- 1 (tan x)) (+ (pow 1 3) (pow (tan x) 3)))
525.0ms
(/ (* (* (* (- 1 (tan x)) (+ 1 (tan x))) (* (- 1 (tan x)) (+ 1 (tan x)))) (* (- 1 (tan x)) (+ 1 (tan x)))) (* (* (+ 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (+ 1 (* (tan x) (tan x)))))

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
136×pow1
44×tan-quot
39×pow-prod-up
26×pow-prod-down
25×pow-sqr
22×add-sqr-sqrt add-cbrt-cube add-exp-log
21×pow-plus
20×frac-times
16×pow2 *-un-lft-identity add-cube-cbrt
14×associate-*l/ associate-*r/
11×prod-exp cbrt-unprod
10×swap-sqr associate-*r* associate-*l*
4×*-commutative insert-posit16 add-log-exp unswap-sqr
Calls
4 calls:
Slowest
68.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
22.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series207.0ms

Calls
4 calls:
Slowest
83.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
43.0ms
(* (tan x) (tan x))
42.0ms
(* (tan x) (tan x))
39.0ms
(* (tan x) (tan x))

simplify5.2s

Calls
202 calls:
Slowest
437.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
341.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
309.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
295.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
283.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.6s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

regimes425.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.5s1455×body1280valid
1.8s1278×body640valid
991.0ms4347×body80valid
424.0ms610×body320valid
131.0ms310×body160valid