Details

Time bar (total: 38.2s)

sample221.0ms

Algorithm
intervals
Results
51.0ms51×body1280valid
45.0ms28×body320valid
30.0ms48×body640valid
16.0ms122×body80valid
2.0ms7×body160valid

simplify562.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
561.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

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))))

rewrite98.0ms

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
Counts
4 → 114
Calls
4 calls:
Slowest
45.0ms
(* (tan x) (tan x))
27.0ms
(* (tan x) (tan x))
14.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms
(- 1 (* (tan x) (tan x)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
60.0ms
(* (tan x) (tan x))
52.0ms
(* (tan x) (tan x))
35.0ms
(- 1 (* (tan x) (tan x)))

simplify6.0s

Counts
111 → 126
Calls
111 calls:
Slowest
559.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
539.0ms
(/ (* (* (- 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)))))
525.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
506.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
349.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
56×*-un-lft-identity
37×times-frac
30×add-cube-cbrt
27×associate-*r*
16×difference-of-squares
13×pow1 add-cbrt-cube add-exp-log
8×distribute-lft-out--
7×associate-*l*
6×associate-/l* add-log-exp
4×flip3-+ tan-quot associate-/r/ flip-+ insert-posit16
3×frac-times associate-/r* swap-sqr associate-*l/ prod-exp cbrt-unprod unswap-sqr
2×cbrt-undiv flip3-- div-exp pow-prod-down associate-*r/ *-commutative div-inv flip-- associate-/l/
1×pow2 clear-num sub-neg frac-2neg pow-plus diff-log div-sub pow-sqr pow-prod-up distribute-lft-out
Counts
4 → 139
Calls
4 calls:
Slowest
59.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
33.0ms
(* (tan x) (tan x))
28.0ms
(/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x))))
9.0ms
(- 1 (tan x))

series330.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(* (+ 1 (tan x)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
86.0ms
(/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x))))
64.0ms
(* (tan x) (tan x))
32.0ms
(- 1 (tan x))

simplify9.9s

Counts
135 → 151
Calls
135 calls:
Slowest
588.0ms
(* (+ (pow 1 3) (pow (tan x) 3)) (/ (- 1 (tan x)) (+ 1 (* (tan x) (tan x)))))
585.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
542.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
527.0ms
(/ (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))) (* (* (+ 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))) (+ 1 (* (tan x) (tan x)))))
491.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
25×pow1
24×*-un-lft-identity
16×add-cube-cbrt
12×tan-quot
10×add-cbrt-cube add-exp-log
9×swap-sqr associate-*r* associate-*l*
8×times-frac
6×add-log-exp difference-of-squares
5×distribute-rgt-out-- div-inv
4×associate-/r/ insert-posit16
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
2×flip3-+ flip-+ distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 115
Calls
4 calls:
Slowest
29.0ms
(* (tan x) (tan x))
28.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
26.0ms
(* (tan x) (tan x))
23.0ms
(* (tan x) (tan x))

series307.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
44.0ms
(* (tan x) (tan x))
44.0ms
(* (tan x) (tan x))
39.0ms
(* (tan x) (tan x))

simplify5.4s

Counts
116 → 127
Calls
116 calls:
Slowest
521.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
437.0ms
(- (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)) (/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))))
398.0ms
(- (/ 1 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)) (/ (pow (sin x) 2) (* (pow (cos x) 2) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))))
374.0ms
(- (/ 1 (+ (pow 1 3) (pow (* (tan x) (tan x)) 3))) (/ (* (tan x) (tan x)) (+ (pow 1 3) (pow (* (tan x) (tan x)) 3))))
318.0ms
(- (/ 1 (- (* 1 1) (* (* (tan x) (tan x)) (* (tan x) (tan x))))) (/ (* (tan x) (tan x)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan x) (tan x))))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.2b
(* (sin x) (tan x))
0.2b
(/ (* (sin x) (tan x)) (cos x))
0.2b
(- 1 (/ (* (sin x) (tan x)) (cos x)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×*-un-lft-identity
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
6×associate-*r* associate-*l* tan-quot add-log-exp
4×insert-posit16
3×associate-/r* times-frac swap-sqr prod-exp associate-*r/ cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative difference-of-squares unswap-sqr
1×pow2 frac-times clear-num sub-neg frac-2neg pow-plus flip3-- diff-log associate-*l/ pow-sqr pow-prod-up div-inv flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 88
Calls
4 calls:
Slowest
18.0ms
(* (tan x) (tan x))
17.0ms
(/ (* (sin x) (tan x)) (cos x))
16.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))
11.0ms
(* (sin x) (tan x))

series273.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(/ (* (sin x) (tan x)) (cos x))
84.0ms
(- 1 (/ (* (sin x) (tan x)) (cos x)))
51.0ms
(* (sin x) (tan x))
48.0ms
(* (tan x) (tan x))

simplify3.4s

Counts
69 → 100
Calls
69 calls:
Slowest
351.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (tan x) (tan x)) (tan x)))
262.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
259.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
228.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
209.0ms
(+ (pow x 2) (+ (* 1/6 (pow x 4)) (* 31/360 (pow x 6))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes192.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.2s1555×body1280valid
1.9s1232×body640valid
794.0ms4281×body80valid
603.0ms319×body160valid
410.0ms613×body320valid