Details

Time bar (total: 32.2s)

sample322.0ms

Algorithm
intervals
Results
111.0ms49×body640valid
87.0ms53×body1280valid
27.0ms126×body80valid
14.0ms19×body320valid
4.0ms9×body160valid

simplify527.0ms

Calls
1 calls:
Slowest
526.0ms
(/ (- 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

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×pow1
10×add-cbrt-cube add-exp-log
9×times-frac
8×tan-quot
6×associate-*r* associate-*l*
4×insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative pow-prod-up cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ div-sub div-exp flip-+ div-inv
Calls
4 calls:
Slowest
7.0ms
(* (tan x) (tan x))
5.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms
(* (tan x) (tan x))
2.0ms
(- 1 (* (tan x) (tan x)))

series251.0ms

Calls
4 calls:
Slowest
103.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
66.0ms
(* (tan x) (tan x))
43.0ms
(* (tan x) (tan x))
39.0ms
(- 1 (* (tan x) (tan x)))

simplify3.5s

Calls
72 calls:
Slowest
536.0ms
(/ (* (* (- 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)))))
463.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
412.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
379.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
138.0ms
(- 1 (+ (pow x 2) (* 2/3 (pow x 4))))

prune960.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
76×pow1
44×tan-quot
26×pow-prod-up
22×add-cbrt-cube add-exp-log
21×pow-prod-down
20×frac-times
15×pow-plus
14×associate-*l/ associate-*r/
12×pow2
11×prod-exp cbrt-unprod
10×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×*-commutative insert-posit16 add-log-exp
Calls
4 calls:
Slowest
41.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
9.0ms
(* (tan x) (tan x))
8.0ms
(* (tan x) (tan x))
4.0ms
(* (tan x) (tan x))

series127.0ms

Calls
4 calls:
Slowest
34.0ms
(* (tan x) (tan x))
33.0ms
(* (tan x) (tan x))
32.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
28.0ms
(* (tan x) (tan x))

simplify2.0s

Calls
132 calls:
Slowest
150.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
130.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))))
111.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (tan x) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
100.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))
63.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
16×log-pow
15×pow1 exp-prod
10×add-cbrt-cube add-exp-log
8×tan-quot
6×associate-*r* associate-*l*
4×associate-/r/ insert-posit16 add-log-exp
3×log-prod associate-/r* associate-/l*
2×pow2 frac-times flip3-+ pow-plus div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip-+ div-inv associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-- exp-diff div-exp rem-log-exp flip--
Calls
4 calls:
Slowest
11.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
10.0ms
(* (tan x) (tan x))
10.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
10.0ms
(* (tan x) (tan x))

series230.0ms

Calls
4 calls:
Slowest
84.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
75.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
42.0ms
(* (tan x) (tan x))
29.0ms
(* (tan x) (tan x))

simplify5.4s

Calls
92 calls:
Slowest
542.0ms
(/ (* (* (- 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)))))
540.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
474.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
379.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
370.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube add-exp-log
26×associate-*r* associate-*l*
14×pow1
9×cbrt-undiv div-exp
8×prod-exp cbrt-unprod
5×div-inv
4×insert-posit16 add-log-exp
3×associate-/r* associate-/l*
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ associate-*r/ associate-/r/ *-commutative pow-prod-up flip-- associate-/l/
1×clear-num sub-neg frac-2neg flip3-+ div-sub flip-+
Calls
4 calls:
Slowest
9.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
8.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
8.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
3.0ms
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

series205.0ms

Calls
4 calls:
Slowest
82.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
51.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
40.0ms
(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))
31.0ms
(- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

simplify7.9s

Calls
124 calls:
Slowest
420.0ms
(- (* 1 1) (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
401.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
336.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
300.0ms
(- (pow 1 3) (pow (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) 3))
297.0ms
(/ (- 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes288.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.3s1469×body1280valid
1.8s4377×body80valid
1.3s1238×body640valid
473.0ms617×body320valid
127.0ms299×body160valid