Details

Time bar (total: 18.5s)

sample268.0ms

Algorithm
intervals
Results
58.0ms20×body320valid
56.0ms47×body1280valid
36.0ms44×body640valid
25.0ms132×body80valid
4.0ms13×body160valid

simplify94.0ms

Calls
1 calls:
Slowest
93.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

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))))
0.1b
(- 1 (* (tan x) (tan x)))

rewrite36.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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
12.0ms
(* (tan x) (tan x))
9.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
8.0ms
(* (tan x) (tan x))
3.0ms
(- 1 (* (tan x) (tan x)))

series298.0ms

Calls
4 calls:
Slowest
146.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
57.0ms
(- 1 (* (tan x) (tan x)))
53.0ms
(* (tan x) (tan x))
42.0ms
(* (tan x) (tan x))

simplify2.9s

Calls
72 calls:
Slowest
352.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
342.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
323.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
129.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
127.0ms
(/ (* (* (- 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)))))

prune987.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

2.3b
(log (exp (* (tan x) (tan x))))
0.5b
(exp (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube tan-quot add-exp-log
7×add-log-exp
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod log-pow
2×pow2 frac-times exp-prod pow-plus exp-to-pow pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod
1×rem-log-exp rem-exp-log
Calls
4 calls:
Slowest
8.0ms
(* (tan x) (tan x))
8.0ms
(exp (* (tan x) (tan x)))
7.0ms
(log (exp (* (tan x) (tan x))))
5.0ms
(* (tan x) (tan x))

series175.0ms

Calls
4 calls:
Slowest
69.0ms
(exp (* (tan x) (tan x)))
37.0ms
(* (tan x) (tan x))
35.0ms
(log (exp (* (tan x) (tan x))))
34.0ms
(* (tan x) (tan x))

simplify753.0ms

Calls
51 calls:
Slowest
67.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
65.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
63.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))
50.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
50.0ms
(exp (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(exp (- 1 (* (tan x) (tan x))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.2b
(log (exp (- 1 (* (tan x) (tan x)))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube tan-quot add-exp-log
6×exp-prod associate-*r* associate-*l*
5×log-prod add-log-exp
4×expm1-log1p-u exp-sum log-pow insert-posit16 log1p-expm1-u
2×pow2 frac-times sub-neg pow-plus exp-diff pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod
1×log-div rem-log-exp rem-exp-log
Calls
4 calls:
Slowest
10.0ms
(* (tan x) (tan x))
10.0ms
(* (tan x) (tan x))
7.0ms
(log (exp (- 1 (* (tan x) (tan x)))))
6.0ms
(exp (- 1 (* (tan x) (tan x))))

series216.0ms

Calls
4 calls:
Slowest
90.0ms
(exp (- 1 (* (tan x) (tan x))))
47.0ms
(log (exp (- 1 (* (tan x) (tan x)))))
42.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))

simplify1.5s

Calls
58 calls:
Slowest
324.0ms
(- E (+ (* 1/6 (* (pow x 4) E)) (* (pow x 2) E)))
126.0ms
(exp (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
105.0ms
(exp (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
105.0ms
(- 1 (+ (pow x 2) (* 2/3 (pow x 4))))
93.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

2.3b
(log (pow (exp (tan x)) (tan x)))
0.5b
(pow (exp (tan x)) (tan x))
0.3b
(exp (tan x))
0.3b
(* (tan x) (tan x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×pow1
7×add-exp-log
6×log-prod exp-prod unpow-prod-down add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u pow-pow tan-quot insert-posit16 log1p-expm1-u
3×pow-unpow rem-log-exp associate-*r* associate-*l*
2×pow-to-exp pow-exp
1×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ log-pow *-commutative pow-prod-up cbrt-unprod rem-exp-log
Calls
4 calls:
Slowest
5.0ms
(* (tan x) (tan x))
4.0ms
(log (pow (exp (tan x)) (tan x)))
3.0ms
(pow (exp (tan x)) (tan x))
2.0ms
(exp (tan x))

series684.0ms

Calls
4 calls:
Slowest
414.0ms
(log (pow (exp (tan x)) (tan x)))
188.0ms
(pow (exp (tan x)) (tan x))
42.0ms
(exp (tan x))
40.0ms
(* (tan x) (tan x))

simplify808.0ms

Calls
52 calls:
Slowest
68.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
65.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))
58.0ms
(log (pow (* (cbrt (exp (tan x))) (cbrt (exp (tan x)))) (tan x)))
57.0ms
(exp (/ (pow (sin x) 2) (pow (cos x) 2)))
54.0ms
(+ (pow x 2) (+ (* 7/6 (pow x 4)) 1))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes348.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch3.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.2s1507×body1280valid
1.4s1232×body640valid
1.2s4344×body80valid
512.0ms579×body320valid
144.0ms338×body160valid