Details

Time bar (total: 39.7s)

sample207.0ms

Algorithm
intervals
Results
83.0ms52×body1280valid
21.0ms36×body640valid
16.0ms144×body80valid
6.0ms13×body320valid
3.0ms11×body160valid

simplify51.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
50.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune6.0ms

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

rewrite47.0ms

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
14.0ms
(* (tan x) (tan x))
13.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
13.0ms
(* (tan x) (tan x))
4.0ms
(- 1 (* (tan x) (tan x)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
48.0ms
(* (tan x) (tan x))
40.0ms
(- 1 (* (tan x) (tan x)))
34.0ms
(* (tan x) (tan x))

simplify6.5s

Counts
111 → 126
Calls
111 calls:
Slowest
652.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
639.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
606.0ms
(/ (* (* (- 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)))))
469.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
370.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
13×pow1
10×add-cube-cbrt
9×associate-*r*
8×add-cbrt-cube add-exp-log add-log-exp
7×associate-*l*
5×frac-times
4×flip3-+ flip3-- tan-quot flip-+ insert-posit16 flip-- difference-of-squares
3×sub-neg swap-sqr associate-*l/ associate-*r/
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out-- unswap-sqr
1×pow2 +-commutative sum-log pow-plus diff-log pow-sqr pow-prod-up
Counts
4 → 93
Calls
4 calls:
Slowest
46.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
27.0ms
(* (tan x) (tan x))
9.0ms
(+ 1 (tan x))
8.0ms
(- 1 (tan x))

series225.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
61.0ms
(* (tan x) (tan x))
36.0ms
(- 1 (tan x))
30.0ms
(+ 1 (tan x))

simplify7.5s

Counts
74 → 105
Calls
74 calls:
Slowest
1.3s
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
706.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
479.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
449.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
396.0ms
(* (+ (pow 1 3) (pow (tan x) 3)) (- (* 1 1) (* (tan x) (tan x))))

prune963.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt
15×pow1
14×add-cube-cbrt
12×exp-prod
11×associate-*l*
10×log-pow
9×associate-*r*
8×add-cbrt-cube add-exp-log
7×add-log-exp
4×log-prod tan-quot insert-posit16
3×swap-sqr associate-*r/ distribute-lft-out
2×distribute-rgt-in sub-neg distribute-lft-in exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
1×pow2 frac-times sum-log pow-plus flip3-- rem-log-exp associate-*l/ pow-sqr pow-prod-up flip-- distribute-lft-out--
Counts
4 → 95
Calls
4 calls:
Slowest
57.0ms
(* (log (exp (+ 1 (tan x)))) (- 1 (tan x)))
14.0ms
(* (tan x) (tan x))
11.0ms
(log (exp (+ 1 (tan x))))
10.0ms
(exp (+ 1 (tan x)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(* (log (exp (+ 1 (tan x)))) (- 1 (tan x)))
47.0ms
(exp (+ 1 (tan x)))
47.0ms
(* (tan x) (tan x))
18.0ms
(log (exp (+ 1 (tan x))))

simplify4.0s

Counts
75 → 107
Calls
75 calls:
Slowest
550.0ms
(* (* (* (log (exp (+ 1 (tan x)))) (log (exp (+ 1 (tan x))))) (log (exp (+ 1 (tan x))))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
471.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
446.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
398.0ms
(+ x (+ (* 1/3 (pow x 3)) 1))
292.0ms
(* (log (exp (+ 1 (tan x)))) (- 1 (tan x)))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×*-un-lft-identity
21×add-cube-cbrt
18×times-frac
13×pow1
10×add-cbrt-cube add-exp-log difference-of-squares
6×associate-*r* associate-*l* associate-/l* add-log-exp
5×tan-quot distribute-lft-out--
4×insert-posit16
3×associate-/r* swap-sqr
2×flip3-- pow-prod-down associate-*l/ prod-exp associate-/r/ *-commutative cbrt-unprod flip-- unswap-sqr associate-/l/
1×pow2 frac-times cbrt-undiv clear-num sub-neg frac-2neg flip3-+ pow-plus diff-log div-sub div-exp associate-*r/ pow-sqr pow-prod-up flip-+ div-inv
Counts
4 → 110
Calls
4 calls:
Slowest
28.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
27.0ms
(* (tan x) (tan x))
16.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))
11.0ms
(* (tan x) (sin x))

series350.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
87.0ms
(- 1 (/ (* (tan x) (sin x)) (cos x)))
56.0ms
(* (tan x) (tan x))
43.0ms
(* (tan x) (sin x))

simplify9.3s

Counts
104 → 122
Calls
104 calls:
Slowest
634.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
550.0ms
(- (pow 1 3) (pow (/ (* (tan x) (sin x)) (cos x)) 3))
547.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
438.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
351.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes394.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.1s1484×body1280valid
1.4s4349×body80valid
1.2s1262×body640valid
530.0ms340×body160valid
467.0ms565×body320valid