Details

Time bar (total: 1.6m)

sample252.0ms

Algorithm
intervals
Results
53.0ms44×body1280valid
42.0ms45×body640valid
28.0ms134×body80valid
13.0ms21×body320valid
5.0ms12×body160valid

simplify115.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
114.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

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

rewrite74.0ms

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
30.0ms
(* (tan x) (tan x))
21.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
13.0ms
(* (tan x) (tan x))
6.0ms
(- 1 (* (tan x) (tan x)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
72.0ms
(* (tan x) (tan x))
60.0ms
(* (tan x) (tan x))
47.0ms
(- 1 (* (tan x) (tan x)))

simplify9.8s

Counts
153 → 126
Calls
153 calls:
Slowest
675.0ms
(/ (* (* (- 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)))))
598.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
596.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
470.0ms
(sqrt (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
378.0ms
(* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×*-un-lft-identity
22×log-pow add-cube-cbrt
21×exp-prod
19×pow1
15×times-frac
8×add-cbrt-cube tan-quot add-exp-log difference-of-squares
6×swap-sqr associate-*r* associate-*l* add-log-exp
4×insert-posit16
3×log-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×log-div sub-neg flip3-+ flip3-- exp-diff diff-log div-sub rem-log-exp flip-+ div-inv flip--
Counts
4 → 108
Calls
4 calls:
Slowest
27.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
18.0ms
(* (tan x) (tan x))
16.0ms
(* (tan x) (tan x))
4.0ms
(- 1 (* (tan x) (tan x)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
53.0ms
(- 1 (* (tan x) (tan x)))
47.0ms
(* (tan x) (tan x))
46.0ms
(* (tan x) (tan x))

simplify8.8s

Counts
133 → 120
Calls
133 calls:
Slowest
667.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
551.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
395.0ms
(* (* (- 1 (* (tan x) (tan x))) (- 1 (* (tan x) (tan x)))) (- 1 (* (tan x) (tan x))))
309.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
295.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
264×tan-quot
233×pow1
147×associate-*r/
113×frac-times
88×associate-*l/
73×pow-prod-up
47×pow-prod-down
45×pow-sqr frac-sub
37×pow-plus
30×add-cbrt-cube add-exp-log
27×pow2
17×prod-exp cbrt-unprod
14×sub-div
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×add-log-exp
5×swap-sqr associate-*r* associate-*l*
4×insert-posit16
3×*-commutative unswap-sqr
1×sub-neg flip3-- distribute-rgt-out-- diff-log flip--
Counts
4 → 260
Calls
4 calls:
Slowest
162.0ms
(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))
87.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
81.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
20.0ms
(* (tan x) (tan x))

series270.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))
61.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))
56.0ms
(* (tan x) (tan x))
54.0ms
(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify40.4s

Counts
340 → 272
Calls
340 calls:
Slowest
918.0ms
(- (/ (pow (sin x) 4) (pow (cos x) 4)) (/ (pow (sin x) 2) (pow (cos x) 2)))
874.0ms
(- (* (* (sin x) (sin x)) (* (tan x) (tan x))) (* 1 (* (sin x) (sin x))))
847.0ms
(- (/ (pow (sin x) 4) (pow (cos x) 4)) (/ (pow (sin x) 2) (pow (cos x) 2)))
548.0ms
(* (* (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x))))) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))
545.0ms
(* (* (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* (* (tan x) (tan x)) (* (tan x) (tan x)))) (* (* (tan x) (tan x)) (* (tan x) (tan x))))

prune3.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize462.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
14×pow1
13×add-cube-cbrt
10×log-pow
9×exp-prod associate-*r*
8×add-cbrt-cube add-exp-log
7×associate-*l*
6×add-log-exp
5×frac-times flip3-+ flip-+
4×tan-quot insert-posit16
3×log-prod times-frac flip3-- swap-sqr associate-*l/ associate-*r/ flip--
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out difference-of-squares unswap-sqr
1×pow2 +-commutative sum-log pow-plus rem-log-exp pow-sqr pow-prod-up div-inv distribute-lft-out--
Counts
4 → 99
Calls
4 calls:
Slowest
39.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
14.0ms
(log (exp (/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))))
13.0ms
(* (tan x) (tan x))
5.0ms
(+ 1 (tan x))

series287.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(log (exp (/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))))
72.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
36.0ms
(* (tan x) (tan x))
24.0ms
(+ 1 (tan x))

simplify22.4s

Counts
125 → 111
Calls
125 calls:
Slowest
817.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
702.0ms
(log (exp (/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))))
689.0ms
(sqrt (log (exp (/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x)))))))
686.0ms
(/ (* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x)))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
680.0ms
(log (sqrt (exp (/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x)))))))

prune1.2s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.6s1507×body1280valid
1.7s1216×body640valid
793.0ms4325×body80valid
482.0ms632×body320valid
129.0ms320×body160valid