Details

Time bar (total: 5.1m)

sample413.0ms

Algorithm
intervals
Results
213.0ms77×body1280valid
79.0ms53×body640valid
63.0ms186×body80valid
31.0ms26×body320valid
7.0ms9×body160valid

simplify584.0ms

Calls
1 calls:
Slowest
584.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.3b

localize47.0ms

Local error

Found 4 expressions with local error:

14.9b
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
3.9b
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
3.1b
(* (/ t (* (/ l t) (/ l t))) (sin k))
1.3b
(/ t (* (/ l t) (/ l t)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
55×times-frac
27×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
19×associate-/r/
15×associate-/l*
14×div-inv
8×associate-*l/
7×cbrt-undiv div-exp associate-*l*
6×pow1 tan-quot
5×associate-/r*
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* prod-exp cbrt-unprod
2×frac-times associate-*r/ associate-/l/
1×flip3-+ pow-prod-down *-commutative flip-+
Calls
4 calls:
Slowest
23.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
7.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
7.0ms
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
2.0ms
(/ t (* (/ l t) (/ l t)))

series1.4s

Calls
4 calls:
Slowest
897.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
316.0ms
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
123.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
57.0ms
(/ t (* (/ l t) (/ l t)))

simplify26.5s

Calls
126 calls:
Slowest
1.0s
(/ (/ (* (* (/ 2 (tan k)) (/ 2 (tan k))) (/ 2 (tan k))) (* (* (* (/ t (* (/ l t) (/ l t))) (/ t (* (/ l t) (/ l t)))) (/ t (* (/ l t) (/ l t)))) (* (* (sin k) (sin k)) (sin k)))) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2)))
999.0ms
(/ (/ (* (* (/ 2 (tan k)) (/ 2 (tan k))) (/ 2 (tan k))) (* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (/ t (* (/ l t) (/ l t))) (sin k)))) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2)))
732.0ms
(/ (* (* (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))) (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2)))
669.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
631.0ms
(- (- (log (/ 2 (tan k))) (+ (log (/ t (* (/ l t) (/ l t)))) (log (sin k)))) (log (+ (* (/ k t) (/ k t)) 2)))

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.7b

localize26.0ms

Local error

Found 4 expressions with local error:

12.9b
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))
4.7b
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
3.9b
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))
3.7b
(/ (sin k) (/ l t))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
1500×times-frac
600×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
311×associate-*r*
301×div-inv
113×associate-/r/
38×add-cbrt-cube add-exp-log
36×flip3-+ flip-+
25×associate-/l*
24×associate-/r*
18×cbrt-undiv div-exp
6×pow1
5×associate-*l* prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
2×associate-/l/
1×frac-times pow-prod-down associate-*l/ tan-quot associate-*r/ *-commutative
Calls
4 calls:
Slowest
14.0ms
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
13.0ms
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))
6.0ms
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))
3.0ms
(/ (sin k) (/ l t))

series608.0ms

Calls
4 calls:
Slowest
308.0ms
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))
157.0ms
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
81.0ms
(/ (sin k) (/ l t))
62.0ms
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))

simplify3.8m

Calls
1063 calls:
Slowest
970.0ms
(+ (log (/ 2 (tan k))) (- (log (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (- (log (sin k)) (log (/ l t)))))
947.0ms
(* (* (* (/ 2 (tan k)) (/ 2 (tan k))) (/ 2 (tan k))) (/ (* (* (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))))
875.0ms
(* (* (* (/ 2 (tan k)) (/ 2 (tan k))) (/ 2 (tan k))) (/ (* (* (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t)))))
873.0ms
(/ (/ (/ 1 t) (cbrt (+ 2 (* (/ k t) (/ k t))))) (/ (sin k) (cbrt (/ l t))))
799.0ms
(/ (/ (* (cbrt (/ (/ l t) t)) (cbrt (/ (/ l t) t))) (* (cbrt (+ 2 (* (/ k t) (/ k t)))) (cbrt (+ 2 (* (/ k t) (/ k t)))))) (* (cbrt (/ (sin k) (/ l t))) (cbrt (/ (sin k) (/ l t)))))

prune12.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.4b

localize27.0ms

Local error

Found 4 expressions with local error:

13.1b
(sqrt (+ 2 (* (/ k t) (/ k t))))
13.1b
(sqrt (+ 2 (* (/ k t) (/ k t))))
9.5b
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
6.1b
(/ (/ l t) (sqrt (+ 2 (* (/ k t) (/ k t)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×add-sqr-sqrt
40×*-un-lft-identity add-cube-cbrt
36×sqrt-prod
16×div-inv
12×associate-/r*
8×add-cbrt-cube sqrt-div add-exp-log associate-/l*
4×pow1 flip3-+ associate-/r/ flip-+ insert-posit16 add-log-exp
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg pow1/2 div-exp associate-/l/
Calls
4 calls:
Slowest
8.0ms
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
8.0ms
(/ (/ l t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

series269.0ms

Calls
4 calls:
Slowest
81.0ms
(/ (/ l t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
72.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
63.0ms
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
53.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

simplify8.0s

Calls
144 calls:
Slowest
428.0ms
(/ (* (* (/ l t) (/ l t)) (/ l t)) (* (* (sqrt (+ 2 (* (/ k t) (/ k t)))) (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (+ 2 (* (/ k t) (/ k t))))))
332.0ms
(/ (* (* (/ 1 t) (/ 1 t)) (/ 1 t)) (* (* (sqrt (+ 2 (* (/ k t) (/ k t)))) (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (+ 2 (* (/ k t) (/ k t))))))
223.0ms
(sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3)))
196.0ms
(sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))
192.0ms
(sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))

prune2.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.4b

localize18.0ms

Local error

Found 4 expressions with local error:

13.1b
(sqrt (+ 2 (* (/ k t) (/ k t))))
13.1b
(sqrt (+ 2 (* (/ k t) (/ k t))))
13.1b
(sqrt (+ 2 (* (/ k t) (/ k t))))
9.5b
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity times-frac add-cube-cbrt sqrt-prod
8×sqrt-div div-inv
6×associate-/r* add-cbrt-cube add-exp-log
4×pow1 flip3-+ flip-+ insert-posit16 associate-/l* add-log-exp
3×rem-sqrt-square pow1/2
2×associate-/r/
1×cbrt-undiv clear-num frac-2neg div-exp associate-/l/
Calls
4 calls:
Slowest
14.0ms
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

series210.0ms

Calls
4 calls:
Slowest
60.0ms
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
53.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
49.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
47.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

simplify4.6s

Calls
90 calls:
Slowest
326.0ms
(/ (* (* (/ 1 t) (/ 1 t)) (/ 1 t)) (* (* (sqrt (+ 2 (* (/ k t) (/ k t)))) (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (+ 2 (* (/ k t) (/ k t))))))
198.0ms
(sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3)))
184.0ms
(sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))
177.0ms
(sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3)))
158.0ms
(sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3)))

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.4b

regimes463.0ms

Accuracy

73.5% (1.2b remaining)

Error of 7.9b against oracle of 6.8b and baseline of 11.2b

bsearch815.0ms

end0.0ms

sample13.5s

Algorithm
intervals
Results
5.2s2047×body1280valid
3.2s5852×body80valid
3.0s1757×body640valid
1.5s893×body320valid
364.0ms464×body160valid