Details

Time bar (total: 4.6m)

sample390.0ms

Algorithm
intervals
Results
124.0ms52×body1280valid
110.0ms214×body80valid
96.0ms60×body640valid
28.0ms25×body320valid
12.0ms18×body160valid

simplify248.0ms

Calls
1 calls:
Slowest
247.0ms
(/ 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: 18.9b

localize37.0ms

Local error

Found 4 expressions with local error:

11.0b
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
5.1b
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
3.1b
(* (/ t (* (/ l t) (/ l t))) (sin k))
0.9b
(/ t (* (/ l t) (/ l t)))

rewrite33.0ms

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
19.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
7.0ms
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
5.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
1.0ms
(/ t (* (/ l t) (/ l t)))

series1.4s

Calls
4 calls:
Slowest
859.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
349.0ms
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
116.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
45.0ms
(/ t (* (/ l t) (/ l t)))

simplify25.0s

Calls
126 calls:
Slowest
1.1s
(/ (* (* (/ (/ 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)))
1.1s
(/ (/ (* (* (/ 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)))
905.0ms
(/ (/ (* (* (/ 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)))
600.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
577.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (sqrt (+ (* (/ k t) (/ k t)) 2)))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.6b

localize27.0ms

Local error

Found 4 expressions with local error:

9.5b
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))
5.3b
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
4.5b
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))
3.1b
(/ (sin k) (/ l t))

rewrite80.0ms

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
13.0ms
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))
12.0ms
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
12.0ms
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))
4.0ms
(/ (sin k) (/ l t))

series651.0ms

Calls
4 calls:
Slowest
346.0ms
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))
135.0ms
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
119.0ms
(/ (sin k) (/ l t))
51.0ms
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))

simplify3.7m

Calls
1063 calls:
Slowest
1.4s
(* (* (* (/ 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)))))
998.0ms
(* (* (* (/ 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)))))
826.0ms
(/ (/ (* (* (/ (/ l t) t) (/ (/ l t) t)) (/ (/ l t) t)) (* (* (+ 2 (* (/ k t) (/ k t))) (+ 2 (* (/ k t) (/ k t)))) (+ 2 (* (/ k t) (/ k t))))) (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t))))
814.0ms
(+ (log (/ 2 (tan k))) (- (log (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (- (log (sin k)) (log (/ l t)))))
772.0ms
(/ (/ (* (* (/ (/ l t) t) (/ (/ l t) t)) (/ (/ l t) t)) (* (* (+ 2 (* (/ k t) (/ k t))) (+ 2 (* (/ k t) (/ k t)))) (+ 2 (* (/ k t) (/ k t))))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t))))

prune7.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.7b

localize19.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (+ 2 (* (/ k t) (/ k t))))
10.3b
(sqrt (+ 2 (* (/ k t) (/ k t))))
7.2b
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
4.8b
(/ (/ l t) (sqrt (+ 2 (* (/ k t) (/ k t)))))

rewrite11.0ms

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
4.0ms
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
4.0ms
(/ (/ l t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

series193.0ms

Calls
4 calls:
Slowest
58.0ms
(/ (/ l t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
50.0ms
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
45.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
40.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

simplify4.9s

Calls
144 calls:
Slowest
267.0ms
(/ (* (* (/ l t) (/ l t)) (/ l t)) (* (* (sqrt (+ 2 (* (/ k t) (/ k t)))) (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (+ 2 (* (/ k t) (/ k t))))))
217.0ms
(/ (* (* (/ 1 t) (/ 1 t)) (/ 1 t)) (* (* (sqrt (+ 2 (* (/ k t) (/ k t)))) (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (+ 2 (* (/ k t) (/ k t))))))
128.0ms
(sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))
126.0ms
(sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))
114.0ms
(sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3)))

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (+ 2 (* (/ k t) (/ k t))))
10.3b
(sqrt (+ 2 (* (/ k t) (/ k t))))
10.3b
(sqrt (+ 2 (* (/ k t) (/ k t))))
6.9b
(sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
19×sqrt-prod
14×add-sqr-sqrt
10×sqrt-div
9×*-un-lft-identity add-cube-cbrt
5×rem-sqrt-square
4×pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Calls
4 calls:
Slowest
1.0ms
(sqrt (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))))

series251.0ms

Calls
4 calls:
Slowest
124.0ms
(sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))
44.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
43.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
39.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

simplify1.6s

Calls
40 calls:
Slowest
163.0ms
(exp (* 1/4 (- (* 2 (log (/ 1 t))) (* 2 (log (/ 1 k))))))
122.0ms
(sqrt (sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3))))
114.0ms
(sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3)))
113.0ms
(sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3)))
112.0ms
(sqrt (+ (pow 2 3) (pow (* (/ k t) (/ k t)) 3)))

prune896.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.7b

regimes372.0ms

Accuracy

72.5% (1.1b remaining)

Error of 8.1b against oracle of 7.0b and baseline of 11.0b

bsearch525.0ms

end0.0ms

sample9.9s

Algorithm
intervals
Results
4.4s2074×body1280valid
2.6s1681×body640valid
1.7s5940×body80valid
749.0ms856×body320valid
266.0ms435×body160valid