Details

Time bar (total: 4.7m)

sample389.0ms

Algorithm
intervals
Results
115.0ms49×body1280valid
89.0ms60×body640valid
84.0ms210×body80valid
69.0ms31×body320valid
8.0ms12×body160valid

simplify248.0ms

Calls
1 calls:
Slowest
248.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.7b

localize51.0ms

Local error

Found 4 expressions with local error:

13.8b
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
3.4b
(* (/ t (* (/ l t) (/ l t))) (sin k))
2.6b
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
2.0b
(/ t (* (/ l t) (/ l t)))

rewrite58.0ms

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
21.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
21.0ms
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
11.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
2.0ms
(/ t (* (/ l t) (/ l t)))

series1.1s

Calls
4 calls:
Slowest
775.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))
262.0ms
(/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))
78.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
21.0ms
(/ t (* (/ l t) (/ l t)))

simplify25.7s

Calls
126 calls:
Slowest
989.0ms
(/ (/ (* (* (/ 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)))
955.0ms
(/ (/ (* (* (/ 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)))
802.0ms
(/ (* (* (/ (/ 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)))
631.0ms
(/ (* (cbrt (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k)))) (cbrt (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))))) 1)
617.0ms
(/ (/ (/ 2 (tan k)) (* (/ t (* (/ l t) (/ l t))) (sin k))) (+ (* (/ k t) (/ k t)) 2))

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

localize16.0ms

Local error

Found 4 expressions with local error:

10.8b
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))
7.0b
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
2.6b
(/ (sin k) (/ l t))
2.4b
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))

rewrite107.0ms

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
30.0ms
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))
23.0ms
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
8.0ms
(/ (sin k) (/ l t))
6.0ms
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))

series568.0ms

Calls
4 calls:
Slowest
289.0ms
(* (/ 2 (tan k)) (/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t))))
141.0ms
(/ (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t)))) (/ (sin k) (/ l t)))
72.0ms
(/ (sin k) (/ l t))
66.0ms
(/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))

simplify3.7m

Calls
1063 calls:
Slowest
1.1s
(* (* (* (/ 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)))))
961.0ms
(+ (log (/ 2 (tan k))) (- (log (/ (/ (/ l t) t) (+ 2 (* (/ k t) (/ k t))))) (- (log (sin k)) (log (/ l t)))))
912.0ms
(/ (* (* (/ (/ (/ 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))))
898.0ms
(* (* (* (/ 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)))))
840.0ms
(/ (/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t))))) (/ (sqrt (sin k)) (/ 1 t)))

prune7.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.2b

localize26.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ 2 (* (/ k t) (/ k t))))
10.6b
(sqrt (+ 2 (* (/ k t) (/ k t))))
8.1b
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
7.1b
(/ (/ 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
(/ (/ l t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
4.0ms
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
1.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

series107.0ms

Calls
4 calls:
Slowest
37.0ms
(/ (/ l t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
27.0ms
(/ (/ 1 t) (sqrt (+ 2 (* (/ k t) (/ k t)))))
21.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
21.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

simplify5.0s

Calls
144 calls:
Slowest
280.0ms
(sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))
266.0ms
(/ (* (* (/ l t) (/ l t)) (/ l t)) (* (* (sqrt (+ 2 (* (/ k t) (/ k t)))) (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (+ 2 (* (/ k t) (/ k t))))))
215.0ms
(/ (* (* (/ 1 t) (/ 1 t)) (/ 1 t)) (* (* (sqrt (+ 2 (* (/ k t) (/ k t)))) (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (+ 2 (* (/ k t) (/ k t))))))
124.0ms
(sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))
121.0ms
(sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))

prune1.5s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.2b

localize15.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ 2 (* (/ k t) (/ k t))))
10.6b
(sqrt (+ 2 (* (/ k t) (/ k t))))
10.6b
(sqrt (+ 2 (* (/ k t) (/ k t))))
8.1b
(/ (/ 1 t) (* (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))))

rewrite11.0ms

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

series89.0ms

Calls
4 calls:
Slowest
24.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
24.0ms
(/ (/ 1 t) (* (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))))
21.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))
20.0ms
(sqrt (+ 2 (* (/ k t) (/ k t))))

simplify2.4s

Calls
53 calls:
Slowest
136.0ms
(* (sqrt (sqrt (- 2 (* (/ k t) (/ k t))))) (sqrt (sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))))
133.0ms
(* (sqrt (sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))) (sqrt (sqrt (- 2 (* (/ k t) (/ k t))))))
124.0ms
(/ (* (* (/ 1 t) (/ 1 t)) (/ 1 t)) (* (* (* (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))) (* (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))))) (* (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))))))
124.0ms
(/ (* (* (/ 1 t) (/ 1 t)) (/ 1 t)) (* (* (* (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))) (* (* (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t)))))) (sqrt (sqrt (+ 2 (* (/ k t) (/ k t))))))))
121.0ms
(* (sqrt (sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))) (sqrt (sqrt (+ (* 2 2) (- (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* 2 (* (/ k t) (/ k t))))))))

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.2b

regimes297.0ms

Accuracy

79% (0.9b remaining)

Error of 7.9b against oracle of 7.0b and baseline of 11.3b

bsearch452.0ms

end0.0ms

sample9.8s

Algorithm
intervals
Results
4.2s2075×body1280valid
2.5s1733×body640valid
1.6s5850×body80valid
741.0ms865×body320valid
506.0ms444×body160valid