Details

Time bar (total: 1.5m)

sample1.2s

Algorithm
intervals
Results
396.0ms137×body1280valid
391.0ms75×body2560valid
194.0ms23×body5120valid
127.0ms70×body640valid
46.0ms38×body320valid
26.0ms70×body80valid
7.0ms8×body160valid

simplify672.0ms

Calls
1 calls:
Slowest
672.0ms
(/ 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: 32.1b

localize40.0ms

Local error

Found 4 expressions with local error:

30.0b
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
4.8b
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
1.0b
(/ t (* (/ l t) (/ l t)))
0.4b
(/ 2 (* (/ k t) (/ k t)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log associate-/r/
11×associate-*r/
9×pow1
7×add-sqr-sqrt frac-times *-un-lft-identity times-frac associate-*l* associate-*l/ add-cube-cbrt associate-/l*
6×prod-exp cbrt-unprod div-inv
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv clear-num associate-/r* frac-2neg div-exp pow-prod-down
1×associate-*r* *-commutative associate-/l/
Calls
4 calls:
Slowest
18.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
14.0ms
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
1.0ms
(/ t (* (/ l t) (/ l t)))
1.0ms
(/ 2 (* (/ k t) (/ k t)))

series638.0ms

Calls
4 calls:
Slowest
308.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
220.0ms
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
62.0ms
(/ t (* (/ l t) (/ l t)))
49.0ms
(/ 2 (* (/ k t) (/ k t)))

simplify11.0s

Calls
61 calls:
Slowest
1.6s
(/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (/ t (* (/ l t) (/ l t))) (/ t (* (/ l t) (/ l t)))) (/ t (* (/ l t) (/ l t)))) (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k)))))
1.3s
(/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))))
1.2s
(/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (/ t (* (/ l t) (/ l t))) (/ t (* (/ l t) (/ l t)))) (/ t (* (/ l t) (/ l t)))) (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k)))))
556.0ms
(- (log (/ 2 (* (/ k t) (/ k t)))) (+ (log (/ t (* (/ l t) (/ l t)))) (log (* (sin k) (tan k)))))
488.0ms
(+ (log (/ t (* (/ l t) (/ l t)))) (log (* (sin k) (tan k))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize19.0ms

Local error

Found 4 expressions with local error:

11.7b
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
5.6b
(* (/ l t) (/ 2 k))
5.4b
(/ (/ k 1) (/ l t))
0.5b
(/ t (* (sin k) (tan k)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
30×associate-*l*
27×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×add-cbrt-cube add-exp-log
25×div-inv
9×associate-*r*
8×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp
5×associate-/r* associate-/r/
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×frac-times clear-num frac-2neg pow-prod-down associate-*l/ tan-quot *-commutative
1×associate-/l/
Calls
4 calls:
Slowest
16.0ms
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
6.0ms
(/ (/ k 1) (/ l t))
4.0ms
(* (/ l t) (/ 2 k))
1.0ms
(/ t (* (sin k) (tan k)))

series593.0ms

Calls
4 calls:
Slowest
296.0ms
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
228.0ms
(/ t (* (sin k) (tan k)))
37.0ms
(* (/ l t) (/ 2 k))
32.0ms
(/ (/ k 1) (/ l t))

simplify11.5s

Calls
111 calls:
Slowest
1.6s
(* (/ (* (* (* (/ l t) (/ 2 k)) (* (/ l t) (/ 2 k))) (* (/ l t) (/ 2 k))) (* (* (/ (/ k 1) (/ l t)) (/ (/ k 1) (/ l t))) (/ (/ k 1) (/ l t)))) (* (* (/ t (* (sin k) (tan k))) (/ t (* (sin k) (tan k)))) (/ t (* (sin k) (tan k)))))
872.0ms
(* (* (* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t)))) (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t)))) (* (* (/ t (* (sin k) (tan k))) (/ t (* (sin k) (tan k)))) (/ t (* (sin k) (tan k)))))
575.0ms
(+ (- (log (* (/ l t) (/ 2 k))) (log (/ (/ k 1) (/ l t)))) (log (/ t (* (sin k) (tan k)))))
541.0ms
(/ (* (* (/ k 1) (/ k 1)) (/ k 1)) (* (* (/ l t) (/ l t)) (/ l t)))
496.0ms
(* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ 2 k) (/ 2 k)) (/ 2 k)))

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

localize35.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (/ (sin k) l) (* t (* k (tan k))))
2.3b
(* t (* k (tan k)))
0.9b
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
0.2b
(* k (tan k))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
13×associate-*r/
11×add-cbrt-cube add-exp-log
6×add-sqr-sqrt pow1 *-un-lft-identity tan-quot add-cube-cbrt
5×associate-*r*
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ associate-/r/ *-commutative
2×frac-times cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×clear-num associate-/r* frac-2neg times-frac pow-prod-down associate-/l* associate-/l/
Calls
4 calls:
Slowest
15.0ms
(* (/ (sin k) l) (* t (* k (tan k))))
12.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
3.0ms
(* t (* k (tan k)))
1.0ms
(* k (tan k))

series647.0ms

Calls
4 calls:
Slowest
275.0ms
(* (/ (sin k) l) (* t (* k (tan k))))
200.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
94.0ms
(* t (* k (tan k)))
77.0ms
(* k (tan k))

simplify7.8s

Calls
40 calls:
Slowest
2.0s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (* t (* k (tan k)))) (* (/ (sin k) l) (* t (* k (tan k))))) (* (/ (sin k) l) (* t (* k (tan k))))))
1.7s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (/ (sin k) l)) (/ (sin k) l)) (* (* (* t (* k (tan k))) (* t (* k (tan k)))) (* t (* k (tan k))))))
623.0ms
(* (/ (sin k) l) (* t (* k (tan k))))
402.0ms
(- (log (* (/ 2 k) l)) (+ (log (/ (sin k) l)) (log (* t (* k (tan k))))))
388.0ms
(- (log (* (/ 2 k) l)) (log (* (/ (sin k) l) (* t (* k (tan k))))))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (/ (sin k) l) (* (* t k) (tan k)))
0.9b
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* (* t k) (tan k))))
0.2b
(* (* t k) (tan k))
0.2b
(* (/ 2 k) l)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
11×pow1
9×associate-*l*
7×add-sqr-sqrt *-un-lft-identity prod-exp associate-*r/ add-cube-cbrt cbrt-unprod
5×tan-quot
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/r/ *-commutative div-inv
2×frac-times
1×clear-num associate-/r* frac-2neg times-frac associate-/l* associate-/l/
Calls
4 calls:
Slowest
30.0ms
(* (/ (sin k) l) (* (* t k) (tan k)))
29.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* (* t k) (tan k))))
8.0ms
(* (* t k) (tan k))
5.0ms
(* (/ 2 k) l)

series726.0ms

Calls
4 calls:
Slowest
298.0ms
(* (/ (sin k) l) (* (* t k) (tan k)))
266.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* (* t k) (tan k))))
133.0ms
(* (* t k) (tan k))
29.0ms
(* (/ 2 k) l)

simplify9.8s

Calls
49 calls:
Slowest
1.7s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (* (* t k) (tan k))) (* (/ (sin k) l) (* (* t k) (tan k)))) (* (/ (sin k) l) (* (* t k) (tan k)))))
1.6s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (/ (sin k) l)) (/ (sin k) l)) (* (* (* (* t k) (* t k)) (* t k)) (* (* (tan k) (tan k)) (tan k)))))
1.4s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (/ (sin k) l)) (/ (sin k) l)) (* (* (* (* t k) (tan k)) (* (* t k) (tan k))) (* (* t k) (tan k)))))
512.0ms
(- (log (* (/ 2 k) l)) (+ (log (/ (sin k) l)) (+ (log (* t k)) (log (tan k)))))
431.0ms
(- (log (* (/ 2 k) l)) (+ (log (/ (sin k) l)) (log (* (* t k) (tan k)))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes258.0ms

Accuracy

-2.4% (4.3b remaining)

Error of 4.4b against oracle of 0.2b and baseline of 4.3b

bsearch285.0ms

end0.0ms

sample40.7s

Algorithm
intervals
Results
12.4s3991×body1280valid
11.0s2220×body2560valid
7.5s932×body5120valid
6.5s2559×body640valid
1.6s1032×body320valid
924.0ms2041×body80valid
406.0ms462×body160valid