Details

Time bar (total: 1.6m)

sample980.0ms

Algorithm
intervals
Results
290.0ms125×body1280valid
230.0ms68×body2560valid
199.0ms32×body5120valid
156.0ms86×body640valid
54.0ms28×body320valid
20.0ms63×body80valid
9.0ms15×body160valid

simplify219.0ms

Calls
1 calls:
Slowest
219.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

localize52.0ms

Local error

Found 4 expressions with local error:

32.1b
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
3.3b
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
1.4b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (sin k) (tan k))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
15×associate-/r/
11×pow1 associate-*r/
10×associate-*l*
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×times-frac prod-exp cbrt-unprod associate-/l*
6×frac-times associate-*l/
5×tan-quot div-inv
4×expm1-log1p-u associate-*r* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×clear-num associate-/r* frac-2neg *-commutative
1×associate-/l/
Calls
4 calls:
Slowest
27.0ms
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
23.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
8.0ms
(* (sin k) (tan k))
1.0ms
(/ t (* (/ l t) (/ l t)))

series541.0ms

Calls
4 calls:
Slowest
265.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
193.0ms
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
55.0ms
(* (sin k) (tan k))
28.0ms
(/ t (* (/ l t) (/ l t)))

simplify12.0s

Calls
68 calls:
Slowest
1.5s
(/ (* (* (/ 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)))))
1.3s
(/ (* (* (/ 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)))))
1.3s
(/ (* (* (/ 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)))))
634.0ms
(/ (/ 2 (* (/ k t) k)) (/ t (* (/ l t) (/ l t))))
548.0ms
(+ (log (/ t (* (/ l t) (/ l t)))) (log (* (sin k) (tan k))))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.9b

localize36.0ms

Local error

Found 4 expressions with local error:

16.1b
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
7.1b
(* (/ l t) (/ 2 k))
6.9b
(/ (/ k 1) (/ l t))
0.4b
(/ t (* (sin k) (tan k)))

rewrite52.0ms

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
31.0ms
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
8.0ms
(* (/ l t) (/ 2 k))
7.0ms
(/ (/ k 1) (/ l t))
3.0ms
(/ t (* (sin k) (tan k)))

series491.0ms

Calls
4 calls:
Slowest
281.0ms
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
175.0ms
(/ t (* (sin k) (tan k)))
19.0ms
(/ (/ k 1) (/ l t))
16.0ms
(* (/ l t) (/ 2 k))

simplify12.0s

Calls
111 calls:
Slowest
1.7s
(* (/ (* (* (* (/ 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)))))
903.0ms
(* (* (* (/ (* (/ 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)))))
666.0ms
(+ (- (log (* (/ l t) (/ 2 k))) (log (/ (/ k 1) (/ l t)))) (log (/ t (* (sin k) (tan k)))))
653.0ms
(/ (* (* (/ k 1) (/ k 1)) (/ k 1)) (* (* (/ l t) (/ l t)) (/ l t)))
546.0ms
(* (* (/ l t) (/ 2 k)) t)

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.1b

localize28.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (/ (sin k) l) (* t (* k (tan k))))
1.7b
(* t (* k (tan k)))
1.0b
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
0.2b
(* (/ 2 k) l)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*r/
11×add-cbrt-cube add-exp-log
8×associate-*l*
6×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
5×tan-quot
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/ *-commutative div-inv
2×frac-times cbrt-undiv div-exp associate-*r* prod-exp cbrt-unprod
1×clear-num associate-/r* frac-2neg times-frac pow-prod-down associate-/l* associate-/l/
Calls
4 calls:
Slowest
23.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
22.0ms
(* (/ (sin k) l) (* t (* k (tan k))))
5.0ms
(* (/ 2 k) l)
5.0ms
(* t (* k (tan k)))

series497.0ms

Calls
4 calls:
Slowest
223.0ms
(* (/ (sin k) l) (* t (* k (tan k))))
170.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
89.0ms
(* t (* k (tan k)))
15.0ms
(* (/ 2 k) l)

simplify7.2s

Calls
39 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))))))
413.0ms
(- (log (* (/ 2 k) l)) (+ (log (/ (sin k) l)) (log (* t (* k (tan k))))))
380.0ms
(- (log (* (/ 2 k) l)) (log (* (/ (sin k) l) (* t (* k (tan k))))))
328.0ms
(- (* 2 (/ (pow l 2) (* t (pow k 4)))) (* 1/3 (/ (pow l 2) (* t (pow k 2)))))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (/ (sin k) l) (* (* t k) (tan k)))
1.0b
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* (* t k) (tan k))))
0.2b
(* (* t k) (tan k))
0.2b
(* (/ 2 k) l)

rewrite60.0ms

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
26.0ms
(* (/ (sin k) l) (* (* t k) (tan k)))
26.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* (* t k) (tan k))))
5.0ms
(* (* t k) (tan k))
2.0ms
(* (/ 2 k) l)

series861.0ms

Calls
4 calls:
Slowest
592.0ms
(* (/ (sin k) l) (* (* t k) (tan k)))
168.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* (* t k) (tan k))))
86.0ms
(* (* t k) (tan k))
15.0ms
(* (/ 2 k) l)

simplify10.0s

Calls
49 calls:
Slowest
1.8s
(/ (* (* (* (/ 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)))))
1.8s
(/ (* (* (* (/ 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)))))
509.0ms
(- (log (* (/ 2 k) l)) (+ (log (/ (sin k) l)) (+ (log (* t k)) (log (tan k)))))
388.0ms
(- (log (* (/ 2 k) l)) (+ (log (/ (sin k) l)) (log (* (* t k) (tan k)))))

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

regimes381.0ms

Accuracy

1.3% (4.1b remaining)

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

bsearch1.1s

end0.0ms

sample41.5s

Algorithm
intervals
Results
13.3s4112×body1280valid
10.8s2250×body2560valid
9.0s977×body5120valid
5.1s2447×body640valid
1.7s982×body320valid
771.0ms2003×body80valid
455.0ms439×body160valid