Details

Time bar (total: 1.6m)

sample1.1s

Algorithm
intervals
Results
347.0ms80×body2560valid
288.0ms117×body1280valid
212.0ms34×body5120valid
144.0ms100×body640valid
31.0ms34×body320valid
22.0ms70×body80valid
12.0ms16×body160valid

simplify236.0ms

Calls
1 calls:
Slowest
236.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize68.0ms

Local error

Found 4 expressions with local error:

26.3b
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
2.4b
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
1.3b
(/ t (* (/ l t) (/ l t)))
0.4b
(/ 2 (* (/ k t) (/ k t)))

rewrite60.0ms

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
29.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
26.0ms
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
2.0ms
(/ t (* (/ l t) (/ l t)))
2.0ms
(/ 2 (* (/ k t) (/ k t)))

series667.0ms

Calls
4 calls:
Slowest
323.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k))))
241.0ms
(* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))
54.0ms
(/ 2 (* (/ k t) (/ k t)))
49.0ms
(/ t (* (/ l t) (/ l t)))

simplify12.3s

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))) (* (sin k) (tan k))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))) (* (/ t (* (/ l t) (/ l t))) (* (sin k) (tan k)))))
1.5s
(/ (* (* (/ 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)))))
1.5s
(/ (* (* (/ 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)))))
546.0ms
(- (log (/ 2 (* (/ k t) (/ k t)))) (+ (log (/ t (* (/ l t) (/ l t)))) (log (* (sin k) (tan k)))))
525.0ms
(+ (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: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

12.2b
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
3.9b
(* (/ l t) (/ 2 k))
3.9b
(/ (/ k 1) (/ l t))
0.2b
(* (sin k) (tan k))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
33×associate-*l*
29×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
24×div-inv
12×associate-*r*
10×pow1
9×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
4×expm1-log1p-u associate-/r* associate-*r/ associate-/r/ insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×pow-prod-down *-commutative
2×frac-times associate-*l/ tan-quot
1×clear-num frac-2neg associate-/l/
Calls
4 calls:
Slowest
16.0ms
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
7.0ms
(* (/ l t) (/ 2 k))
5.0ms
(* (sin k) (tan k))
4.0ms
(/ (/ k 1) (/ l t))

series449.0ms

Calls
4 calls:
Slowest
302.0ms
(* (/ (* (/ l t) (/ 2 k)) (/ (/ k 1) (/ l t))) (/ t (* (sin k) (tan k))))
67.0ms
(* (sin k) (tan k))
54.0ms
(* (/ l t) (/ 2 k))
26.0ms
(/ (/ k 1) (/ l t))

simplify12.1s

Calls
118 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)))))
834.0ms
(* (* (* (/ (* (/ 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)))))
661.0ms
(+ (- (log (* (/ l t) (/ 2 k))) (log (/ (/ k 1) (/ l t)))) (log (/ t (* (sin k) (tan k)))))
561.0ms
(/ (* (* (/ k 1) (/ k 1)) (/ k 1)) (* (* (/ l t) (/ l t)) (/ l t)))
552.0ms
(* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ 2 k) (/ 2 k)) (/ 2 k)))

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 1.5b

localize15.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (/ (sin k) l) (* t (* k (tan k))))
1.6b
(* t (* k (tan k)))
0.4b
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
0.2b
(* (/ 2 k) l)

rewrite35.0ms

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
13.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
12.0ms
(* (/ (sin k) l) (* t (* k (tan k))))
6.0ms
(* (/ 2 k) l)
3.0ms
(* t (* k (tan k)))

series653.0ms

Calls
4 calls:
Slowest
289.0ms
(* (/ (sin k) l) (* t (* k (tan k))))
227.0ms
(/ (* (/ 2 k) l) (* (/ (sin k) l) (* t (* k (tan k)))))
115.0ms
(* t (* k (tan k)))
21.0ms
(* (/ 2 k) l)

simplify8.1s

Calls
39 calls:
Slowest
2.3s
(/ (* (* (* (/ 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))))))
2.1s
(/ (* (* (* (/ 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))))))
410.0ms
(- (log (* (/ 2 k) l)) (+ (log (/ (sin k) l)) (log (* t (* k (tan k))))))
373.0ms
(- (* 2 (/ (pow l 2) (* t (pow k 4)))) (* 1/3 (/ (pow l 2) (* t (pow k 2)))))
341.0ms
(- (log (* (/ 2 k) l)) (log (* (/ (sin k) l) (* t (* k (tan k))))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (* (/ (sin k) l) t) (* k (tan k)))
0.4b
(/ (* (/ 2 k) l) (* (* (/ (sin k) l) t) (* k (tan k))))
0.2b
(* (/ 2 k) l)
0.2b
(* (/ (sin k) l) t)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube add-exp-log
9×associate-*l* associate-*l/
6×add-sqr-sqrt pow1 *-un-lft-identity associate-*r/ add-cube-cbrt
4×expm1-log1p-u tan-quot insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/ *-commutative div-inv
2×frac-times cbrt-undiv div-exp prod-exp cbrt-unprod
1×clear-num associate-/r* frac-2neg times-frac associate-*r* pow-prod-down associate-/l* associate-/l/
Calls
4 calls:
Slowest
28.0ms
(/ (* (/ 2 k) l) (* (* (/ (sin k) l) t) (* k (tan k))))
14.0ms
(* (* (/ (sin k) l) t) (* k (tan k)))
6.0ms
(* (/ 2 k) l)
5.0ms
(* (/ (sin k) l) t)

series688.0ms

Calls
4 calls:
Slowest
300.0ms
(* (* (/ (sin k) l) t) (* k (tan k)))
269.0ms
(/ (* (/ 2 k) l) (* (* (/ (sin k) l) t) (* k (tan k))))
90.0ms
(* (/ (sin k) l) t)
28.0ms
(* (/ 2 k) l)

simplify8.1s

Calls
39 calls:
Slowest
2.6s
(/ (* (* (* (/ 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)))))
1.9s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (* (/ (sin k) l) t) (* (/ (sin k) l) t)) (* (/ (sin k) l) t)) (* (* (* k (tan k)) (* k (tan k))) (* k (tan k)))))
388.0ms
(- (* 2 (/ (pow l 2) (* t (pow k 4)))) (* 1/3 (/ (pow l 2) (* t (pow k 2)))))
386.0ms
(- (log (* (/ 2 k) l)) (+ (log (* (/ (sin k) l) t)) (log (* k (tan k)))))
359.0ms
(- (log (* (/ 2 k) l)) (log (* (* (/ (sin k) l) t) (* k (tan k)))))

prune957.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes375.0ms

Accuracy

34.9% (2.7b remaining)

Error of 3.0b against oracle of 0.3b and baseline of 4.5b

bsearch1.1s

end0.0ms

sample41.4s

Algorithm
intervals
Results
12.4s4102×body1280valid
11.2s2319×body2560valid
8.8s930×body5120valid
5.1s2535×body640valid
1.7s975×body320valid
1.2s2058×body80valid
473.0ms434×body160valid