Details

Time bar (total: 48.5s)

sample808.0ms

Algorithm
intervals
Results
561.0ms68×body1280valid
104.0ms53×body640valid
78.0ms202×body80valid
29.0ms21×body320valid
10.0ms11×body160valid

simplify3.5s

Counts
1 → 1
Iterations
IterNodes
46637
31079
2183
152
019

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k)))
0.9b
(/ t (* (/ l t) (/ l t)))
3.0b
(* (/ t (* (/ l t) (/ l t))) (sin k))
14.7b
(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
172×add-cbrt-cube add-exp-log
82×cbrt-undiv div-exp
52×prod-exp cbrt-unprod
24×times-frac
19×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
14×associate-/l*
10×associate-*l* associate-/r/
7×associate-*l/
6×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num associate-/r* frac-2neg associate-*r*
2×frac-times associate-*r/ unswap-sqr
1×pow-prod-down tan-quot *-commutative associate-/l/
Counts
4 → 172
Calls
4 calls:
37.0ms
(/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k)))
21.0ms
(/ t (* (/ l t) (/ l t)))
68.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
97.0ms
(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

series686.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k)))
48.0ms
(/ t (* (/ l t) (/ l t)))
126.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
392.0ms
(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

simplify1.3s

Counts
184 → 184
Iterations
IterNodes
23420
1811
0282

prune2.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ l t) (/ l t))
0.3b
(* (tan k) (fma (/ k t) (/ k t) 2))
4.4b
(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
12.9b
(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
251×add-cbrt-cube add-exp-log
132×times-frac
131×cbrt-undiv div-exp
74×add-sqr-sqrt
68×prod-exp cbrt-unprod
60×*-un-lft-identity add-cube-cbrt
28×associate-/r/
23×div-inv
16×associate-*r* associate-*l*
13×pow1 swap-sqr
12×associate-*l/
10×frac-times associate-*r/
9×associate-/r*
8×associate-/l*
5×unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg pow-prod-down tan-quot *-commutative fma-udef associate-/l/
1×pow2 distribute-rgt-in distribute-lft-in pow-plus pow-sqr pow-prod-up
Counts
4 → 286
Calls
4 calls:
18.0ms
(* (/ l t) (/ l t))
18.0ms
(* (tan k) (fma (/ k t) (/ k t) 2))
58.0ms
(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
37.0ms
(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

series926.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (/ l t) (/ l t))
149.0ms
(* (tan k) (fma (/ k t) (/ k t) 2))
526.0ms
(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
214.0ms
(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

simplify2.5s

Counts
298 → 298
Iterations
IterNodes
26649
11448
0472

prune4.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.3b
(* (/ k l) (/ k l))
3.4b
(* (* (/ t l) (/ t l)) (/ (sin k) (cos k)))
4.4b
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* 2 (* (* (/ t l) (/ t l)) (/ (sin k) (cos k))))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
110×add-sqr-sqrt
83×*-un-lft-identity add-cube-cbrt
78×add-cbrt-cube add-exp-log
39×associate-*r*
27×associate-*l* prod-exp cbrt-unprod
26×cbrt-undiv swap-sqr div-exp
23×pow1
14×div-inv
10×unswap-sqr
7×frac-times associate-*l/ associate-/l*
5×pow-prod-down associate-*r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
2×pow2 pow-plus pow-sqr pow-prod-up
1×clear-num frac-2neg associate-/l/
Counts
4 → 247
Calls
4 calls:
17.0ms
(* (/ t l) (/ t l))
14.0ms
(* (/ k l) (/ k l))
54.0ms
(* (* (/ t l) (/ t l)) (/ (sin k) (cos k)))
22.0ms
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* 2 (* (* (/ t l) (/ t l)) (/ (sin k) (cos k))))))

series946.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (/ t l) (/ t l))
51.0ms
(* (/ k l) (/ k l))
166.0ms
(* (* (/ t l) (/ t l)) (/ (sin k) (cos k)))
683.0ms
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* 2 (* (* (/ t l) (/ t l)) (/ (sin k) (cos k))))))

simplify1.5s

Counts
259 → 259
Iterations
IterNodes
24568
11303
0421

prune4.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.8b

localize84.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (* (cbrt (/ (sin k) (cos k))) (/ t l)) (* (cbrt (/ (sin k) (cos k))) (/ t l))) (cbrt (/ (sin k) (cos k))))
0.9b
(* (cbrt (/ (sin k) (cos k))) (/ t l))
0.9b
(* (cbrt (/ (sin k) (cos k))) (/ t l))
4.4b
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* 2 (* (* (* (cbrt (/ (sin k) (cos k))) (/ t l)) (* (cbrt (/ (sin k) (cos k))) (/ t l))) (cbrt (/ (sin k) (cos k)))))))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
89×times-frac
70×add-exp-log
58×*-un-lft-identity add-cube-cbrt
52×cbrt-div
51×frac-times
49×cbrt-prod
44×add-cbrt-cube
42×associate-*r*
39×associate-*l/
36×prod-exp cbrt-unprod
33×associate-*l*
26×pow1
25×associate-*r/
15×pow-prod-down unswap-sqr
13×cbrt-undiv div-exp
10×div-inv
7×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
1×clear-num frac-2neg associate-/l/
Counts
4 → 246
Calls
4 calls:
194.0ms
(* (* (* (cbrt (/ (sin k) (cos k))) (/ t l)) (* (cbrt (/ (sin k) (cos k))) (/ t l))) (cbrt (/ (sin k) (cos k))))
22.0ms
(* (cbrt (/ (sin k) (cos k))) (/ t l))
14.0ms
(* (cbrt (/ (sin k) (cos k))) (/ t l))
14.0ms
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* 2 (* (* (* (cbrt (/ (sin k) (cos k))) (/ t l)) (* (cbrt (/ (sin k) (cos k))) (/ t l))) (cbrt (/ (sin k) (cos k)))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (* (* (cbrt (/ (sin k) (cos k))) (/ t l)) (* (cbrt (/ (sin k) (cos k))) (/ t l))) (cbrt (/ (sin k) (cos k))))
246.0ms
(* (cbrt (/ (sin k) (cos k))) (/ t l))
224.0ms
(* (cbrt (/ (sin k) (cos k))) (/ t l))
686.0ms
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* 2 (* (* (* (cbrt (/ (sin k) (cos k))) (/ t l)) (* (cbrt (/ (sin k) (cos k))) (/ t l))) (cbrt (/ (sin k) (cos k)))))))

simplify1.6s

Counts
258 → 258
Iterations
IterNodes
24183
11151
0425

prune4.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 2.8b

regimes676.0ms

Accuracy

23.7% (2.4b remaining)

Error of 5.8b against oracle of 3.4b and baseline of 6.6b

bsearch489.0ms

Steps
ItersRangePoint
8
2.499933334344595e+48
1.4328256796740934e+53
1.5748242425025286e+51
6
-1.2073965072632987e+85
-2.305467920545603e+84
-5.3958085813923515e+84

simplify15.0ms

Iterations
IterNodes
247
147
041

end0.0ms

sample15.4s

Algorithm
intervals
Results
7.0s2053×body1280valid
4.0s1759×body640valid
2.4s5917×body80valid
1.2s829×body320valid
409.0ms443×body160valid