Details

Time bar (total: 38.7s)

sample367.0ms

Algorithm
intervals
Results
143.0ms77×body1280valid
97.0ms52×body640valid
52.0ms188×body80valid
46.0ms27×body320valid
8.0ms11×body160valid

simplify3.6s

Counts
1 → 1
Iterations
IterNodes
46637
31079
2183
152
019

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.5b

localize75.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (tan k) (fma (/ k t) (/ k t) 2))
0.7b
(/ t (* (/ l t) (/ l t)))
2.2b
(* (/ t (* (/ l t) (/ l t))) (sin k))
17.0b
(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
141×add-cbrt-cube add-exp-log
66×cbrt-undiv div-exp
43×prod-exp cbrt-unprod
21×add-sqr-sqrt times-frac
15×*-un-lft-identity add-cube-cbrt
13×associate-*l*
11×associate-/l*
9×associate-/r/
8×pow1
7×associate-*l/
6×associate-*r*
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×unswap-sqr
2×frac-times clear-num associate-/r* frac-2neg pow-prod-down tan-quot associate-*r/ *-commutative fma-udef
1×distribute-rgt-in distribute-lft-in associate-/l/
Counts
4 → 161
Calls
4 calls:
11.0ms
(* (tan k) (fma (/ k t) (/ k t) 2))
12.0ms
(/ t (* (/ l t) (/ l t)))
49.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
56.0ms
(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

series596.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (tan k) (fma (/ k t) (/ k t) 2))
49.0ms
(/ t (* (/ l t) (/ l t)))
113.0ms
(* (/ t (* (/ l t) (/ l t))) (sin k))
322.0ms
(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

simplify1.6s

Counts
173 → 173
Iterations
IterNodes
23709
1856
0303

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2 (* t (sin k)))
0.5b
(* (tan k) (fma (/ k t) (/ k t) 2))
4.6b
(/ (/ 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)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
244×add-cbrt-cube add-exp-log
129×cbrt-undiv div-exp
95×times-frac
65×prod-exp cbrt-unprod
36×add-sqr-sqrt
34×*-un-lft-identity add-cube-cbrt
28×associate-/r/
20×div-inv
11×associate-*l/ associate-/l*
10×associate-/r*
9×frac-times associate-*r/
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r* associate-*l*
2×tan-quot fma-udef associate-/l/
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 240
Calls
4 calls:
16.0ms
(/ 2 (* t (sin k)))
21.0ms
(* (tan k) (fma (/ k t) (/ k t) 2))
54.0ms
(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
44.0ms
(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

series934.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ 2 (* t (sin k)))
106.0ms
(* (tan k) (fma (/ k t) (/ k t) 2))
521.0ms
(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
238.0ms
(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

simplify2.6s

Counts
252 → 252
Iterations
IterNodes
25317
11169
0408

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2 (* t (sin k)))
0.3b
(fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k)))))
2.0b
(* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k))))
4.6b
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k))))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
87×add-cbrt-cube add-exp-log
39×prod-exp cbrt-unprod
36×times-frac
24×cbrt-undiv div-exp
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×pow1
10×associate-/l*
8×pow-prod-down
7×associate-*r/
6×div-inv
5×frac-times associate-*l/
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×associate-*r* associate-*l* *-commutative fma-udef associate-/l/
Counts
4 → 140
Calls
4 calls:
16.0ms
(/ 2 (* t (sin k)))
1.0ms
(fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k)))))
60.0ms
(* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k))))
21.0ms
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ 2 (* t (sin k)))
283.0ms
(fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k)))))
183.0ms
(* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k))))
640.0ms
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (* (* (/ t l) (/ t l)) (* 2 (/ (sin k) (cos k))))))

simplify1.0s

Counts
152 → 152
Iterations
IterNodes
22712
1734
0272

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.2b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2 (* t (sin k)))
0.3b
(fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (/ (* (* (/ t l) (/ t l)) (* 2 (sin k))) (cos k)))
2.0b
(* (* (/ t l) (/ t l)) (* 2 (sin k)))
4.6b
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (/ (* (* (/ t l) (/ t l)) (* 2 (sin k))) (cos k))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
59×add-cbrt-cube add-exp-log
36×times-frac
25×prod-exp cbrt-unprod
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×pow1
15×cbrt-undiv div-exp
10×associate-/l*
8×pow-prod-down
6×div-inv
4×expm1-log1p-u associate-/r* associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×frac-times associate-*r* associate-*l* associate-*r/ *-commutative fma-udef associate-/l/
Counts
4 → 126
Calls
4 calls:
8.0ms
(/ 2 (* t (sin k)))
0.0ms
(fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (/ (* (* (/ t l) (/ t l)) (* 2 (sin k))) (cos k)))
58.0ms
(* (* (/ t l) (/ t l)) (* 2 (sin k)))
32.0ms
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (/ (* (* (/ t l) (/ t l)) (* 2 (sin k))) (cos k))))

series1.1s

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ 2 (* t (sin k)))
286.0ms
(fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (/ (* (* (/ t l) (/ t l)) (* 2 (sin k))) (cos k)))
96.0ms
(* (* (/ t l) (/ t l)) (* 2 (sin k)))
613.0ms
(/ (/ 2 (* t (sin k))) (fma (/ (sin k) (cos k)) (* (/ k l) (/ k l)) (/ (* (* (/ t l) (/ t l)) (* 2 (sin k))) (cos k))))

simplify857.0ms

Counts
138 → 138
Iterations
IterNodes
22339
1646
0247

prune1.8s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.2b

regimes554.0ms

Accuracy

73.3% (1.3b remaining)

Error of 4.8b against oracle of 3.5b and baseline of 8.5b

bsearch402.0ms

Steps
ItersRangePoint
8
2.2212064663307164e-112
1.4363447819687245e-107
1.3938029669432637e-107
8
-1.0636527976393348e-45
-1.815859316551941e-49
-1.2722592561226503e-48

simplify10.0ms

Iterations
IterNodes
255
155
047

end0.0ms

sample15.3s

Algorithm
intervals
Results
6.6s2129×body1280valid
3.5s1668×body640valid
2.9s5948×body80valid
1.4s818×body320valid
477.0ms437×body160valid