Details

Time bar (total: 5.2m)

sample448.0ms

Algorithm
intervals
Results
153.0ms48×body640valid
138.0ms56×body1280valid
83.0ms200×body80valid
37.0ms29×body320valid
10.0ms13×body160valid

simplify282.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
282.0ms
(/ 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: 23.5b

localize40.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.6b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.8b
(/ t (* (/ l t) (/ l t)))
0.2b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
233×add-cbrt-cube add-exp-log
103×cbrt-undiv div-exp
82×prod-exp cbrt-unprod
46×times-frac
30×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-/l*
10×associate-*r*
9×pow1 associate-/r/
8×associate-*r/
6×div-inv
5×associate-/r*
4×expm1-log1p-u frac-times associate-*l/ tan-quot insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*l* *-commutative associate-/l/
Counts
4 → 210
Calls
4 calls:
Slowest
94.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
65.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
20.0ms
(/ t (* (/ l t) (/ l t)))
8.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
915.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
215.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
63.0ms
(/ 2 (fma (/ k t) (/ k t) 2))
49.0ms
(/ t (* (/ l t) (/ l t)))

simplify59.5s

Counts
189 → 222
Calls
189 calls:
Slowest
2.2s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
2.0s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
1.9s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
1.7s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))))
1.7s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))

prune3.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize53.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.0b
(/ (sin k) (/ l t))
3.0b
(/ (sin k) (/ l t))
0.2b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
364×times-frac
196×add-cbrt-cube add-exp-log
180×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
117×cbrt-undiv div-exp
42×prod-exp cbrt-unprod
36×associate-/r*
34×div-inv
22×associate-/l*
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/
1×associate-/l/
Counts
4 → 358
Calls
4 calls:
Slowest
54.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
11.0ms
(/ (sin k) (/ l t))
9.0ms
(/ (sin k) (/ l t))
4.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.3s
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
109.0ms
(/ (sin k) (/ l t))
97.0ms
(/ (sin k) (/ l t))
71.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.5m

Counts
488 → 370
Calls
488 calls:
Slowest
2.5s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (cos k) (cos k)) (cos k))))
1.9s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.8s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (* t (/ (sin k) (/ l t)))) (* t (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.7s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.6s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))

prune5.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.3b

localize79.0ms

Local error

Found 4 expressions with local error:

10.3b
(* (/ (/ l (* (sin k) t)) t) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)))
5.1b
(/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))
0.9b
(/ l (* (sin k) t))
0.9b
(/ (* (sin k) t) l)

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
298×add-cbrt-cube add-exp-log
144×cbrt-undiv div-exp
97×prod-exp cbrt-unprod
60×times-frac
34×add-sqr-sqrt
29×*-un-lft-identity add-cube-cbrt
25×associate-*l*
12×associate-*r*
11×associate-/r* div-inv
6×pow1
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×associate-*l/ associate-/r/ unswap-sqr
1×frac-times pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
4 → 230
Calls
4 calls:
Slowest
82.0ms
(* (/ (/ l (* (sin k) t)) t) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)))
24.0ms
(/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))
17.0ms
(/ (* (sin k) t) l)
16.0ms
(/ l (* (sin k) t))

series799.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
369.0ms
(/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))
268.0ms
(* (/ (/ l (* (sin k) t)) t) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)))
87.0ms
(/ l (* (sin k) t))
75.0ms
(/ (* (sin k) t) l)

simplify47.9s

Counts
202 → 242
Calls
202 calls:
Slowest
1.8s
(* (/ (/ (* (* l l) l) (* (* (* (sin k) t) (* (sin k) t)) (* (sin k) t))) (* (* t t) t)) (* (* (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))))
1.7s
(* (* (* (/ (/ l (* (sin k) t)) t) (/ (/ l (* (sin k) t)) t)) (/ (/ l (* (sin k) t)) t)) (/ (* (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k))) (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k))) (* (* (/ (* (sin k) t) l) (/ (* (sin k) t) l)) (/ (* (sin k) t) l))))
1.6s
(* (/ (* (* (/ l (* (sin k) t)) (/ l (* (sin k) t))) (/ l (* (sin k) t))) (* (* t t) t)) (* (* (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))))
1.6s
(* (/ (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* t t) t))) (* (* t t) t)) (* (* (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))))
1.5s
(* (* (* (/ (/ l (* (sin k) t)) t) (/ (/ l (* (sin k) t)) t)) (/ (/ l (* (sin k) t)) t)) (/ (* (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (cos k) (cos k)) (cos k))) (* (* (/ (* (sin k) t) l) (/ (* (sin k) t) l)) (/ (* (sin k) t) l))))

prune3.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.2b

localize86.0ms

Local error

Found 4 expressions with local error:

10.3b
(* (/ (* (/ 1 (sin k)) (/ l t)) t) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)))
5.1b
(/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))
3.0b
(* (/ 1 (sin k)) (/ l t))
0.9b
(/ (* (sin k) t) l)

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
767×add-exp-log
469×add-cbrt-cube
378×div-exp
288×prod-exp
222×cbrt-undiv
168×cbrt-unprod
54×times-frac
48×add-sqr-sqrt
31×*-un-lft-identity
29×add-cube-cbrt
25×associate-*r*
22×rec-exp 1-exp
20×associate-*l*
10×associate-/r*
9×div-inv
8×pow1
7×unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/
2×frac-times clear-num frac-2neg pow-prod-down associate-*r/ associate-/r/ *-commutative associate-/l*
1×associate-/l/
Counts
4 → 326
Calls
4 calls:
Slowest
55.0ms
(* (/ (* (/ 1 (sin k)) (/ l t)) t) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)))
21.0ms
(* (/ 1 (sin k)) (/ l t))
20.0ms
(/ (* (sin k) t) l)
18.0ms
(/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))

series845.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
391.0ms
(/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))
315.0ms
(* (/ (* (/ 1 (sin k)) (/ l t)) t) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)))
73.0ms
(/ (* (sin k) t) l)
67.0ms
(* (/ 1 (sin k)) (/ l t))

simplify1.2m

Counts
302 → 338
Calls
302 calls:
Slowest
1.8s
(* (/ (* (/ (* (* 1 1) 1) (* (* (sin k) (sin k)) (sin k))) (* (* (/ l t) (/ l t)) (/ l t))) (* (* t t) t)) (* (* (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))))
1.7s
(* (/ (* (* (* (/ 1 (sin k)) (/ 1 (sin k))) (/ 1 (sin k))) (* (* (/ l t) (/ l t)) (/ l t))) (* (* t t) t)) (* (* (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))))
1.7s
(* (/ (* (* (* (/ 1 (sin k)) (/ l t)) (* (/ 1 (sin k)) (/ l t))) (* (/ 1 (sin k)) (/ l t))) (* (* t t) t)) (* (* (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l)) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))) (/ (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (/ (* (sin k) t) l))))
1.6s
(* (* (* (/ (* (/ 1 (sin k)) (/ l t)) t) (/ (* (/ 1 (sin k)) (/ l t)) t)) (/ (* (/ 1 (sin k)) (/ l t)) t)) (/ (* (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k)) (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k))) (* (/ 2 (fma (/ k t) (/ k t) 2)) (cos k))) (* (* (/ (* (sin k) t) l) (/ (* (sin k) t) l)) (/ (* (sin k) t) l))))
1.4s
(/ (* (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (cos k) (cos k)) (cos k))) (/ (* (* (* (sin k) (sin k)) (sin k)) (* (* t t) t)) (* (* l l) l)))

prune5.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.2b

regimes321.0ms

Accuracy

63.4% (0.7b remaining)

Error of 11.3b against oracle of 10.6b and baseline of 12.5b

bsearch917.0ms

end0.0ms

sample15.8s

Algorithm
intervals
Results
7.3s2002×body1280valid
3.4s1736×body640valid
2.5s5903×body80valid
1.3s861×body320valid
951.0ms434×body160valid