Details

Time bar (total: 3.2m)

sample914.0ms

Algorithm
intervals
Results
613.0ms61×body1280valid
126.0ms60×body640valid
84.0ms191×body80valid
46.0ms29×body320valid
11.0ms11×body160valid

simplify317.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
317.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.9b

localize34.0ms

Local error

Found 4 expressions with local error:

12.5b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
11.7b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.0b
(/ t (* (/ l t) (/ l t)))
0.3b
(* (/ l t) (/ l t))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
243×add-cbrt-cube add-exp-log
106×cbrt-undiv div-exp
86×prod-exp cbrt-unprod
77×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
23×associate-*r*
16×pow1 associate-/l*
14×associate-*l*
13×swap-sqr
9×associate-*r/ associate-/r/ div-inv
5×frac-times associate-*l/
4×expm1-log1p-u pow-prod-down tan-quot insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×clear-num associate-/r* frac-2neg *-commutative
1×pow2 pow-plus pow-sqr pow-prod-up associate-/l/
Counts
4 → 250
Calls
4 calls:
Slowest
89.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
53.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
25.0ms
(* (/ l t) (/ l t))
20.0ms
(/ t (* (/ l t) (/ l t)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
905.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
222.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
59.0ms
(/ t (* (/ l t) (/ l t)))
27.0ms
(* (/ l t) (/ l t))

simplify1.0m

Counts
239 → 262
Calls
239 calls:
Slowest
2.2s
(/ (* (* (/ 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 l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
2.0s
(/ (* (* (/ 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))))))
1.9s
(/ (* (* (/ 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))))))
1.8s
(/ (/ (* (* 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))))))
1.8s
(/ (* (* (/ 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))))))

prune3.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.9b

localize35.0ms

Local error

Found 4 expressions with local error:

12.5b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)))
2.4b
(/ t (/ l (sin k)))
2.4b
(/ t (/ l (sin k)))
0.2b
(* t (/ t (/ l (sin k))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
424×times-frac
217×add-sqr-sqrt
208×*-un-lft-identity add-cube-cbrt
203×add-cbrt-cube add-exp-log
119×cbrt-undiv div-exp
45×prod-exp cbrt-unprod
44×associate-*r*
37×div-inv
33×associate-/r*
19×associate-/l*
6×pow1
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* unswap-sqr
1×pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
4 → 397
Calls
4 calls:
Slowest
53.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)))
22.0ms
(* t (/ t (/ l (sin k))))
13.0ms
(/ t (/ l (sin k)))
8.0ms
(/ t (/ l (sin k)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
837.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (cos k)))
104.0ms
(* t (/ t (/ l (sin k))))
97.0ms
(/ t (/ l (sin k)))
86.0ms
(/ t (/ l (sin k)))

simplify1.5m

Counts
525 → 409
Calls
525 calls:
Slowest
2.4s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (* (* (cos k) (cos k)) (cos k))))
2.2s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (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) (/ (* (* t t) t) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))))) (/ (* (* t t) t) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))))) (* (* (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 t) t) (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (/ t (/ l (sin k))) (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (cos k) (cos k)) (cos k))))
1.7s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (cos k) (cos k)) (cos k))))

prune6.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.4b

localize112.0ms

Local error

Found 4 expressions with local error:

16.4b
(cbrt (fma (/ k t) (/ k t) 2))
16.4b
(cbrt (fma (/ k t) (/ k t) 2))
16.4b
(cbrt (fma (/ k t) (/ k t) 2))
4.7b
(* (/ t l) (sin k))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×associate-*l*
10×times-frac
9×cbrt-prod add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*r*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 77
Calls
4 calls:
Slowest
25.0ms
(* (/ t l) (sin k))
2.0ms
(cbrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))

series629.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(cbrt (fma (/ k t) (/ k t) 2))
174.0ms
(cbrt (fma (/ k t) (/ k t) 2))
170.0ms
(cbrt (fma (/ k t) (/ k t) 2))
105.0ms
(* (/ t l) (sin k))

simplify2.4s

Counts
45 → 89
Calls
45 calls:
Slowest
282.0ms
(- (/ (* t k) l) (* 1/6 (/ (* t (pow k 3)) l)))
243.0ms
(* (* (* (/ t l) (/ t l)) (/ t l)) (* (* (sin k) (sin k)) (sin k)))
213.0ms
(exp (* 1/3 (- (* 2 (log (/ -1 t))) (* 2 (log (/ -1 k))))))
184.0ms
(exp (* 1/3 (- (* 2 (log (/ -1 t))) (* 2 (log (/ -1 k))))))
170.0ms
(exp (* 1/3 (- (* 2 (log (/ -1 t))) (* 2 (log (/ -1 k))))))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.4b

localize81.0ms

Local error

Found 4 expressions with local error:

16.4b
(cbrt (fma (/ k t) (/ k t) 2))
16.4b
(cbrt (fma (/ k t) (/ k t) 2))
16.4b
(cbrt (fma (/ k t) (/ k t) 2))
4.7b
(* (/ t l) (sin k))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×associate-*l*
10×times-frac
9×cbrt-prod add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*r*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 77
Calls
4 calls:
Slowest
12.0ms
(* (/ t l) (sin k))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))

series682.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
219.0ms
(cbrt (fma (/ k t) (/ k t) 2))
197.0ms
(cbrt (fma (/ k t) (/ k t) 2))
172.0ms
(cbrt (fma (/ k t) (/ k t) 2))
95.0ms
(* (/ t l) (sin k))

simplify2.4s

Counts
45 → 89
Calls
45 calls:
Slowest
255.0ms
(* (* (* (/ t l) (/ t l)) (/ t l)) (* (* (sin k) (sin k)) (sin k)))
228.0ms
(- (/ (* t k) l) (* 1/6 (/ (* t (pow k 3)) l)))
215.0ms
(exp (* 1/3 (- (* 2 (log (/ 1 t))) (* 2 (log (/ 1 k))))))
201.0ms
(exp (* 1/3 (- (* 2 (log (/ -1 t))) (* 2 (log (/ -1 k))))))
190.0ms
(exp (* 1/3 (- (* 2 (log (/ 1 t))) (* 2 (log (/ 1 k))))))

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.4b

regimes267.0ms

Accuracy

44.8% (0.8b remaining)

Error of 11.4b against oracle of 10.6b and baseline of 12.0b

bsearch843.0ms

end0.0ms

sample15.5s

Algorithm
intervals
Results
6.7s2055×body1280valid
3.9s1691×body640valid
2.8s5895×body80valid
1.4s880×body320valid
416.0ms428×body160valid