Details

Time bar (total: 1.1m)

sample309.0ms

Algorithm
intervals
Results
140.0ms62×body1280valid
62.0ms59×body640valid
44.0ms191×body80valid
28.0ms35×body320valid
4.0ms9×body160valid

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done5000
3903
2161
148
019

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.3b

localize66.0ms

Local error

Found 4 expressions with local error:

2.4b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
5.0b
(/ (pow t 3.0) l)
9.4b
(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
19.4b
(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
614×times-frac
245×add-sqr-sqrt
240×*-un-lft-identity add-cube-cbrt
157×add-exp-log
94×add-cbrt-cube
93×unpow-prod-down
90×associate-/l*
87×div-exp
85×associate-*l*
45×cbrt-undiv
37×prod-exp
31×sqr-pow
23×cbrt-unprod
17×div-inv
13×associate-*r*
7×pow-to-exp associate-/r* pow-exp
6×pow1
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r/
2×tan-quot unswap-sqr
1×frac-times pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 417
Calls
4 calls:
4.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
7.0ms
(/ (pow t 3.0) l)
51.0ms
(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
116.0ms
(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.4s

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
245.0ms
(/ (pow t 3.0) l)
957.0ms
(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
1.1s
(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify1.3s

Counts
429 → 429
Iterations
IterNodes
done5000
12324
0752

prune4.0s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 18.6b

localize127.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (/ l (fma 2 1.0 (pow (/ k t) 2.0))) (/ (* (/ (sqrt 2.0) (pow (cbrt t) 3.0)) (cbrt l)) (tan k)))
4.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
5.8b
(/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
13.7b
(* (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ l (fma 2 1.0 (pow (/ k t) 2.0))) (/ (* (/ (sqrt 2.0) (pow (cbrt t) 3.0)) (cbrt l)) (tan k))))

rewrite560.0ms

Algorithm
rewrite-expression-head
Rules
1246×add-exp-log
960×times-frac
650×div-exp
473×prod-exp
357×add-sqr-sqrt
352×*-un-lft-identity add-cube-cbrt
309×add-cbrt-cube
194×associate-*l*
189×sqrt-prod
164×cbrt-undiv
128×cbrt-unprod
84×pow-exp
64×associate-/l*
54×pow-to-exp div-inv
44×unpow-prod-down sqr-pow
11×pow1
9×associate-*r*
8×associate-/r/
6×frac-times associate-*r/
4×expm1-log1p-u associate-/r* pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative unswap-sqr
1×tan-quot associate-/l/
Counts
4 → 745
Calls
4 calls:
89.0ms
(* (/ l (fma 2 1.0 (pow (/ k t) 2.0))) (/ (* (/ (sqrt 2.0) (pow (cbrt t) 3.0)) (cbrt l)) (tan k)))
12.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
39.0ms
(/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
304.0ms
(* (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ l (fma 2 1.0 (pow (/ k t) 2.0))) (/ (* (/ (sqrt 2.0) (pow (cbrt t) 3.0)) (cbrt l)) (tan k))))

series3.0s

Counts
4 → 12
Calls
4 calls:
740.0ms
(* (/ l (fma 2 1.0 (pow (/ k t) 2.0))) (/ (* (/ (sqrt 2.0) (pow (cbrt t) 3.0)) (cbrt l)) (tan k)))
341.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
637.0ms
(/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
1.3s
(* (/ (/ (sqrt 2.0) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (* (/ l (fma 2 1.0 (pow (/ k t) 2.0))) (/ (* (/ (sqrt 2.0) (pow (cbrt t) 3.0)) (cbrt l)) (tan k))))

simplify1.4s

Counts
757 → 757
Iterations
IterNodes
done5000
13635
01057

prune7.0s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 12.2b

localize127.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
4.0b
(* (/ (/ (sqrt (sqrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))))
5.5b
(* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0))))
8.2b
(/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
10648×add-exp-log
5712×div-exp
4406×prod-exp
1358×add-cbrt-cube
944×times-frac
823×cbrt-undiv
764×pow-exp
705×cbrt-unprod
481×pow-to-exp
335×associate-*l*
322×add-sqr-sqrt
315×sqrt-prod
288×*-un-lft-identity add-cube-cbrt
166×cbrt-prod
64×unpow-prod-down sqr-pow
42×associate-*r*
15×div-inv unswap-sqr
13×pow1
8×associate-*r/
6×frac-times
5×pow-prod-down associate-*l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
2×associate-/r/
1×clear-num frac-2neg associate-/l* associate-/l/
Counts
4 → 1670
Calls
4 calls:
26.0ms
(* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
731.0ms
(* (/ (/ (sqrt (sqrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))))
182.0ms
(* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0))))
50.0ms
(/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))

series4.6s

Counts
4 → 12
Calls
4 calls:
343.0ms
(* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
1.9s
(* (/ (/ (sqrt (sqrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))))
1.2s
(* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0))))
1.2s
(/ (* (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.1s

Counts
1682 → 1682
Iterations
IterNodes
done5000
01710

prune12.4s

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 12.0b

localize145.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (* (/ (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) (sqrt (fma 2 1.0 (pow (/ k t) 2.0)))) (/ l (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))))
8.0b
(/ (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))
10.8b
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
10.8b
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite374.0ms

Algorithm
rewrite-expression-head
Rules
1082×add-exp-log
795×times-frac
568×div-exp
418×prod-exp
297×add-sqr-sqrt
295×*-un-lft-identity add-cube-cbrt
270×add-cbrt-cube
159×sqrt-prod
145×cbrt-undiv
126×unpow-prod-down
115×cbrt-unprod
68×pow-exp
63×cbrt-prod
49×pow-to-exp
47×associate-/l*
30×div-inv
21×sqr-pow
14×associate-*l*
11×pow1
8×associate-/r/
7×tan-quot
6×associate-/r* associate-*r/
5×frac-times
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down associate-*l/
2×rem-sqrt-square sqrt-pow1 pow1/2
1×clear-num frac-2neg associate-*r* *-commutative associate-/l/
Counts
4 → 601
Calls
4 calls:
252.0ms
(* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (* (/ (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) (sqrt (fma 2 1.0 (pow (/ k t) 2.0)))) (/ l (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))))
45.0ms
(/ (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))
1.0ms
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
3.0ms
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))

series2.5s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (/ (sqrt (sqrt 2.0)) (* (cbrt (sin k)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (* (/ (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) (sqrt (fma 2 1.0 (pow (/ k t) 2.0)))) (/ l (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))))
1.1s
(/ (/ (/ (* (sqrt 2.0) (cbrt l)) (pow (cbrt t) 3.0)) (tan k)) (sqrt (fma 2 1.0 (pow (/ k t) 2.0))))
140.0ms
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))
141.0ms
(sqrt (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.4s

Counts
613 → 613
Iterations
IterNodes
done5001
13066
01022

prune5.8s

Pruning

28 alts after pruning (26 fresh and 2 done)

Merged error: 12.0b

regimes1.3s

Accuracy

0% (1.4b remaining)

Error of 12.5b against oracle of 11.1b and baseline of 12.5b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done41
141
036

end0.0ms

sample11.0s

Algorithm
intervals
Results
5.0s2138×body1280valid
2.4s1651×body640valid
1.5s5902×body80valid
790.0ms860×body320valid
658.0ms453×body160valid