Details

Time bar (total: 2.8m)

sample283.0ms

Algorithm
intervals
Results
100.0ms63×body1280valid
69.0ms53×body640valid
48.0ms203×body80valid
22.0ms30×body320valid
8.0ms16×body160valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done5000
3903
2161
148
019

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize49.0ms

Local error

Found 4 expressions with local error:

1.8b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.7b
(/ (pow t 3.0) l)
9.5b
(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
20.6b
(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite285.0ms

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:
10.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
13.0ms
(/ (pow t 3.0) l)
58.0ms
(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
161.0ms
(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.0s

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
228.0ms
(/ (pow t 3.0) l)
671.0ms
(/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k)))
982.0ms
(* (/ (/ 2.0 (/ (pow t 3.0) l)) (* (sin k) (tan k))) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify1.4s

Counts
429 → 429
Iterations
IterNodes
done5000
12324
0752

prune3.9s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 20.9b

localize171.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
5.9b
(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
6.7b
(/ (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))
13.1b
(* (/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (/ (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite821.0ms

Algorithm
rewrite-expression-head
Rules
1504×add-exp-log
884×div-exp
481×prod-exp
307×add-cbrt-cube
220×cbrt-undiv
205×times-frac
120×cbrt-unprod
97×pow-exp
76×add-sqr-sqrt
61×*-un-lft-identity add-cube-cbrt
59×pow-to-exp
46×associate-*l*
20×associate-/l*
19×div-inv
10×unpow-prod-down sqr-pow
7×associate-/r* associate-*r* associate-/r/
6×pow1 unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×associate-*l/ associate-/l/
1×frac-times pow-prod-down associate-*r/ *-commutative
Counts
4 → 444
Calls
4 calls:
21.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
25.0ms
(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
131.0ms
(/ (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))
559.0ms
(* (/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (/ (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0))))

series3.6s

Counts
4 → 12
Calls
4 calls:
387.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
684.0ms
(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k))
923.0ms
(/ (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0)))
1.6s
(* (/ (/ (* (cbrt 2.0) (cbrt 2.0)) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (sin k)) (/ (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (tan k)) l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify1.0s

Counts
456 → 456
Iterations
IterNodes
done5000
12679
0722

prune4.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 12.0b

localize253.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
2.9b
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))))
3.8b
(/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
4.4b
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

rewrite8.4s

Algorithm
rewrite-expression-head
Rules
9539×add-exp-log
9118×times-frac
6251×div-exp
4791×cbrt-prod
4249×add-sqr-sqrt
3604×*-un-lft-identity add-cube-cbrt
2784×prod-exp
2731×associate-*l*
1560×unpow-prod-down
1537×cbrt-undiv
1495×add-cbrt-cube
790×cbrt-unprod
460×pow-to-exp pow-exp
276×sqr-pow
175×associate-*r*
117×unswap-sqr
108×div-inv
90×associate-/r/
54×tan-quot
33×frac-times associate-*r/
31×associate-*l/
16×associate-/r* associate-/l*
11×pow1
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative
1×associate-/l/
Counts
4 → 4556
Calls
4 calls:
7.0ms
(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
1.1s
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))))
30.0ms
(/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
6.4s
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

series3.1s

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
1.1s
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (cbrt (sin k)) (cbrt (sin k)))) (* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))))
881.0ms
(/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
1.0s
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

simplify2.3s

Counts
4568 → 4568
Iterations
IterNodes
done5000
03189

prune1.0m

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 11.4b

localize373.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (* (/ (* (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l))))) (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))))) (* (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)) (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)))) (/ (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l))))) (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)))))
20.6b
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
20.6b
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
20.6b
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
6798×times-frac
4056×cbrt-prod
2964×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
2338×associate-*l*
1740×add-exp-log
1296×unpow-prod-down
930×div-exp
636×prod-exp
552×cbrt-undiv
424×add-cbrt-cube cbrt-unprod
216×sqr-pow
43×div-inv
34×pow-to-exp pow-exp
9×pow1
6×associate-/r/
5×frac-times associate-*r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down associate-*l/
1×associate-*r* *-commutative
Counts
4 → 2737
Calls
4 calls:
1.6s
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (* (/ (* (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l))))) (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))))) (* (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)) (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)))) (/ (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l))))) (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)))))
1.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
1.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
2.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
983.0ms
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (* (/ (* (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l))))) (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))))) (* (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)) (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)))) (/ (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l))))) (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)))))
172.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
163.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
571.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.2s

Counts
2749 → 2749
Iterations
IterNodes
done5001
01805

prune56.1s

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 11.4b

regimes1.5s

Accuracy

0% (1.1b remaining)

Error of 12.4b against oracle of 11.3b and baseline of 12.4b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done38
138
034

end0.0ms

sample10.9s

Algorithm
intervals
Results
4.6s2044×body1280valid
2.6s1826×body640valid
2.2s5812×body80valid
743.0ms819×body320valid
252.0ms439×body160valid