Details

Time bar (total: 39.4s)

sample502.0ms

Algorithm
intervals
Results
171.0ms89×body2560valid
144.0ms32×body5120valid
106.0ms131×body1280valid
42.0ms83×body640valid
9.0ms23×body320valid
8.0ms67×body80valid
3.0ms13×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (665.0ms)

IterNodesCost
01925
14425
214325
371023
4381821
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (pow t 3.0) (sin k))
5.7b
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
8.0b
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
31.2b
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
376×add-exp-log
181×prod-exp
144×div-exp
94×add-cbrt-cube
43×pow-exp
38×cbrt-unprod
31×pow-to-exp
30×cbrt-undiv
25×times-frac
23×add-sqr-sqrt
20×associate-*l*
16×add-cube-cbrt *-un-lft-identity
11×pow1
9×associate-*r*
8×associate-/l*
5×div-inv
4×unpow-prod-down pow-prod-down add-log-exp unswap-sqr
3×tan-quot associate-*r/ associate-*l/ associate-/r/ *-commutative
2×sqr-pow
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 190
Calls
4 calls:
6.0ms
(* (pow t 3.0) (sin k))
101.0ms
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
38.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
14.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

series1.7s

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (pow t 3.0) (sin k))
714.0ms
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
526.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
320.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

simplify1.4s

Counts
202 → 202
Iterations

Useful iterations: 2 (470.0ms)

IterNodesCost
02924965
18404526
233103678
done50003678

prune654.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.3b

localize23.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (* (cos k) l) (pow (sin k) 2))
5.7b
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
6.0b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
8.5b
(* (pow k 2.0) (pow t 1.0))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
2134×add-exp-log
1515×prod-exp
826×pow-exp
682×div-exp
406×pow-to-exp
140×rec-exp 1-exp
40×add-cbrt-cube
36×add-sqr-sqrt
29×unpow-prod-down
22×associate-*r*
19×add-cube-cbrt *-un-lft-identity times-frac associate-*l* cbrt-unprod
13×sqr-pow
12×unswap-sqr
9×pow1
8×associate-/r*
6×cbrt-undiv
4×add-log-exp
3×associate-*r/ pow-prod-down *-commutative div-inv unpow2
1×frac-2neg associate-*l/ clear-num associate-/l*
Counts
4 → 598
Calls
4 calls:
6.0ms
(/ (* (cos k) l) (pow (sin k) 2))
128.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
33.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
9.0ms
(* (pow k 2.0) (pow t 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (* (cos k) l) (pow (sin k) 2))
712.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
485.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
339.0ms
(* (pow k 2.0) (pow t 1.0))

simplify1.6s

Counts
610 → 610
Iterations

Useful iterations: 2 (868.0ms)

IterNodesCost
059716175
1176514076
2421713392
done500013392

prune594.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.9b
(/ (* (cos k) l) (pow (sin k) 2))
5.7b
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
6.0b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))

rewrite538.0ms

Algorithm
rewrite-expression-head
Rules
7247×add-exp-log
5835×prod-exp
2962×pow-exp
2088×div-exp
1660×pow-to-exp
465×rec-exp 1-exp
47×add-cbrt-cube
22×add-sqr-sqrt times-frac
21×cbrt-unprod
17×add-cube-cbrt unpow-prod-down *-un-lft-identity
15×associate-*r*
12×associate-*l*
10×pow1
9×cbrt-undiv associate-/r*
5×sqr-pow
4×div-inv associate-/l* add-log-exp
3×associate-*r/ pow-prod-down unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*l/ inv-pow
Counts
4 → 1554
Calls
4 calls:
21.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms
(/ (* (cos k) l) (pow (sin k) 2))
198.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
55.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
350.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
94.0ms
(/ (* (cos k) l) (pow (sin k) 2))
724.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
494.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))

simplify1.2s

Counts
1566 → 1566
Iterations

Useful iterations: done (1.1s)

IterNodesCost
090055558
1285035952
done500035204

prune583.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.9b

localize36.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.9b
(/ (* (cos k) l) (pow (sin k) 2))
5.0b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
5.7b
(* (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
15926×add-exp-log
12183×prod-exp
6198×pow-exp
4798×div-exp
2706×pow-to-exp
710×rec-exp 1-exp
50×add-cbrt-cube
25×cbrt-unprod
22×add-sqr-sqrt times-frac
17×add-cube-cbrt unpow-prod-down *-un-lft-identity
15×associate-*r*
12×associate-*l*
10×pow1
9×associate-/r*
8×cbrt-undiv
5×sqr-pow
4×associate-*r/ div-inv associate-/l* add-log-exp
3×pow-prod-down unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*l/ inv-pow
Counts
4 → 2466
Calls
4 calls:
8.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
5.0ms
(/ (* (cos k) l) (pow (sin k) 2))
31.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
521.0ms
(* (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

series1.6s

Counts
4 → 12
Calls
4 calls:
342.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
86.0ms
(/ (* (cos k) l) (pow (sin k) 2))
487.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
686.0ms
(* (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

simplify1.0s

Counts
2478 → 2478
Iterations

Useful iterations: 0 (317.0ms)

IterNodesCost
01992112944
done5000112944

prune5.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.3b

regimes281.0ms

Accuracy

24.8% (2.8b remaining)

Error of 7.9b against oracle of 5.1b and baseline of 8.9b

bsearch267.0ms

Steps
ItersRangePoint
7
-2572101730117.1323
-122779302734.49355
-1689046141557.5872

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03795
15095
done5095

end0.0ms

sample14.6s

Algorithm
intervals
Results
4.3s991×body5120valid
4.1s2208×body2560valid
3.5s4202×body1280valid
1.3s2414×body640valid
434.0ms2025×body80valid
365.0ms1012×body320valid
115.0ms431×body160valid