Details

Time bar (total: 30.9s)

sample422.0ms

Algorithm
intervals
Results
112.0ms57×body2560valid
112.0ms142×body1280valid
110.0ms30×body5120valid
45.0ms80×body640valid
12.0ms34×body320valid
7.0ms63×body80valid
4.0ms16×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (404.0ms)

IterNodesCost
01925
14425
214525
372123
4391021
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin k) (tan k))
0.4b
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
18.7b
(* (/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0))) (* l l))
32.5b
(/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
553×add-exp-log
268×prod-exp
215×div-exp
122×times-frac
97×add-cbrt-cube
79×pow-exp
60×add-sqr-sqrt
57×add-cube-cbrt *-un-lft-identity
53×pow-to-exp
43×cbrt-unprod
40×unpow-prod-down
34×associate-*l*
27×cbrt-undiv
25×associate-/l*
21×associate-*r*
11×pow1
10×sqr-pow
6×div-inv
4×tan-quot expm1-log1p-u associate-*r/ pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
3×*-commutative
2×associate-/r/ unswap-sqr
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 300
Calls
4 calls:
4.0ms
(* (sin k) (tan k))
18.0ms
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
67.0ms
(* (/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0))) (* l l))
20.0ms
(/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sin k) (tan k))
237.0ms
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
797.0ms
(* (/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0))) (* l l))
399.0ms
(/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

simplify470.0ms

Counts
312 → 312
Iterations

Useful iterations: done (456.0ms)

IterNodesCost
04577244
114086594
done50016505

prune794.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.5b
(* (pow k 2.0) (pow t 1.0))
13.9b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
1645×add-exp-log
1122×prod-exp
899×pow-exp
688×div-exp
509×pow-to-exp
140×rec-exp 1-exp
37×add-sqr-sqrt
29×unpow-prod-down
25×add-cbrt-cube
22×times-frac
20×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×associate-*l*
13×sqr-pow
12×unswap-sqr
9×associate-/r*
7×cbrt-unprod
6×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 608
Calls
4 calls:
8.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.0ms
(* (pow k 2.0) (pow t 1.0))
34.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
339.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
341.0ms
(* (pow k 2.0) (pow t 1.0))
659.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.5s

Counts
620 → 620
Iterations

Useful iterations: 2 (722.0ms)

IterNodesCost
049115125
1123412973
2358612703
done500112703

prune651.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.9b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite321.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1468
Calls
4 calls:
1.0ms
(pow (sin k) 2)
21.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
65.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
24.0ms
(pow (sin k) 2)
339.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
641.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.2s

Counts
1480 → 1480
Iterations

Useful iterations: 2 (562.0ms)

IterNodesCost
060550477
1170031964
2386731674
done500131674

prune608.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.7b
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
9.6b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite744.0ms

Algorithm
rewrite-expression-head
Rules
13973×add-exp-log
10155×prod-exp
8251×pow-exp
5914×div-exp
4231×pow-to-exp
920×rec-exp 1-exp
81×unpow-prod-down
64×times-frac
61×associate-*l*
49×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
21×sqrt-prod
14×cbrt-unprod
13×associate-*r*
12×sqr-pow
9×associate-/r*
8×cbrt-undiv
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 3211
Calls
4 calls:
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
122.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
35.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
336.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
652.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
650.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.4s

Counts
3223 → 3223
Iterations

Useful iterations: done (948.0ms)

IterNodesCost
01021126601
12930106350
done5001106274

prune922.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

regimes326.0ms

Accuracy

41.4% (2.4b remaining)

Error of 16.7b against oracle of 14.3b and baseline of 18.4b

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04065
15165
done5165

end0.0ms

sample14.0s

Algorithm
intervals
Results
4.1s2242×body2560valid
4.0s940×body5120valid
3.4s4083×body1280valid
1.4s2589×body640valid
358.0ms990×body320valid
221.0ms1930×body80valid
103.0ms393×body160valid