Details

Time bar (total: 31.7s)

sample446.0ms

Algorithm
intervals
Results
129.0ms70×body2560valid
111.0ms27×body5120valid
109.0ms132×body1280valid
45.0ms83×body640valid
13.0ms35×body320valid
10.0ms21×body160valid
7.0ms59×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (652.0ms)

IterNodesCost
01925
14425
214325
371023
4377821
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
0.8b
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
18.4b
(/ (pow t 3.0) (* l l))
27.3b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
333×times-frac
291×add-exp-log
149×unpow-prod-down
137×div-exp
135×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
111×prod-exp
70×add-cbrt-cube
60×associate-*l/
57×associate-/r/
40×tan-quot
34×pow-exp
32×div-inv
25×cbrt-unprod
24×cbrt-undiv pow-to-exp
20×frac-times associate-*r/ associate-/l*
19×associate-/r*
13×sqr-pow
9×pow1
4×add-log-exp
3×frac-2neg associate-*r* pow-prod-down clear-num
1×associate-*l* *-commutative associate-/l/
Counts
4 → 350
Calls
4 calls:
33.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
36.0ms
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
5.0ms
(/ (pow t 3.0) (* l l))
51.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
327.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
469.0ms
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
183.0ms
(/ (pow t 3.0) (* l l))
573.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify630.0ms

Counts
362 → 362
Iterations

Useful iterations: done (610.0ms)

IterNodesCost
064710499
115889978
done50019945

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.6b
(* (pow k 2.0) (pow t 1.0))
15.9b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
1597×add-exp-log
1095×prod-exp
882×pow-exp
668×div-exp
492×pow-to-exp
130×rec-exp 1-exp
37×add-sqr-sqrt
32×unpow-prod-down
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
19×times-frac associate-*r*
18×associate-*l*
14×sqr-pow
12×unswap-sqr
8×associate-/r*
6×cbrt-unprod
5×pow1
4×cbrt-undiv unpow2 add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 567
Calls
4 calls:
1.0ms
(pow (sin k) 2)
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms
(* (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (sin k) 2)
92.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
343.0ms
(* (pow k 2.0) (pow t 1.0))
667.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify888.0ms

Counts
579 → 579
Iterations

Useful iterations: 2 (426.0ms)

IterNodesCost
043814412
1112812754
2292212085
done500012085

prune643.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b
(pow (sin k) 2)
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.9b
(* (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)))

rewrite315.0ms

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×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 → 1460
Calls
4 calls:
26.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.0ms
(pow (sin k) 2)
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
59.0ms
(* (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)))

series1.3s

Counts
4 → 12
Calls
4 calls:
348.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
23.0ms
(pow (sin k) 2)
295.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
683.0ms
(* (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)))

simplify1.1s

Counts
1472 → 1472
Iterations

Useful iterations: 2 (619.0ms)

IterNodesCost
059750343
1168633112
2356331574
done500131574

prune599.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.8b
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.9b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
25023×add-exp-log
19197×prod-exp
16899×pow-exp
11140×div-exp
7959×pow-to-exp
2990×rec-exp 1-exp
51×unpow-prod-down
43×times-frac
41×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
12×associate-*r*
9×associate-/r* sqr-pow
8×cbrt-undiv
5×pow1 div-inv
4×associate-/l* add-log-exp
3×unpow2 unswap-sqr
2×frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 5762
Calls
4 calls:
18.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
141.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
37.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
353.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
397.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
89.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
390.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify2.0s

Counts
5774 → 5774
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01477226017
14285201321
done5001190555

prune884.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.0b

regimes351.0ms

Accuracy

37.8% (3.5b remaining)

Error of 16.3b against oracle of 12.8b and baseline of 18.4b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04374
15374
done5374

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.0s2164×body2560valid
3.9s913×body5120valid
3.4s4089×body1280valid
1.3s2490×body640valid
364.0ms1005×body320valid
249.0ms2023×body80valid
111.0ms444×body160valid