Details

Time bar (total: 31.4s)

sample480.0ms

Algorithm
intervals
Results
149.0ms78×body2560valid
138.0ms33×body5120valid
107.0ms131×body1280valid
43.0ms79×body640valid
14.0ms40×body320valid
7.0ms61×body80valid
1.0ms5×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (387.0ms)

IterNodesCost
01925
14425
214525
372123
4391021
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.8b
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
22.8b
(* (/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0))) (* l l))
28.3b
(/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
554×add-exp-log
267×prod-exp
216×div-exp
131×times-frac
95×add-cbrt-cube
81×pow-exp
64×add-sqr-sqrt
63×add-cube-cbrt *-un-lft-identity
54×pow-to-exp
53×unpow-prod-down
42×cbrt-unprod
31×associate-*l*
27×cbrt-undiv
25×associate-/l*
18×associate-*r*
11×sqr-pow
10×pow1
7×div-inv
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×tan-quot pow-unpow associate-*r/ pow-prod-down
2×associate-/r/ *-commutative
1×pow-pow frac-2neg clear-num associate-/r* associate-/l/ unswap-sqr
Counts
4 → 309
Calls
4 calls:
4.0ms
(pow (/ k t) 2.0)
19.0ms
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
69.0ms
(* (/ (/ 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:
65.0ms
(pow (/ k t) 2.0)
231.0ms
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
744.0ms
(* (/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0))) (* l l))
411.0ms
(/ (/ 2.0 (pow t 3.0)) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

simplify473.0ms

Counts
321 → 321
Iterations

Useful iterations: done (462.0ms)

IterNodesCost
04747395
114496730
done50006678

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.3b
(* (pow k 2.0) (pow t 1.0))
8.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.2b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite124.0ms

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)))
11.0ms
(* (pow k 2.0) (pow t 1.0))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
35.0ms
(* (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:
324.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
323.0ms
(* (pow k 2.0) (pow t 1.0))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
634.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.4s

Counts
620 → 620
Iterations

Useful iterations: 2 (523.0ms)

IterNodesCost
049115125
1123412973
2358612707
done500012707

prune639.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.2b
(* (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)))

rewrite307.0ms

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)
22.0ms
(/ 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))
64.0ms
(* (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:
23.0ms
(pow (sin k) 2)
325.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
637.0ms
(* (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 (547.0ms)

IterNodesCost
060550477
1170031964
2386731674
done500131674

prune568.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.1b
(* (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) (pow l 2)) (pow (sin k) 2))))
8.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.4b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
22078×add-exp-log
15966×prod-exp
12575×pow-exp
9172×div-exp
6095×pow-to-exp
1310×rec-exp 1-exp
37×add-cbrt-cube
31×unpow-prod-down
29×times-frac
26×associate-*l*
25×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r*
8×cbrt-undiv
7×sqr-pow
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 → 4466
Calls
4 calls:
8.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
118.0ms
(* (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) (pow l 2)) (pow (sin k) 2))))
7.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
39.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
326.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
612.0ms
(* (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) (pow l 2)) (pow (sin k) 2))))
83.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
618.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.6s

Counts
4478 → 4478
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01213193011
13558150255
done5000150187

prune757.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 15.9b

regimes357.0ms

Accuracy

45.4% (2.6b remaining)

Error of 16.0b against oracle of 13.4b and baseline of 18.1b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
058109
172107
done72107

end0.0ms

sample14.1s

Algorithm
intervals
Results
4.3s2286×body2560valid
3.9s950×body5120valid
3.4s4108×body1280valid
1.3s2436×body640valid
360.0ms978×body320valid
261.0ms2156×body80valid
117.0ms465×body160valid