Details

Time bar (total: 1.1m)

sample934.0ms

Algorithm
intervals
Results
270.0ms140×body1280valid
227.0ms63×body2560valid
205.0ms30×body5120valid
143.0ms79×body640valid
29.0ms37×body320valid
14.0ms61×body80valid
8.0ms17×body160valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
01925
14425
214825
381623
4462521
done500021

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ k t) 2.0)
1.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.4b
(/ (pow t 3.0) (* l l))
31.2b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
339×times-frac
254×add-exp-log
162×unpow-prod-down
141×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
123×div-exp
93×prod-exp
57×associate-*l/
54×associate-/r/
50×add-cbrt-cube
38×tan-quot
34×pow-exp
32×div-inv
23×pow-to-exp
19×frac-times associate-*r/
18×associate-/r*
17×cbrt-undiv cbrt-unprod associate-/l*
14×sqr-pow
10×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* pow-prod-down
2×frac-2neg clear-num
1×pow-pow associate-*l* *-commutative associate-/l/
Counts
4 → 352
Calls
4 calls:
7.0ms
(pow (/ k t) 2.0)
115.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
24.0ms
(/ (pow t 3.0) (* l l))
196.0ms
(/ (/ 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:
102.0ms
(pow (/ k t) 2.0)
515.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
237.0ms
(/ (pow t 3.0) (* l l))
731.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.3s

Counts
364 → 364
Iterations

Useful iterations: done (1.3s)

IterNodesCost
065910082
114739582
done50019141

prune2.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.6b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.5b
(* (pow k 2.0) (pow t 1.0))
17.7b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite354.0ms

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:
23.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
21.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
30.0ms
(* (pow k 2.0) (pow t 1.0))
173.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts
4 → 12
Calls
4 calls:
557.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
126.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
493.0ms
(* (pow k 2.0) (pow t 1.0))
1.0s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.0s

Counts
620 → 620
Iterations

Useful iterations: done (2.0s)

IterNodesCost
049115125
1122012973
2298412703
done500012259

prune1.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 14.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
1.0b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.7b
(* (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)))

rewrite798.0ms

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:
7.0ms
(pow (sin k) 2)
72.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
24.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
271.0ms
(* (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)))

series1.7s

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (sin k) 2)
516.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
145.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.0s
(* (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)))

simplify2.1s

Counts
1480 → 1480
Iterations

Useful iterations: done (2.0s)

IterNodesCost
060550477
1152531964
2321231674
done500130411

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.8b

localize47.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.3b
(* (pow (/ 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))))
12.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite3.0s

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
40×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r* sqr-pow
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 → 5770
Calls
4 calls:
35.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
26.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
392.0ms
(* (pow (/ 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))))
123.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.7s

Counts
4 → 12
Calls
4 calls:
560.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
110.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
949.0ms
(* (pow (/ 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))))
1.1s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify3.4s

Counts
5782 → 5782
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01484226187
13385190742
done5000190248

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.7b

regimes867.0ms

Accuracy

40.2% (5.4b remaining)

Error of 14.9b against oracle of 9.6b and baseline of 18.5b

bsearch2.8s

Steps
ItersRangePoint
7
1.1813803138111518e+133
5.341589198600723e+134
1.9828345357880333e+134
7
7.467145750396128e-130
1.6869664113331816e-127
8.12579963110894e-130
7
-3.0887872207957604e-86
-1.8160848739954498e-88
-1.926172283746209e-88
10
-3.532061719522406e+155
-1.1497817806407875e+145
-1.350083645795688e+154

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
067209
185209
done85209

end0.0ms

sample30.2s

Algorithm
intervals
Results
8.7s2190×body2560valid
7.8s4128×body1280valid
7.4s938×body5120valid
3.0s2482×body640valid
1.4s991×body320valid
944.0ms2066×body80valid
182.0ms424×body160valid