Details

Time bar (total: 1.0m)

sample1.0s

Algorithm
intervals
Results
533.0ms30×body5120valid
210.0ms140×body1280valid
135.0ms63×body2560valid
72.0ms79×body640valid
21.0ms37×body320valid
11.0ms61×body80valid
6.0ms17×body160valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
01925
14425
214625
379823
4446721
done500021

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.9b

localize24.0ms

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))

rewrite348.0ms

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×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 → 344
Calls
4 calls:
11.0ms
(pow (/ k t) 2.0)
139.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.0ms
(/ (pow t 3.0) (* l l))
140.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
95.0ms
(pow (/ k t) 2.0)
470.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
276.0ms
(/ (pow t 3.0) (* l l))
831.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify787.0ms

Counts
356 → 356
Iterations

Useful iterations: done (772.0ms)

IterNodesCost
06519982
114619483
done50009042

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.6b

localize25.0ms

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)))

rewrite229.0ms

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×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
Calls
4 calls:
20.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
19.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
21.0ms
(* (pow k 2.0) (pow t 1.0))
84.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.1s

Counts
4 → 12
Calls
4 calls:
503.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
162.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
543.0ms
(* (pow k 2.0) (pow t 1.0))
850.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.7s

Counts
612 → 612
Iterations

Useful iterations: 2 (709.0ms)

IterNodesCost
048315017
1109613295
2284012595
done500012595

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 15.4b

localize46.0ms

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)))

rewrite845.0ms

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:
8.0ms
(pow (sin k) 2)
102.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
20.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
295.0ms
(* (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:
30.0ms
(pow (sin k) 2)
499.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
132.0ms
(/ (* (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)))

simplify1.9s

Counts
1472 → 1472
Iterations

Useful iterations: 2 (921.0ms)

IterNodesCost
059750343
1126233112
2294031574
done500031574

prune832.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.9b

localize63.0ms

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

rewrite2.1s

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
27×associate-*l*
25×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
12×associate-*r*
9×associate-/r*
8×cbrt-undiv
7×sqr-pow
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 → 4458
Calls
4 calls:
24.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
20.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
325.0ms
(* (pow (/ (* (cbrt 1) (cbrt 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)))
124.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
549.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
164.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
590.0ms
(* (pow (/ (* (cbrt 1) (cbrt 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)))
545.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify3.1s

Counts
4470 → 4470
Iterations

Useful iterations: 2 (1.8s)

IterNodesCost
01206192833
12045154383
24168149588
done5000149588

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

regimes538.0ms

Accuracy

31.8% (4.3b remaining)

Error of 16.9b against oracle of 12.6b and baseline of 18.9b

bsearch1.7s

Steps
ItersRangePoint
11
5.0870872402752674e+144
1.2662851632966894e+177
1.3240566892815342e+154
10
-3.532061719522406e+155
-1.1497817806407875e+145
-1.350083645795688e+154

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
053104
165104
done65104

end0.0ms

sample32.6s

Algorithm
intervals
Results
8.9s2190×body2560valid
8.5s4128×body1280valid
7.5s938×body5120valid
4.8s2482×body640valid
1.2s991×body320valid
630.0ms2066×body80valid
270.0ms424×body160valid