Details

Time bar (total: 32.6s)

sample475.0ms

Algorithm
intervals
Results
149.0ms78×body2560valid
136.0ms33×body5120valid
102.0ms131×body1280valid
40.0ms79×body640valid
15.0ms40×body320valid
7.0ms61×body80valid
6.0ms5×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (671.0ms)

IterNodesCost
01925
14425
214525
372123
4390121
done500021

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
1.0b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
17.6b
(/ (pow t 3.0) (* l l))
30.3b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
272×add-exp-log
153×unpow-prod-down
144×add-sqr-sqrt
137×add-cube-cbrt *-un-lft-identity
128×div-exp
103×prod-exp
59×add-cbrt-cube
58×associate-*l/
54×associate-/r/
38×tan-quot
34×pow-exp
32×div-inv
24×pow-to-exp
21×cbrt-unprod
19×cbrt-undiv frac-times associate-*r/
18×associate-/r*
17×associate-/l*
15×sqr-pow
12×associate-*l*
11×pow1
6×associate-*r*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 362
Calls
4 calls:
15.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
37.0ms
(* (* (/ (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))

series1.5s

Counts
4 → 12
Calls
4 calls:
254.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
318.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
179.0ms
(/ (pow t 3.0) (* l l))
767.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify632.0ms

Counts
374 → 374
Iterations

Useful iterations: done (617.0ms)

IterNodesCost
067010352
116489848
done50019820

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.9b

localize23.0ms

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)))

rewrite122.0ms

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:
10.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
9.0ms
(* (pow k 2.0) (pow t 1.0))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
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:
347.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
334.0ms
(* (pow k 2.0) (pow t 1.0))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
653.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Counts
620 → 620
Iterations

Useful iterations: 2 (572.0ms)

IterNodesCost
049115125
1123412973
2329612703
done500012703

prune695.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.1b

localize29.0ms

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)))

rewrite317.0ms

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))
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:
25.0ms
(pow (sin k) 2)
342.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
661.0ms
(* (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 (656.0ms)

IterNodesCost
060550477
1170031964
2360431674
done500131674

prune613.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.5b

localize30.0ms

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)))
113.0ms
(* (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))))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
38.0ms
(* (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:
341.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
656.0ms
(* (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))))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
651.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.5s

Counts
4478 → 4478
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01213193011
13558150255
done5001150187

prune777.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.2b

regimes306.0ms

Accuracy

16.4% (6.0b remaining)

Error of 16.9b against oracle of 11.0b and baseline of 18.1b

bsearch428.0ms

Steps
ItersRangePoint
10
2.703506994090381e+152
1.2380274094212003e+162
1.0106088911309665e+154

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
04782
15680
done5680

end0.0ms

sample14.1s

Algorithm
intervals
Results
4.4s2286×body2560valid
3.9s950×body5120valid
3.3s4108×body1280valid
1.3s2436×body640valid
359.0ms978×body320valid
255.0ms2156×body80valid
116.0ms465×body160valid