Details

Time bar (total: 1.1m)

sample672.0ms

Algorithm
intervals
Results
217.0ms29×body5120valid
184.0ms134×body1280valid
163.0ms73×body2560valid
54.0ms79×body640valid
16.0ms35×body320valid
10.0ms64×body80valid
3.0ms10×body160valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
01925
14425
214625
379823
4446721
done500021

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.5b

localize46.0ms

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))
16.9b
(/ (pow t 3.0) (* l l))
26.1b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite372.0ms

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×pow-prod-down add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 354
Calls
4 calls:
34.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
103.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
20.0ms
(/ (pow t 3.0) (* l l))
191.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
394.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
435.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
259.0ms
(/ (pow t 3.0) (* l l))
757.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.2s

Counts
366 → 366
Iterations

Useful iterations: done (1.1s)

IterNodesCost
066210242
115049739
done50019233

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0b
(* (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)))

rewrite281.0ms

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:
19.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
29.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
36.0ms
(* (pow k 2.0) (pow t 1.0))
104.0ms
(* (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:
527.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
148.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
522.0ms
(* (pow k 2.0) (pow t 1.0))
959.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.9s

Counts
612 → 612
Iterations

Useful iterations: 2 (758.0ms)

IterNodesCost
048315017
1109613295
2284012595
done500012595

prune962.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.0b
(/ (* (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)))

rewrite640.0ms

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:
7.0ms
(pow (sin k) 2)
101.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
32.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
182.0ms
(* (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)))

series2.1s

Counts
4 → 12
Calls
4 calls:
37.0ms
(pow (sin k) 2)
494.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
117.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.5s
(* (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 (943.0ms)

IterNodesCost
059750343
1126233112
2294031574
done500031574

prune925.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.6b
(* (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)))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.2b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite1.6s

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:
41.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
267.0ms
(* (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)))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
141.0ms
(* (/ (* (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:
564.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
568.0ms
(* (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)))
97.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
595.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify3.4s

Counts
4470 → 4470
Iterations

Useful iterations: 2 (1.7s)

IterNodesCost
01206192833
12046154383
24168149588
done5001149588

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

regimes474.0ms

Accuracy

34.5% (3.7b remaining)

Error of 15.9b against oracle of 12.2b and baseline of 17.8b

bsearch2.0s

Steps
ItersRangePoint
9
4.61796087672408e+142
4.211818690154182e+148
4.1624864010972877e+148
10
-6.354265220965125e+156
-1.7344183351890289e+146
-7.341974747858959e+153

simplify17.0ms

Iterations

Useful iterations: done (17.0ms)

IterNodesCost
060116
172114
done72112

end0.0ms

sample33.1s

Algorithm
intervals
Results
9.6s2235×body2560valid
8.5s4188×body1280valid
8.3s950×body5120valid
3.2s2468×body640valid
1.5s2058×body80valid
1.0s1065×body320valid
322.0ms489×body160valid