Details

Time bar (total: 1.3m)

sample1.1s

Algorithm
intervals
Results
303.0ms33×body5120valid
291.0ms134×body1280valid
263.0ms69×body2560valid
104.0ms89×body640valid
35.0ms10×body160valid
23.0ms28×body320valid
16.0ms61×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01925
14425
214625
384823
done500121

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ (pow t 3.0) (* l l)) (sin k))
0.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.6b
(/ (pow t 3.0) (* l l))
28.3b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite486.0ms

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:
60.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
142.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
21.0ms
(/ (pow t 3.0) (* l l))
220.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series2.5s

Counts
4 → 12
Calls
4 calls:
479.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
596.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
324.0ms
(/ (pow t 3.0) (* l l))
1.1s
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.3s

Counts
366 → 366
Iterations

Useful iterations: done (1.3s)

IterNodesCost
066210242
117649771
done50009289

prune3.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.2b
(* (pow k 2.0) (pow t 1.0))
16.0b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite410.0ms

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:
42.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
35.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
38.0ms
(* (pow k 2.0) (pow t 1.0))
163.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.8s

Counts
4 → 12
Calls
4 calls:
625.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
174.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
691.0ms
(* (pow k 2.0) (pow t 1.0))
1.3s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify974.0ms

Counts
612 → 612
Iterations

Useful iterations: done (941.0ms)

IterNodesCost
048315017
1135513309
done500013047

prune1.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.2b

localize79.0ms

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))))
3.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0b
(* (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)))

rewrite882.0ms

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)
103.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
36.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
298.0ms
(* (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)))

series2.3s

Counts
4 → 12
Calls
4 calls:
39.0ms
(pow (sin k) 2)
694.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
183.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.3s
(* (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)))

simplify1.4s

Counts
1472 → 1472
Iterations

Useful iterations: done (1.3s)

IterNodesCost
059750343
1180834674
done500132849

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.9b

localize96.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.4b
(* (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)))
12.0b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite2.9s

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:
42.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
36.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
368.0ms
(* (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)))
181.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
680.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
173.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
747.0ms
(* (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)))
743.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify4.1s

Counts
4470 → 4470
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01206192833
13934158239
done5000153931

prune1.7s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.5b

regimes1.1s

Accuracy

-11.6% (7.9b remaining)

Error of 19.2b against oracle of 11.3b and baseline of 18.4b

bsearch1.1s

Steps
ItersRangePoint
7
2.623809242582247e-58
6.233201459981176e-56
2.8690391325584677e-58
9
2.1434769218230827e-162
1.6991669529309395e-155
1.6783233808706762e-155

simplify24.0ms

Iterations

Useful iterations: 3 (19.0ms)

IterNodesCost
046129
15778
25978
36176
done6176

end0.0ms

sample39.8s

Algorithm
intervals
Results
12.1s2225×body2560valid
11.9s4071×body1280valid
8.5s985×body5120valid
3.9s2512×body640valid
1.0s1010×body320valid
796.0ms2094×body80valid
246.0ms434×body160valid