Details

Time bar (total: 1.1m)

sample769.0ms

Algorithm
intervals
Results
217.0ms73×body2560valid
184.0ms29×body5120valid
171.0ms134×body1280valid
113.0ms79×body640valid
36.0ms35×body320valid
13.0ms64×body80valid
4.0ms10×body160valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.8s)

IterNodesCost
01925
14425
214825
381623
4462521
done500021

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.5b

localize21.0ms

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))

rewrite375.0ms

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:
55.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
116.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
20.0ms
(/ (pow t 3.0) (* l l))
143.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
377.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
505.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
204.0ms
(/ (pow t 3.0) (* l l))
849.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify744.0ms

Counts
374 → 374
Iterations

Useful iterations: done (730.0ms)

IterNodesCost
067010352
115169848
done50009342

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.7b

localize46.0ms

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)))

rewrite271.0ms

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:
18.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
20.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.0ms
(* (pow k 2.0) (pow t 1.0))
92.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.3s

Counts
4 → 12
Calls
4 calls:
587.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
120.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
595.0ms
(* (pow k 2.0) (pow t 1.0))
962.0ms
(* (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

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.9b

localize40.0ms

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)))

rewrite568.0ms

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:
8.0ms
(pow (sin k) 2)
65.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
214.0ms
(* (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)))

series1.8s

Counts
4 → 12
Calls
4 calls:
38.0ms
(pow (sin k) 2)
603.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
128.0ms
(/ (* (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)))

simplify2.2s

Counts
1480 → 1480
Iterations

Useful iterations: done (2.1s)

IterNodesCost
060550477
1152531964
2321231674
done500130411

prune1.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.2b

localize42.0ms

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

rewrite1.7s

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:
26.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
221.0ms
(* (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))))
35.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
154.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series3.3s

Counts
4 → 12
Calls
4 calls:
553.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.0s
(* (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))))
164.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.5s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify3.7s

Counts
4478 → 4478
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01213193011
12777150255
24937145890
done5000137704

prune1.2s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.5b

regimes852.0ms

Accuracy

57.5% (4.1b remaining)

Error of 12.6b against oracle of 8.5b and baseline of 18.1b

bsearch2.8s

Steps
ItersRangePoint
9
4.61796087672408e+142
4.211818690154182e+148
4.1624864010972877e+148
9
3.929527623715718e-159
3.7389345848081986e-153
2.708612359830993e-156
4
-2.335379401697989e-114
-1.4891061273467242e-114
-1.5657819025722365e-114
10
-6.354265220965125e+156
-1.7344183351890289e+146
-7.341974747858959e+153

simplify22.0ms

Iterations

Useful iterations: done (21.0ms)

IterNodesCost
068193
185187
done85181

end0.0ms

sample33.7s

Algorithm
intervals
Results
10.3s4188×body1280valid
8.7s2235×body2560valid
7.4s950×body5120valid
3.5s2468×body640valid
1.4s1065×body320valid
1.1s2058×body80valid
287.0ms489×body160valid