Details

Time bar (total: 1.4m)

sample489.0ms

Algorithm
intervals
Results
169.0ms34×body5120valid
114.0ms57×body2560valid
114.0ms137×body1280valid
42.0ms82×body640valid
14.0ms37×body320valid
7.0ms57×body80valid
4.0ms15×body160valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114713
285712
3500211
done500211

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
1.3b
(* (pow t 3.0) (tan k))
19.3b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
31.5b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
392×add-exp-log
265×prod-exp
74×div-exp add-cbrt-cube
61×pow-exp
41×pow-to-exp
40×cbrt-unprod
25×associate-*l*
21×add-sqr-sqrt
17×unpow-prod-down
16×add-cube-cbrt *-un-lft-identity
12×cbrt-undiv
10×times-frac
7×associate-*r/ associate-*r*
6×pow1
4×tan-quot add-log-exp
3×*-commutative unswap-sqr sqr-pow
2×associate-*l/ div-inv
1×frac-2neg pow-prod-down clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 185
Calls
4 calls:
87.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
15.0ms
(* (pow t 3.0) (tan k))
96.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
44.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.2s

Counts
4 → 12
Calls
4 calls:
281.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
247.0ms
(* (pow t 3.0) (tan k))
391.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
254.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify124.0ms

Counts
197 → 197
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
09082174
147741790
250021790
done50021790

prune404.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
9.5b
(* (pow k 2.0) (pow t 1.0))
14.7b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite182.0ms

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:
18.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
17.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms
(* (pow k 2.0) (pow t 1.0))
74.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts
4 → 12
Calls
4 calls:
355.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
352.0ms
(* (pow k 2.0) (pow t 1.0))
666.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify147.0ms

Counts
612 → 612
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
013167194
141627025
250027018
done50027018

prune606.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.7b
(* (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)))

rewrite436.0ms

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:
4.0ms
(pow (sin k) 2)
48.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
24.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
161.0ms
(* (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:
19.0ms
(pow (sin k) 2)
353.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
92.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
669.0ms
(* (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)))

simplify264.0ms

Counts
1472 → 1472
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
0174223543
1457419111
2500217858
done500217858

prune560.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.9b
(pow (cbrt (sin k)) 4)
1.0b
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
14.7b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

rewrite3.7s

Algorithm
rewrite-expression-head
Rules
28004×times-frac
11423×add-sqr-sqrt
10970×add-cube-cbrt *-un-lft-identity
10470×add-exp-log
7729×unpow-prod-down
6478×div-exp
5244×prod-exp
4340×pow-exp
3843×cbrt-prod
3557×associate-*r*
2573×pow-to-exp
1342×sqr-pow
668×unpow2
620×rec-exp 1-exp
326×associate-/l*
303×div-inv
108×unswap-sqr
47×add-cbrt-cube
23×cbrt-undiv associate-/r/
12×associate-/r*
11×associate-*l*
8×cbrt-unprod
6×pow1
4×add-log-exp
3×pow-unpow
2×pow-pow frac-2neg clear-num
1×pow-flip pow1/3 associate-*r/ *-commutative associate-/l/ inv-pow
Counts
4 → 9570
Calls
4 calls:
47.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.0ms
(pow (cbrt (sin k)) 4)
212.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.9s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series1.2s

Counts
4 → 12
Calls
4 calls:
348.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
123.0ms
(pow (cbrt (sin k)) 4)
90.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
652.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify2.4s

Counts
9582 → 9582
Iterations

Useful iterations: 0 (115.0ms)

IterNodesCost
010771265606
done10771265606

prune54.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.1b

regimes572.0ms

Accuracy

-13.3% (5.6b remaining)

Error of 13.2b against oracle of 7.6b and baseline of 12.6b

bsearch306.0ms

Steps
ItersRangePoint
3
3.2295551677899267e+146
4.4479863906389105e+146
3.291577486523162e+146
4
-4.729836199435154e-65
-2.4676323392845753e-65
-3.309694515652526e-65

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06155
16155
done6155

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.1s2259×body2560valid
3.9s925×body5120valid
3.3s4147×body1280valid
1.3s2505×body640valid
360.0ms1008×body320valid
231.0ms2016×body80valid
98.0ms403×body160valid