Details

Time bar (total: 1.1m)

sample882.0ms

Algorithm
intervals
Results
266.0ms131×body1280valid
238.0ms87×body2560valid
167.0ms32×body5120valid
118.0ms92×body640valid
31.0ms39×body320valid
13.0ms69×body80valid
7.0ms17×body160valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
01925
14425
214825
381623
4462521
done500021

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (pow t 3.0) (* l l)) (sin k))
1.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
15.3b
(/ (pow t 3.0) (* l l))
30.9b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite407.0ms

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:
49.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
129.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.0ms
(/ (pow t 3.0) (* l l))
170.0ms
(/ (/ 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:
388.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
464.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
221.0ms
(/ (pow t 3.0) (* l l))
862.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.0s

Counts
374 → 374
Iterations

Useful iterations: done (984.0ms)

IterNodesCost
067010352
115169848
done50009342

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.9b
(* (pow k 2.0) (pow t 1.0))
16.9b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite255.0ms

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:
20.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.0ms
(* (pow k 2.0) (pow t 1.0))
83.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.4s

Counts
4 → 12
Calls
4 calls:
574.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
121.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
444.0ms
(* (pow k 2.0) (pow t 1.0))
1.2s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.9s

Counts
620 → 620
Iterations

Useful iterations: done (1.9s)

IterNodesCost
049115125
1122012973
2298412703
done500012259

prune1.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 12.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.9b
(* (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)))

rewrite678.0ms

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:
4.0ms
(pow (sin k) 2)
59.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
34.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
228.0ms
(* (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)))

series1.7s

Counts
4 → 12
Calls
4 calls:
36.0ms
(pow (sin k) 2)
541.0ms
(/ 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))
953.0ms
(* (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)))

simplify2.1s

Counts
1480 → 1480
Iterations

Useful iterations: done (2.0s)

IterNodesCost
060550477
1152531964
2321231674
done500130411

prune953.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.3b
(* (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))))
4.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.5b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.8s

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:
32.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
220.0ms
(* (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))
162.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series3.0s

Counts
4 → 12
Calls
4 calls:
602.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.1s
(* (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))))
160.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.1s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify3.6s

Counts
4478 → 4478
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01213193011
12777150255
24937145890
done5000137704

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.2b

regimes800.0ms

Accuracy

57.5% (4.1b remaining)

Error of 12.6b against oracle of 8.6b and baseline of 18.1b

bsearch2.3s

Steps
ItersRangePoint
5
2.952614080243469e+151
1.0433798175544735e+152
1.0281204503862052e+152
6
2.2059711987342793e-156
1.222115874959613e-155
1.1340605354997585e-155
10
-2.1451944706886585e-142
-1.4706596976628528e-154
-7.734098822155092e-149
10
-1.411670626970749e+155
-2.269311495064533e+143
-1.0390438859415391e+154

simplify12.0ms

Iterations

Useful iterations: done (12.0ms)

IterNodesCost
075199
195193
done95187

end0.0ms

sample30.3s

Algorithm
intervals
Results
9.5s4047×body1280valid
7.7s2189×body2560valid
7.0s941×body5120valid
3.5s2526×body640valid
761.0ms984×body320valid
486.0ms1979×body80valid
389.0ms458×body160valid