Details

Time bar (total: 1.1m)

sample268.0ms

Algorithm
intervals
Results
90.0ms65×body1280valid
74.0ms192×body80valid
57.0ms58×body640valid
16.0ms27×body320valid
3.0ms8×body160valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01925
14825
216025
391925
done500024

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.5b

localize31.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.7b
(/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (fma 2 1.0 (pow (/ k t) 2.0)))
14.6b
(/ (pow t 3.0) (* l l))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
269×times-frac
129×add-exp-log
125×add-sqr-sqrt
118×add-cube-cbrt *-un-lft-identity
68×div-exp
65×add-cbrt-cube
43×associate-/l*
33×prod-exp
32×cbrt-undiv
24×div-inv
17×associate-*l/ associate-/r/
13×cbrt-unprod
11×associate-*l*
10×unpow-prod-down
8×pow-to-exp pow-exp
7×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×frac-2neg associate-*r* clear-num
2×associate-/l/
1×tan-quot pow-prod-down *-commutative
Counts
4 → 282
Calls
4 calls:
81.0ms
(/ (/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
65.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
47.0ms
(/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (fma 2 1.0 (pow (/ k t) 2.0)))
24.0ms
(/ (pow t 3.0) (* l l))

series2.3s

Counts
4 → 12
Calls
4 calls:
944.0ms
(/ (/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
431.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
715.0ms
(/ (/ 2.0 (* (/ (pow t 3.0) (* l l)) (sin k))) (fma 2 1.0 (pow (/ k t) 2.0)))
248.0ms
(/ (pow t 3.0) (* l l))

simplify986.0ms

Counts
294 → 294
Iterations

Useful iterations: done (965.0ms)

IterNodesCost
05549148
114988883
done50008246

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.7b

localize33.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (/ (/ 2.0 (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
3.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.8b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.7b
(/ (/ 2.0 (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite712.0ms

Algorithm
rewrite-expression-head
Rules
361×add-exp-log
349×times-frac
211×div-exp
170×add-sqr-sqrt
157×add-cube-cbrt *-un-lft-identity
105×prod-exp
97×add-cbrt-cube
51×cbrt-undiv
49×associate-*l/ associate-/r/ associate-/l*
34×associate-*l*
33×pow-exp
24×unpow-prod-down div-inv
22×pow-to-exp cbrt-unprod
16×frac-times associate-*r/
10×cbrt-prod
9×associate-/r*
8×sqr-pow
6×pow1
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* clear-num
2×associate-/l/
1×tan-quot pow-prod-down *-commutative
Counts
4 → 381
Calls
4 calls:
507.0ms
(/ (/ (/ 2.0 (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
48.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
93.0ms
(/ (/ 2.0 (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.4s

Counts
4 → 12
Calls
4 calls:
976.0ms
(/ (/ (/ 2.0 (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
397.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
256.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
790.0ms
(/ (/ 2.0 (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.1s

Counts
393 → 393
Iterations

Useful iterations: done (1.1s)

IterNodesCost
075715209
1207614749
done500013548

prune3.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
1.9b
(/ (/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
3.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.7b
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite487.0ms

Algorithm
rewrite-expression-head
Rules
910×add-exp-log
505×div-exp
358×prod-exp
334×times-frac
163×add-sqr-sqrt
150×add-cube-cbrt *-un-lft-identity
140×add-cbrt-cube
98×pow-to-exp pow-exp
67×cbrt-undiv
49×associate-*l/ associate-/r/
48×associate-*r/
44×cbrt-unprod associate-/l*
34×associate-*l*
26×unpow-prod-down
23×div-inv
16×frac-times
13×cbrt-prod
7×pow1
6×associate-/r*
5×unswap-sqr sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r*
2×pow-pow frac-2neg clear-num associate-/l/
1×tan-quot pow1/3 pow-prod-down *-commutative
Counts
4 → 450
Calls
4 calls:
8.0ms
(pow (cbrt t) 3.0)
186.0ms
(/ (/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
35.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
177.0ms
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.5s

Counts
4 → 12
Calls
4 calls:
485.0ms
(pow (cbrt t) 3.0)
1.0s
(/ (/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0))) (tan k))
284.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
708.0ms
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.3s

Counts
462 → 462
Iterations

Useful iterations: done (1.3s)

IterNodesCost
078819351
1236318720
done500015646

prune3.6s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 12.5b

localize37.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (/ (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))))) (tan k))
3.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.1b
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))))
10.4b
(/ (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k)))))

rewrite859.0ms

Algorithm
rewrite-expression-head
Rules
7452×times-frac
2239×add-sqr-sqrt
2226×add-cube-cbrt *-un-lft-identity
1383×add-exp-log
1089×sqrt-prod
1012×div-exp
437×associate-/l*
427×div-inv
426×associate-/r/
288×prod-exp
265×add-cbrt-cube
191×associate-*r/
174×cbrt-undiv
173×associate-*l/
128×pow-to-exp pow-exp
52×associate-/r*
40×cbrt-unprod
34×associate-*l*
20×unpow-prod-down
10×cbrt-prod
6×pow1
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×frac-2neg associate-*r* clear-num
2×associate-/l/
1×tan-quot pow-prod-down *-commutative
Counts
4 → 2558
Calls
4 calls:
243.0ms
(/ (/ (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))))) (tan k))
32.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
27.0ms
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))))
95.0ms
(/ (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k)))))

series3.3s

Counts
4 → 12
Calls
4 calls:
1.3s
(/ (/ (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))))) (tan k))
318.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
810.0ms
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))))
877.0ms
(/ (/ (sqrt 2.0) (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (/ (sqrt 2.0) (* (/ (pow (cbrt t) 3.0) l) (sin k)))))

simplify2.5s

Counts
2570 → 2570
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03457147093
done5000138804

prune22.0s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.6b

regimes1.7s

Accuracy

0% (0.8b remaining)

Error of 12.0b against oracle of 11.2b and baseline of 12.0b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03284
13484
done3484

end0.0ms

sample11.1s

Algorithm
intervals
Results
5.6s2138×body1280valid
2.1s1708×body640valid
1.7s5949×body80valid
735.0ms830×body320valid
253.0ms398×body160valid