Details

Time bar (total: 1.6m)

sample1.2s

Algorithm
intervals
Results
445.0ms130×body1280valid
276.0ms70×body2560valid
236.0ms29×body5120valid
162.0ms70×body640valid
45.0ms35×body320valid
27.0ms64×body80valid
10.0ms13×body160valid

simplify4.7s

Counts
1 → 1
Iterations
IterNodes
47081
3997
2172
149
019

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize52.0ms

Local error

Found 4 expressions with local error:

8.8b
(/ (* (* (/ k t) t) (* (/ k t) t)) l)
11.9b
(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
12.5b
(* (/ k t) t)
12.5b
(* (/ k t) t)

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
589×add-cbrt-cube add-exp-log
252×cbrt-undiv div-exp
250×prod-exp cbrt-unprod
199×times-frac
102×add-sqr-sqrt
92×*-un-lft-identity add-cube-cbrt
45×associate-/l*
26×associate-*l*
12×div-inv
8×pow1 associate-*l/
6×associate-*r*
5×associate-/r/
4×associate-/r* associate-*r/ insert-posit16 add-log-exp unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg pow-prod-down tan-quot *-commutative
Counts
4 → 349
Calls
4 calls:
40.0ms
(/ (* (* (/ k t) t) (* (/ k t) t)) l)
170.0ms
(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
19.0ms
(* (/ k t) t)
10.0ms
(* (/ k t) t)

series460.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* (* (/ k t) t) (* (/ k t) t)) l)
415.0ms
(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
7.0ms
(* (/ k t) t)
7.0ms
(* (/ k t) t)

simplify5.9s

Counts
361 → 361
Iterations
IterNodes
210742
11954
0616

prune5.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt 2) (tan k))
0.8b
(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
1.7b
(/ (* t (/ k 1)) (/ l (/ k 1)))
2.7b
(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
2212×times-frac
801×add-exp-log
756×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
483×div-exp
472×add-cbrt-cube
309×sqrt-prod
299×associate-*l*
252×cbrt-undiv
246×prod-exp
141×cbrt-unprod
96×associate-/r*
77×div-inv
56×1-exp
32×associate-/r/
13×associate-/l*
9×pow1
6×associate-*r/
5×frac-times
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*l/
1×associate-*r* tan-quot *-commutative associate-/l/
Counts
4 → 1019
Calls
4 calls:
12.0ms
(/ (sqrt 2) (tan k))
27.0ms
(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
29.0ms
(/ (* t (/ k 1)) (/ l (/ k 1)))
102.0ms
(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))

series896.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (sqrt 2) (tan k))
119.0ms
(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
48.0ms
(/ (* t (/ k 1)) (/ l (/ k 1)))
633.0ms
(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))

simplify2.2s

Counts
1031 → 1031
Iterations
IterNodes
14199
01291

prune16.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt 2) (tan k))
0.7b
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
2.7b
(/ t (/ l k))
2.8b
(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k)))))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
568×add-exp-log
461×add-cbrt-cube
379×times-frac
239×cbrt-undiv div-exp prod-exp cbrt-unprod
167×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
60×associate-/r*
49×associate-*l*
20×div-inv
17×frac-times associate-*r/
13×pow1
12×sqrt-prod
10×associate-/l*
7×associate-*l/ associate-/r/
6×pow-prod-down
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
1×associate-*r* tan-quot *-commutative
Counts
4 → 456
Calls
4 calls:
12.0ms
(/ (sqrt 2) (tan k))
28.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
11.0ms
(/ t (/ l k))
188.0ms
(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (sqrt 2) (tan k))
404.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
36.0ms
(/ t (/ l k))
614.0ms
(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k)))))

simplify955.0ms

Counts
468 → 468
Iterations
IterNodes
12291
0706

prune8.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) l))
0.4b
(/ (sqrt 2) (tan k))
1.6b
(* (/ t (/ l k)) (sin k))
2.7b
(/ t (/ l k))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
189×times-frac
125×add-sqr-sqrt
116×*-un-lft-identity add-cube-cbrt
75×associate-*l*
41×add-exp-log
38×add-cbrt-cube
21×sqrt-prod
18×cbrt-prod
16×associate-/r*
13×prod-exp cbrt-unprod
12×cbrt-undiv div-exp
11×pow1 div-inv
9×associate-/l*
4×associate-*r* pow-prod-down associate-*l/ insert-posit16 add-log-exp
3×associate-/r/ unswap-sqr
2×clear-num frac-2neg *-commutative
1×frac-times tan-quot associate-*r/
Counts
4 → 237
Calls
4 calls:
36.0ms
(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) l))
20.0ms
(/ (sqrt 2) (tan k))
32.0ms
(* (/ t (/ l k)) (sin k))
5.0ms
(/ t (/ l k))

series816.0ms

Counts
4 → 12
Calls
4 calls:
534.0ms
(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) l))
86.0ms
(/ (sqrt 2) (tan k))
164.0ms
(* (/ t (/ l k)) (sin k))
32.0ms
(/ t (/ l k))

simplify2.4s

Counts
249 → 249
Iterations
IterNodes
23797
11016
0400

prune3.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes327.0ms

Accuracy

-29.6% (1.6b remaining)

Error of 1.6b against oracle of 0.1b and baseline of 1.3b

bsearch672.0ms

Steps
ItersRangePoint
7
1.0332070815447668e-16
9.0826679191265e-15
3.9776562910929405e-16
8
-2.6993146519211728e+212
-2.8152842380861584e+209
-2.8470394918342432e+209

simplify8.0ms

Iterations
IterNodes
243
143
032

end0.0ms

sample41.6s

Algorithm
intervals
Results
12.6s4074×body1280valid
10.6s2234×body2560valid
9.1s976×body5120valid
5.7s2567×body640valid
1.8s1014×body320valid
895.0ms1977×body80valid
434.0ms435×body160valid