Details

Time bar (total: 1.3m)

sample290.0ms

Algorithm
intervals
Results
94.0ms60×body640valid
87.0ms51×body1280valid
52.0ms202×body80valid
29.0ms30×body320valid
5.0ms7×body160valid

simplify2.4s

Counts
1 → 1
Iterations
IterNodes
46079
31031
2181
154
019

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.2b

localize46.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (/ t (/ l t)) (/ (tan k) (/ l t)))
4.1b
(/ (tan k) (/ l t))
4.1b
(* (sin k) (* (/ t (/ l t)) (/ (tan k) (/ l t))))
11.0b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* (/ t (/ l t)) (/ (tan k) (/ l t)))))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
258×times-frac
221×add-cbrt-cube add-exp-log
167×add-sqr-sqrt
131×*-un-lft-identity add-cube-cbrt
108×cbrt-undiv div-exp
66×prod-exp cbrt-unprod
47×associate-*l*
45×associate-*r*
18×associate-/l*
16×div-inv
14×associate-/r*
11×pow1
10×associate-/r/
9×associate-*r/ unswap-sqr
4×pow-prod-down insert-posit16 add-log-exp
3×frac-times associate-*l/
2×clear-num frac-2neg flip3-+ *-commutative flip-+ associate-/l/
1×tan-quot
Counts
4 → 328
Calls
4 calls:
21.0ms
(* (/ t (/ l t)) (/ (tan k) (/ l t)))
7.0ms
(/ (tan k) (/ l t))
65.0ms
(* (sin k) (* (/ t (/ l t)) (/ (tan k) (/ l t))))
85.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* (/ t (/ l t)) (/ (tan k) (/ l t)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
184.0ms
(* (/ t (/ l t)) (/ (tan k) (/ l t)))
155.0ms
(/ (tan k) (/ l t))
233.0ms
(* (sin k) (* (/ t (/ l t)) (/ (tan k) (/ l t))))
897.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* (/ t (/ l t)) (/ (tan k) (/ l t)))))

simplify3.5s

Counts
340 → 340
Iterations
IterNodes
28344
11805
0558

prune5.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.7b

localize45.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (sin k) (* t (/ (tan k) (/ l t))))
4.1b
(/ (tan k) (/ l t))
5.0b
(* (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* t (/ (tan k) (/ l t))))) (/ l t))
8.6b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* t (/ (tan k) (/ l t)))))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
193×add-cbrt-cube add-exp-log
142×times-frac
81×add-sqr-sqrt
80×cbrt-undiv div-exp
76×*-un-lft-identity add-cube-cbrt
71×prod-exp cbrt-unprod
23×associate-*l*
18×associate-/l*
14×associate-/r* associate-*r*
11×pow1 div-inv
9×associate-/r/
7×associate-*r/
4×pow-prod-down insert-posit16 add-log-exp
3×flip3-+ flip-+
2×clear-num frac-2neg *-commutative unswap-sqr associate-/l/
1×frac-times associate-*l/ tan-quot
Counts
4 → 252
Calls
4 calls:
28.0ms
(* (sin k) (* t (/ (tan k) (/ l t))))
9.0ms
(/ (tan k) (/ l t))
164.0ms
(* (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* t (/ (tan k) (/ l t))))) (/ l t))
75.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* t (/ (tan k) (/ l t)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (sin k) (* t (/ (tan k) (/ l t))))
160.0ms
(/ (tan k) (/ l t))
821.0ms
(* (/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* t (/ (tan k) (/ l t))))) (/ l t))
435.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (sin k) (* t (/ (tan k) (/ l t)))))

simplify2.7s

Counts
264 → 264
Iterations
IterNodes
26360
11305
0435

prune4.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.1b

localize64.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (sin k) (* t (/ (tan k) (/ l t))))
4.1b
(/ (tan k) (/ l t))
5.0b
(* (/ (/ (sqrt 2) 1) (/ (* (sin k) (* t (/ (tan k) (/ l t)))) (/ (sqrt 2) (+ (* (/ k t) (/ k t)) 2)))) (/ l t))
8.5b
(/ (* (sin k) (* t (/ (tan k) (/ l t)))) (/ (sqrt 2) (+ (* (/ k t) (/ k t)) 2)))

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
2252×times-frac
810×add-sqr-sqrt
770×*-un-lft-identity
766×add-cube-cbrt
646×associate-*l*
536×add-exp-log
481×sqrt-prod
389×add-cbrt-cube
297×div-exp
200×cbrt-undiv
173×prod-exp
123×cbrt-unprod
83×div-inv
73×associate-/r/
37×associate-/r*
24×flip3-+ flip-+
22×1-exp
14×associate-*r*
12×unswap-sqr
11×pow1
5×associate-*r/
4×pow-prod-down insert-posit16 associate-/l* add-log-exp
2×clear-num frac-2neg *-commutative associate-/l/
1×frac-times associate-*l/ tan-quot
Counts
4 → 973
Calls
4 calls:
32.0ms
(* (sin k) (* t (/ (tan k) (/ l t))))
7.0ms
(/ (tan k) (/ l t))
219.0ms
(* (/ (/ (sqrt 2) 1) (/ (* (sin k) (* t (/ (tan k) (/ l t)))) (/ (sqrt 2) (+ (* (/ k t) (/ k t)) 2)))) (/ l t))
98.0ms
(/ (* (sin k) (* t (/ (tan k) (/ l t)))) (/ (sqrt 2) (+ (* (/ k t) (/ k t)) 2)))

series2.1s

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (sin k) (* t (/ (tan k) (/ l t))))
196.0ms
(/ (tan k) (/ l t))
1.2s
(* (/ (/ (sqrt 2) 1) (/ (* (sin k) (* t (/ (tan k) (/ l t)))) (/ (sqrt 2) (+ (* (/ k t) (/ k t)) 2)))) (/ l t))
468.0ms
(/ (* (sin k) (* t (/ (tan k) (/ l t)))) (/ (sqrt 2) (+ (* (/ k t) (/ k t)) 2)))

simplify2.5s

Counts
985 → 985
Iterations
IterNodes
14728
01289

prune18.1s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.0b

localize61.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (/ (sin k) (sqrt (sqrt 2))) (/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2))))
4.1b
(/ (tan k) (/ l t))
5.0b
(* (/ (/ (sqrt 2) 1) (* (/ (sin k) (sqrt (sqrt 2))) (/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2))))) (/ l t))
8.0b
(/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2)))

rewrite685.0ms

Algorithm
rewrite-expression-head
Rules
1026×add-exp-log
743×add-cbrt-cube
584×div-exp
399×cbrt-undiv
332×prod-exp
302×times-frac
234×cbrt-unprod
160×add-sqr-sqrt
144×*-un-lft-identity add-cube-cbrt
120×sqrt-prod
60×associate-*l*
51×associate-*r*
46×associate-/r*
38×1-exp
14×div-inv
12×associate-/r/
8×pow1
6×unswap-sqr
4×associate-*r/ insert-posit16 associate-/l* add-log-exp
3×frac-times flip3-+ associate-*l/ flip-+
2×clear-num frac-2neg pow-prod-down *-commutative associate-/l/
1×tan-quot
Counts
4 → 541
Calls
4 calls:
77.0ms
(* (/ (sin k) (sqrt (sqrt 2))) (/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2))))
7.0ms
(/ (tan k) (/ l t))
530.0ms
(* (/ (/ (sqrt 2) 1) (* (/ (sin k) (sqrt (sqrt 2))) (/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2))))) (/ l t))
49.0ms
(/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2)))

series2.3s

Counts
4 → 12
Calls
4 calls:
363.0ms
(* (/ (sin k) (sqrt (sqrt 2))) (/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2))))
134.0ms
(/ (tan k) (/ l t))
1.2s
(* (/ (/ (sqrt 2) 1) (* (/ (sin k) (sqrt (sqrt 2))) (/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2))))) (/ l t))
650.0ms
(/ (* t (/ (tan k) (/ l t))) (/ (sqrt (sqrt 2)) (+ (* (/ k t) (/ k t)) 2)))

simplify1.2s

Counts
553 → 553
Iterations
IterNodes
13022
0927

prune9.2s

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 5.0b

regimes661.0ms

Accuracy

71.9% (1.9b remaining)

Error of 8.6b against oracle of 6.7b and baseline of 13.4b

bsearch568.0ms

Steps
ItersRangePoint
3
0.0191017208438795
0.025588075918097277
0.02437188434168144
9
-1.8538953032927157e-24
-7.399531600622762e-32
-1.0865304981214163e-31

simplify22.0ms

Iterations
IterNodes
262
162
048

end0.0ms

sample16.2s

Algorithm
intervals
Results
6.6s2113×body1280valid
4.0s1733×body640valid
3.5s5886×body80valid
1.2s843×body320valid
434.0ms412×body160valid