Details

Time bar (total: 25.8s)

sample54.0ms

Algorithm
intervals
Results
15.0ms238×body80valid
4.0ms17×body320valid
3.0ms14×body640valid
3.0ms10×body1280valid
0.0ms1×body2560valid
0.0ms3×body160valid

simplify9.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01113
12213
25213
310713
418613
538013
652913
766813
882013
996913
10122213
11153113
12227913
13356413
done500013

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- z t) y)
1.4b
(- (+ x y) (/ (* (- z t) y) (- a t)))
10.9b
(/ (* (- z t) y) (- a t))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
17×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
5×pow1 times-frac associate-*l* associate-/r* distribute-lft-out--
4×flip3-- associate-*l/ flip-- difference-of-squares
3×associate-*r*
2×cbrt-undiv diff-log div-exp prod-exp associate-/r/ frac-sub cbrt-unprod associate-/l/
1×sub-neg frac-2neg flip3-+ pow-prod-down associate--l+ clear-num sum-log *-commutative flip-+ div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
3 → 70
Calls
3 calls:
30.0ms
(* (- z t) y)
52.0ms
(- (+ x y) (/ (* (- z t) y) (- a t)))
32.0ms
(/ (* (- z t) y) (- a t))

series282.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* (- z t) y)
167.0ms
(- (+ x y) (/ (* (- z t) y) (- a t)))
74.0ms
(/ (* (- z t) y) (- a t))

simplify1.1s

Counts
79 → 79
Iterations

Useful iterations: 2 (252.0ms)

IterNodesCost
01501010
1382951
21543873
done5000873

prune264.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a t))
0.5b
(cbrt (- a t))
4.1b
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
8.5b
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
36×times-frac
35×*-un-lft-identity
30×associate-*r*
27×cbrt-prod
25×add-exp-log
23×add-cube-cbrt
18×cbrt-div add-cbrt-cube
17×associate-*l*
10×flip3-- associate-/r/ flip--
9×add-log-exp
8×prod-exp cbrt-unprod
7×cbrt-undiv frac-times div-exp
6×pow1 frac-sub distribute-lft-out-- difference-of-squares unswap-sqr
5×associate-*r/ associate-*l/
3×flip3-+ flip-+
2×pow1/3 diff-log div-inv
1×sub-neg pow-prod-down associate--l+ sum-log *-commutative
Counts
4 → 127
Calls
4 calls:
4.0ms
(cbrt (- a t))
5.0ms
(cbrt (- a t))
139.0ms
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
76.0ms
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series659.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(cbrt (- a t))
187.0ms
(cbrt (- a t))
134.0ms
(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
134.0ms
(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify1.7s

Counts
139 → 139
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02743197
17643031
228542480
done50012289

prune679.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (- a t)))
0.6b
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
2.2b
(* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
8.2b
(- (+ x y) (* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
160×times-frac
132×add-sqr-sqrt
96×cbrt-div
93×cbrt-prod
80×associate-*l*
69×*-un-lft-identity
53×add-cube-cbrt
42×associate-/r/
39×flip3-- associate-*r* flip--
36×add-exp-log
27×frac-times
22×add-cbrt-cube
20×unswap-sqr
15×associate-*r/ associate-*l/
14×cbrt-undiv div-exp
10×prod-exp cbrt-unprod
9×add-log-exp
8×distribute-lft-out-- difference-of-squares
6×pow1 frac-sub div-inv
3×flip3-+ flip-+
2×pow1/3 diff-log
1×sub-neg pow-prod-down associate--l+ sum-log *-commutative
Counts
4 → 222
Calls
4 calls:
5.0ms
(cbrt (cbrt (- a t)))
16.0ms
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
212.0ms
(* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
43.0ms
(- (+ x y) (* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

series707.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(cbrt (cbrt (- a t)))
201.0ms
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
112.0ms
(* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))
182.0ms
(- (+ x y) (* (/ (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))

simplify2.4s

Counts
234 → 234
Iterations

Useful iterations: done (2.4s)

IterNodesCost
04928060
114087774
246117384
done50017285

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (- a t)))
0.6b
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
2.9b
(* (/ (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) 1) (* (/ (/ (cbrt (- z t)) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))
6.8b
(- (+ x y) (* (/ (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) 1) (* (/ (/ (cbrt (- z t)) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))))

rewrite419.0ms

Algorithm
rewrite-expression-head
Rules
270×add-exp-log
133×div-exp
105×prod-exp
90×add-cbrt-cube
71×cbrt-undiv
66×times-frac
59×cbrt-unprod
46×associate-*l*
38×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt cbrt-div
29×cbrt-prod
21×1-exp
19×frac-times
17×associate-*r/
14×frac-sub
11×flip3-- associate-*l/ flip--
9×pow1 add-log-exp
7×flip3-+ flip-+
6×associate-/r/
4×div-inv distribute-lft-out-- difference-of-squares
3×pow-prod-down
2×pow1/3 diff-log
1×sub-neg associate-*r* associate--l+ sum-log *-commutative
Counts
4 → 204
Calls
4 calls:
5.0ms
(cbrt (cbrt (- a t)))
17.0ms
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
301.0ms
(* (/ (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) 1) (* (/ (/ (cbrt (- z t)) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))
74.0ms
(- (+ x y) (* (/ (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) 1) (* (/ (/ (cbrt (- z t)) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))))

series737.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(cbrt (cbrt (- a t)))
168.0ms
(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
166.0ms
(* (/ (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) 1) (* (/ (/ (cbrt (- z t)) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t))))))
184.0ms
(- (+ x y) (* (/ (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) 1) (* (/ (/ (cbrt (- z t)) (cbrt (- a t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))) (/ y (cbrt (cbrt (- a t)))))))

simplify2.4s

Counts
216 → 216
Iterations

Useful iterations: done (2.4s)

IterNodesCost
048410951
111849990
243448428
done50008172

prune865.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

regimes529.0ms

Accuracy

19.3% (5.7b remaining)

Error of 9.7b against oracle of 3.9b and baseline of 11.0b

bsearch132.0ms

Steps
ItersRangePoint
5
6.0100183000681985e-12
1.507024095617085e-11
9.934875400147096e-12
1
5.613152505814407e-44
6.021187163235515e-44
5.919178498880238e-44
5
1.528161398260382e-110
5.73399000111342e-110
1.8890840391698757e-110
9
-1.643003965912255e-110
-2.0128244664799053e-117
-9.693527876338159e-114

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
049236
157236
done57236

end0.0ms

sample1.4s

Algorithm
intervals
Results
577.0ms7381×body80valid
146.0ms458×body640valid
64.0ms257×body1280valid
59.0ms409×body320valid
25.0ms250×body160valid
4.0ms13×body2560valid