Details

Time bar (total: 16.7s)

sample25.0ms

Algorithm
intervals
Results
8.0ms250×body80valid
2.0ms14×body640valid
1.0ms15×body320valid
1.0ms9×body160valid
0.0ms3×body1280valid
0.0ms1×body2560valid

simplify6.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01113
12013
24513
311113
425013
552513
6111913
7214313
8344113
9463613
done500013

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- y z) (- t x))
2.6b
(+ x (/ (* (- y z) (- t x)) (- a z)))
17.1b
(/ (* (- y z) (- t x)) (- a z))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
13×flip3-- flip--
10×add-exp-log add-cbrt-cube
8×frac-times associate-/l/
7×add-cube-cbrt
5×pow1 times-frac associate-*r* associate-*l* associate-/r* add-log-exp
4×associate-*r/ associate-*l/ distribute-lft-out-- difference-of-squares
2×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in div-exp prod-exp associate-/r/ cbrt-unprod
1×+-commutative frac-2neg flip3-+ pow-prod-down clear-num sum-log *-commutative flip-+ div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
3 → 81
Calls
3 calls:
20.0ms
(* (- y z) (- t x))
10.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
13.0ms
(/ (* (- y z) (- t x)) (- a z))

series313.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(* (- y z) (- t x))
151.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
127.0ms
(/ (* (- y z) (- t x)) (- a z))

simplify582.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (137.0ms)

IterNodesCost
01621284
14731213
220181111
done50001111

prune234.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.8b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.2b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
59×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
27×add-cube-cbrt
25×add-exp-log
18×cbrt-div add-cbrt-cube
17×associate-*l*
16×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×flip3-- flip--
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×pow1 add-log-exp unswap-sqr
5×frac-times
3×associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 134
Calls
4 calls:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
75.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series743.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(cbrt (- a z))
150.0ms
(cbrt (- a z))
295.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
153.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify996.0ms

Counts
146 → 146
Iterations

Useful iterations: 2 (225.0ms)

IterNodesCost
02553364
17453200
231822663
done50002663

prune474.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
1.1b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
8.4b
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
36×cbrt-div
26×add-sqr-sqrt
22×add-cbrt-cube
17×associate-*l*
16×*-un-lft-identity times-frac associate-*r* associate-/r/
15×prod-exp cbrt-unprod
14×flip3-- flip--
13×cbrt-prod
12×cbrt-undiv div-exp
10×add-cube-cbrt
9×frac-times
6×pow1 add-log-exp unswap-sqr
5×associate-*r/ associate-*l/
3×distribute-lft-out-- difference-of-squares
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 110
Calls
4 calls:
2.0ms
(cbrt (- t x))
4.0ms
(cbrt (- t x))
76.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series768.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(cbrt (- t x))
154.0ms
(cbrt (- t x))
303.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
154.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify944.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (258.0ms)

IterNodesCost
02944294
18454149
232383588
done50003588

prune581.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.8b
(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
6.0b
(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
772×times-frac
686×add-sqr-sqrt
600×*-un-lft-identity
487×cbrt-prod
374×associate-*l*
270×add-cube-cbrt
165×distribute-lft-out-- difference-of-squares
46×associate-*r*
25×add-exp-log
24×cbrt-div
21×unswap-sqr
20×associate-/r/
16×add-cbrt-cube
12×flip3-- flip--
10×div-inv
9×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod add-log-exp
2×pow1/3
1×+-commutative frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip-+
Counts
4 → 506
Calls
4 calls:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
315.0ms
(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
3.0ms
(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

series972.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (- a z))
372.0ms
(cbrt (- a z))
295.0ms
(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
156.0ms
(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

simplify459.0ms

Counts
518 → 518
Iterations

Useful iterations: done (437.0ms)

IterNodesCost
052412813
1169012650
done500212579

prune1.6s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 3.6b

regimes425.0ms

Accuracy

-7.9% (9.0b remaining)

Error of 13.1b against oracle of 4.1b and baseline of 12.4b

bsearch112.0ms

Steps
ItersRangePoint
6
7.867046341610554e+209
6.299026182130298e+210
3.374713558534679e+210
7
1.6972765783681638e+139
2.993516045954254e+140
2.1794134156627861e+139
6
-4.356485418338831e+232
-1.0295582727544921e+232
-1.4882279988111647e+232

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03275
13875
done3875

end0.0ms

sample695.0ms

Algorithm
intervals
Results
254.0ms7795×body80valid
54.0ms460×body640valid
41.0ms255×body1280valid
39.0ms434×body320valid
19.0ms280×body160valid
3.0ms14×body2560valid