Details

Time bar (total: 7.9s)

sample38.0ms

Algorithm
intervals
Results
10.0ms239×body80valid
3.0ms18×body640valid
2.0ms17×body320valid
2.0ms10×body1280valid
1.0ms7×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01113
12013
24513
311113
425013
552513
6111813
7188413
8340313
done500113

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.4b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- y z) (- t x))
1.7b
(+ x (/ (* (- y z) (- t x)) (- a z)))
20.2b
(/ (* (- y z) (- t x)) (- a z))

rewrite39.0ms

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:
15.0ms
(* (- y z) (- t x))
8.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
13.0ms
(/ (* (- y z) (- t x)) (- a z))

series108.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(* (- y z) (- t x))
58.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
39.0ms
(/ (* (- y z) (- t x)) (- a z))

simplify517.0ms

Counts
90 → 90
Iterations

Useful iterations: done (515.0ms)

IterNodesCost
01621284
14731217
220341115
done50001111

prune149.0ms

Filtered
67 candidates to 90 candidates (-34.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New81990
Fresh000
Picked101
Done000
Total82991

Merged error: 4.1b

Counts
91 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(cbrt (- a z))
2.2b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.0b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite59.0ms

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:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
42.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series181.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(cbrt (- a z))
32.0ms
(cbrt (- a z))
61.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
60.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify703.0ms

Counts
146 → 146
Iterations

Useful iterations: done (697.0ms)

IterNodesCost
02603378
17533211
230602715
done50002655

prune214.0ms

Filtered
108 candidates to 146 candidates (-35.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1406146
Fresh268
Picked101
Done000
Total14312155

Merged error: 4.1b

Counts
155 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (- a z)))
0.6b
(cbrt (cbrt (- a z)))
2.2b
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.7b
(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
100×cbrt-prod
98×times-frac
76×*-un-lft-identity
69×add-exp-log
61×associate-*r*
48×cbrt-div
42×add-cbrt-cube
38×add-cube-cbrt
29×associate-*l*
27×cbrt-undiv div-exp
24×prod-exp cbrt-unprod
19×distribute-lft-out-- difference-of-squares
18×associate-/r/
15×flip3-- flip--
12×unswap-sqr
9×frac-times
6×pow1 add-log-exp
5×associate-*r/ associate-*l/
3×div-inv
2×pow1/3
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 189
Calls
4 calls:
8.0ms
(cbrt (cbrt (- a z)))
4.0ms
(cbrt (cbrt (- a z)))
66.0ms
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
7.0ms
(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series183.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(cbrt (cbrt (- a z)))
29.0ms
(cbrt (cbrt (- a z)))
66.0ms
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
56.0ms
(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify342.0ms

Counts
201 → 201
Iterations

Useful iterations: done (333.0ms)

IterNodesCost
03737254
111406931
done50016879

prune260.0ms

Filtered
156 candidates to 201 candidates (-28.8%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2001201
Fresh11011
Picked011
Done000
Total20112213

Merged error: 4.1b

Counts
213 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (- a z)))
0.6b
(cbrt (cbrt (- a z)))
2.2b
(* (/ (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.7b
(+ x (* (/ (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite442.0ms

Algorithm
rewrite-expression-head
Rules
1209×times-frac
745×add-sqr-sqrt
617×*-un-lft-identity
565×cbrt-prod
386×associate-*l*
281×add-cube-cbrt
168×distribute-lft-out-- difference-of-squares
69×add-exp-log
61×associate-*r*
54×cbrt-div
38×add-cbrt-cube
32×unswap-sqr
31×cbrt-undiv div-exp
28×associate-/r/
20×prod-exp cbrt-unprod
18×flip3-- flip--
11×div-inv
6×pow1 add-log-exp
5×frac-times
3×associate-*r/ associate-*l/
2×pow1/3
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 566
Calls
4 calls:
4.0ms
(cbrt (cbrt (- a z)))
4.0ms
(cbrt (cbrt (- a z)))
358.0ms
(* (/ (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
4.0ms
(+ x (* (/ (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series182.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(cbrt (cbrt (- a z)))
29.0ms
(cbrt (cbrt (- a z)))
66.0ms
(* (/ (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
56.0ms
(+ x (* (/ (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify572.0ms

Counts
578 → 578
Iterations

Useful iterations: done (538.0ms)

IterNodesCost
076019735
1243119438
done500019420

prune532.0ms

Filtered
400 candidates to 578 candidates (-44.5%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New5771578
Fresh01010
Picked011
Done011
Total57713590

Merged error: 4.1b

Counts
590 → 13

regimes723.0ms

Accuracy

38.4% (5.1b remaining)

Error of 9.4b against oracle of 4.3b and baseline of 12.6b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
032119
14283
done4283

end0.0ms

sample1.1s

Algorithm
intervals
Results
340.0ms7840×body80valid
74.0ms462×body640valid
56.0ms293×body1280valid
53.0ms421×body320valid
20.0ms256×body160valid
4.0ms15×body2560valid

Profiling

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