Details

Time bar (total: 5.7s)

sample31.0ms

Algorithm
intervals
Results
11.0ms278×body80valid

simplify496.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01011
11911
23811
35211
48011
510811
615311
735811
8185811
done500011

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 10.6b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(- t (* a z))
10.4b
(/ (- x (* y z)) (- t (* a z)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-- associate-/r* flip-- associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 44
Calls
2 calls:
10.0ms
(- t (* a z))
7.0ms
(/ (- x (* y z)) (- t (* a z)))

series29.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(- t (* a z))
22.0ms
(/ (- x (* y z)) (- t (* a z)))

simplify605.0ms

Counts
50 → 50
Iterations

Useful iterations: done (604.0ms)

IterNodesCost
085724
1221706
2686652
32267652
done5000650

prune97.0ms

Filtered
39 candidates to 50 candidates (-28.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New42850
Fresh000
Picked011
Done000
Total42951

Merged error: 8.2b

Counts
51 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ x (- t (* a z))) (* y (/ z (- t (* a z)))))
2.6b
(* y (/ z (- t (* a z))))
4.1b
(/ x (- t (* a z)))
9.2b
(/ z (- t (* a z)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity times-frac
15×associate-*r*
13×add-exp-log add-cbrt-cube
6×pow1 associate-/r* associate-/r/ associate-/l* add-log-exp
4×flip3-- flip--
3×cbrt-undiv associate-*r/ div-exp associate-*l* div-inv
2×frac-2neg prod-exp clear-num cbrt-unprod unswap-sqr
1×sub-neg diff-log pow-prod-down *-commutative frac-sub sub-div
Counts
4 → 106
Calls
4 calls:
8.0ms
(- (/ x (- t (* a z))) (* y (/ z (- t (* a z)))))
9.0ms
(* y (/ z (- t (* a z))))
5.0ms
(/ x (- t (* a z)))
5.0ms
(/ z (- t (* a z)))

series73.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (/ x (- t (* a z))) (* y (/ z (- t (* a z)))))
14.0ms
(* y (/ z (- t (* a z))))
15.0ms
(/ x (- t (* a z)))
11.0ms
(/ z (- t (* a z)))

simplify825.0ms

Counts
118 → 118
Iterations

Useful iterations: done (822.0ms)

IterNodesCost
01591582
13781504
211951386
337161386
done50001384

prune158.0ms

Filtered
91 candidates to 118 candidates (-29.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1144118
Fresh167
Picked101
Done101
Total11710127

Merged error: 8.2b

Counts
127 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (- t (* a z)))
2.6b
(* y (* z (/ 1 (- t (* a z)))))
4.1b
(/ x (- t (* a z)))
9.2b
(* z (/ 1 (- t (* a z))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
34×add-exp-log
30×*-un-lft-identity
29×add-cube-cbrt times-frac
22×add-cbrt-cube
16×associate-*r*
13×prod-exp
12×pow1
7×div-exp cbrt-unprod
6×associate-*l* associate-/r* associate-/r/ associate-/l*
4×cbrt-undiv associate-*r/ pow-prod-down add-log-exp
3×rec-exp flip3-- 1-exp flip-- div-inv unswap-sqr
2×frac-2neg clear-num un-div-inv *-commutative
1×pow-flip inv-pow
Counts
4 → 124
Calls
4 calls:
5.0ms
(/ 1 (- t (* a z)))
9.0ms
(* y (* z (/ 1 (- t (* a z)))))
5.0ms
(/ x (- t (* a z)))
13.0ms
(* z (/ 1 (- t (* a z))))

series49.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ 1 (- t (* a z)))
14.0ms
(* y (* z (/ 1 (- t (* a z)))))
12.0ms
(/ x (- t (* a z)))
12.0ms
(* z (/ 1 (- t (* a z))))

simplify857.0ms

Counts
136 → 136
Iterations

Useful iterations: done (854.0ms)

IterNodesCost
01621626
13911444
212521222
339901222
done50011220

prune148.0ms

Filtered
86 candidates to 136 candidates (-58.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1360136
Fresh099
Picked011
Done000
Total13610146

Merged error: 8.2b

Counts
146 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (/ (- t (* a z)) z))
2.6b
(* y (/ 1 (/ (- t (* a z)) z)))
4.1b
(/ x (- t (* a z)))
9.2b
(/ (- t (* a z)) z)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
112×add-sqr-sqrt
100×*-un-lft-identity
98×add-cube-cbrt
44×associate-*r*
38×add-exp-log
22×add-cbrt-cube
19×associate-/r*
16×div-exp
11×div-inv
9×associate-/l*
8×cbrt-undiv
7×pow1 prod-exp
5×unswap-sqr
4×rec-exp 1-exp associate-/r/ add-log-exp
3×frac-2neg associate-*l* clear-num cbrt-unprod
2×flip3-- flip-- associate-/l/
1×pow-flip div-sub associate-*r/ pow-prod-down un-div-inv *-commutative inv-pow
Counts
4 → 208
Calls
4 calls:
8.0ms
(/ 1 (/ (- t (* a z)) z))
20.0ms
(* y (/ 1 (/ (- t (* a z)) z)))
5.0ms
(/ x (- t (* a z)))
6.0ms
(/ (- t (* a z)) z)

series49.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(/ 1 (/ (- t (* a z)) z))
15.0ms
(* y (/ 1 (/ (- t (* a z)) z)))
12.0ms
(/ x (- t (* a z)))
8.0ms
(/ (- t (* a z)) z)

simplify462.0ms

Counts
220 → 220
Iterations

Useful iterations: 2 (196.0ms)

IterNodesCost
02783288
16992930
222592491
done50002491

prune172.0ms

Filtered
140 candidates to 220 candidates (-57.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2182220
Fresh268
Picked101
Done101
Total2228230

Merged error: 2.0b

Counts
230 → 8

regimes513.0ms

Accuracy

90.5% (0.1b remaining)

Error of 1.8b against oracle of 1.6b and baseline of 3.2b

bsearch49.0ms

Steps
ItersRangePoint
8
602010.8647626698
555912312.1893992
1147648.309126432
9
-7.192129389508435e-19
-2.577733556719633e-26
-3.7721167568229886e-25

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02359
13143
done3143

end0.0ms

sample896.0ms

Algorithm
intervals
Results
364.0ms8751×body80valid

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