Details

Time bar (total: 16.3s)

sample77.0ms

Algorithm
intervals
Results
27.0ms289×body80valid
8.0ms101×body80nan

simplify158.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12114
24514
36714
49214
510714
done10714

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
2.2b
(* (* x y) z)
9.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) z)
39.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms
(sqrt (- (* z z) (* t a)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* z z) (* t a))
49.0ms
(* (* x y) z)
152.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
109.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
88 → 88
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01341237
13411135
21495975
done5001974

prune399.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.4b
(- (* z z) (* t a))
2.6b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
19.0ms
(/ (sqrt (- (* z z) (* t a))) z)
9.0ms
(- (* z z) (* t a))
38.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
16.0ms
(sqrt (- (* z z) (* t a)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (sqrt (- (* z z) (* t a))) z)
60.0ms
(- (* z z) (* t a))
147.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
98.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
144 → 144
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02102654
15002421
216412221
done50002218

prune602.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

localize47.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (/ x (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z)))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
23.0b
(sqrt (- (* z z) (* t a)))
23.0b
(sqrt (- (* z z) (* t a)))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
417×times-frac
284×add-sqr-sqrt
210×cbrt-prod
186×add-cube-cbrt *-un-lft-identity
179×associate-*r*
97×add-exp-log
69×sqrt-prod
61×add-cbrt-cube
45×cbrt-undiv div-exp
30×prod-exp cbrt-unprod
24×unswap-sqr
20×associate-*l*
9×pow1
8×div-inv
6×sqrt-div
4×add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×associate-/r/
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 316
Calls
4 calls:
286.0ms
(* (/ x (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z)))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
10.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))
29.0ms
(sqrt (- (* z z) (* t a)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(* (/ x (/ (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a))))) (* (cbrt z) (cbrt z)))) (/ y (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
89.0ms
(sqrt (- (* z z) (* t a)))
104.0ms
(sqrt (- (* z z) (* t a)))
88.0ms
(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts
328 → 328
Iterations

Useful iterations: done (1.2s)

IterNodesCost
060615017
1194714103
done500112530

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize34.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* z z) (* t a)))
23.0b
(sqrt (- (* z z) (* t a)))
23.0b
(sqrt (- (* z z) (* t a)))
23.0b
(sqrt (- (* z z) (* t a)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
12.0ms
(sqrt (- (* z z) (* t a)))
10.0ms
(sqrt (- (* z z) (* t a)))
10.0ms
(sqrt (- (* z z) (* t a)))
18.0ms
(sqrt (- (* z z) (* t a)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(sqrt (- (* z z) (* t a)))
78.0ms
(sqrt (- (* z z) (* t a)))
90.0ms
(sqrt (- (* z z) (* t a)))
76.0ms
(sqrt (- (* z z) (* t a)))

simplify3.8s

Counts
72 → 72
Iterations

Useful iterations: 3 (219.0ms)

IterNodesCost
050956
1123848
2339776
3811772
41547772
53996772
done5001772

prune537.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.8b

regimes544.0ms

Accuracy

88.4% (2.1b remaining)

Error of 5.4b against oracle of 3.3b and baseline of 21.5b

bsearch121.0ms

Steps
ItersRangePoint
8
6.123155016714887e+131
5.341589198600723e+134
3.2435286845379817e+132
8
-4.750953680063193e+156
-2.2976360399374818e+153
-6.5067060621114526e+153

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02657
13357
23557
done3557

end0.0ms

sample1.8s

Algorithm
intervals
Results
523.0ms8867×body80valid
267.0ms3005×body80nan