Details

Time bar (total: 17.4s)

sample77.0ms

Algorithm
intervals
Results
37.0ms289×body80valid
9.0ms101×body80nan

simplify101.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36714
49214
510714
done10714

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize13.0ms

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)))

rewrite85.0ms

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))
20.0ms
(* (* x y) z)
44.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms
(sqrt (- (* z z) (* t a)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- (* z z) (* t a))
41.0ms
(* (* x y) z)
243.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
71.0ms
(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts
88 → 88
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01341237
13411135
21495975
done5001974

prune406.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize20.0ms

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)))

rewrite110.0ms

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:
33.0ms
(/ (sqrt (- (* z z) (* t a))) z)
9.0ms
(- (* z z) (* t a))
39.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
19.0ms
(sqrt (- (* z z) (* t a)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (sqrt (- (* z z) (* t a))) z)
59.0ms
(- (* z z) (* t a))
146.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
85.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
144 → 144
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02102654
15002421
216412221
done50002218

prune480.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize45.0ms

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)))

rewrite369.0ms

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:
304.0ms
(* (/ 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))))
19.0ms
(sqrt (- (* z z) (* t a)))
13.0ms
(sqrt (- (* z z) (* t a)))
10.0ms
(sqrt (- (* z z) (* t a)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(* (/ 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))))
95.0ms
(sqrt (- (* z z) (* t a)))
87.0ms
(sqrt (- (* z z) (* t a)))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts
328 → 328
Iterations

Useful iterations: done (1.4s)

IterNodesCost
060615017
1194714103
done500112530

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.8b

localize76.0ms

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)))

rewrite74.0ms

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:
17.0ms
(sqrt (- (* z z) (* t a)))
18.0ms
(sqrt (- (* z z) (* t a)))
18.0ms
(sqrt (- (* z z) (* t a)))
19.0ms
(sqrt (- (* z z) (* t a)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* z z) (* t a)))
99.0ms
(sqrt (- (* z z) (* t a)))
101.0ms
(sqrt (- (* z z) (* t a)))
92.0ms
(sqrt (- (* z z) (* t a)))

simplify3.9s

Counts
72 → 72
Iterations

Useful iterations: 3 (239.0ms)

IterNodesCost
050956
1123848
2339776
3811772
41547772
53996772
done5001772

prune660.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.8b

regimes681.0ms

Accuracy

88.4% (2.1b remaining)

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

bsearch125.0ms

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

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02657
13357
23557
done3557

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.4s8867×body80valid
260.0ms3005×body80nan