Details

Time bar (total: 16.5s)

sample43.0ms

Algorithm
intervals
Results
15.0ms289×body80valid
5.0ms101×body80nan

simplify137.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize28.0ms

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)))

rewrite98.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
16.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) z)
32.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
18.0ms
(sqrt (- (* z z) (* t a)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* z z) (* t a))
39.0ms
(* (* x y) z)
141.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
97.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
98 → 98
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune445.0ms

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)))

rewrite121.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
25.0ms
(/ (sqrt (- (* z z) (* t a))) z)
17.0ms
(- (* z z) (* t a))
51.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.0ms
(sqrt (- (* z z) (* t a)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (sqrt (- (* z z) (* t a))) z)
45.0ms
(- (* z z) (* t a))
108.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
110.0ms
(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts
154 → 154
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02222758
15222513
216932314
done50012309

prune571.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

localize37.0ms

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)))

rewrite328.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 324
Calls
4 calls:
216.0ms
(* (/ 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))))
16.0ms
(sqrt (- (* z z) (* t a)))
30.0ms
(sqrt (- (* z z) (* t a)))
19.0ms
(sqrt (- (* z z) (* t a)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(* (/ 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))))
81.0ms
(sqrt (- (* z z) (* t a)))
72.0ms
(sqrt (- (* z z) (* t a)))
71.0ms
(sqrt (- (* z z) (* t a)))

simplify1.2s

Counts
336 → 336
Iterations

Useful iterations: done (1.1s)

IterNodesCost
061015157
1195814231
done500112653

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize54.0ms

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 expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
12.0ms
(sqrt (- (* z z) (* t a)))
20.0ms
(sqrt (- (* z z) (* t a)))
20.0ms
(sqrt (- (* z z) (* t a)))
21.0ms
(sqrt (- (* z z) (* t a)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* z z) (* t a)))
84.0ms
(sqrt (- (* z z) (* t a)))
79.0ms
(sqrt (- (* z z) (* t a)))
77.0ms
(sqrt (- (* z z) (* t a)))

simplify4.0s

Counts
80 → 80
Iterations

Useful iterations: 3 (228.0ms)

IterNodesCost
0521028
1132904
2376836
3958828
41911828
54805828
done5000828

prune636.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.8b

regimes533.0ms

Accuracy

88.4% (2.1b remaining)

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

bsearch162.0ms

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02657
13357
23557
done3557

end0.0ms

sample2.2s

Algorithm
intervals
Results
940.0ms8867×body80valid
223.0ms3005×body80nan