Details

Time bar (total: 14.5s)

sample59.0ms

Algorithm
intervals
Results
20.0ms279×body80valid
11.0ms90×body80nan

simplify111.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36714
49214
510714
done10714

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.8b
(* (* x y) z)
10.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
28.2b
(sqrt (- (* z z) (* t a)))

rewrite108.0ms

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:
11.0ms
(- (* z z) (* t a))
35.0ms
(* (* x y) z)
44.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
16.0ms
(sqrt (- (* z z) (* t a)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* z z) (* t a))
40.0ms
(* (* x y) z)
147.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
88 → 88
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01341237
13411135
21495975
done5001974

prune367.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
2.5b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
28.2b
(sqrt (- (* z z) (* t a)))

rewrite76.0ms

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:
29.0ms
(/ (sqrt (- (* z z) (* t a))) z)
8.0ms
(- (* z z) (* t a))
25.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
10.0ms
(sqrt (- (* z z) (* t a)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (sqrt (- (* z z) (* t a))) z)
62.0ms
(- (* z z) (* t a))
165.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
83.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
144 → 144
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02102654
15002421
216412221
done50002218

prune529.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.1b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
2.1b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
28.2b
(sqrt (- (* z z) (* t a)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×add-cube-cbrt *-un-lft-identity
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-exp-log add-cbrt-cube
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 227
Calls
4 calls:
15.0ms
(- (* z z) (* t a))
88.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
20.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
18.0ms
(sqrt (- (* z z) (* t a)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* z z) (* t a))
174.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
85.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
94.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
239 → 239
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03304875
17824362
222704138
done50004135

prune816.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
2.5b
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
28.2b
(sqrt (- (* z z) (* t a)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
347×times-frac
149×add-sqr-sqrt
148×add-cube-cbrt *-un-lft-identity
83×associate-/r*
69×sqrt-prod
51×add-exp-log
29×div-exp
27×add-cbrt-cube
17×associate-/r/
16×sqrt-div
13×cbrt-undiv
10×div-inv
9×flip3-- flip--
7×prod-exp
6×add-log-exp
5×pow1
4×rec-exp 1-exp associate-/l*
3×cbrt-unprod
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 254
Calls
4 calls:
15.0ms
(/ z (sqrt (- (* z z) (* t a))))
13.0ms
(- (* z z) (* t a))
71.0ms
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ z (sqrt (- (* z z) (* t a))))
41.0ms
(- (* z z) (* t a))
132.0ms
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
87.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
266 → 266
Iterations

Useful iterations: 2 (779.0ms)

IterNodesCost
04756155
111224989
226664504
done50014504

prune774.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.3b

regimes421.0ms

Accuracy

85% (2.9b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 22.6b

bsearch134.0ms

Steps
ItersRangePoint
10
4.3064310246787576e+110
1.1096282980114098e+126
2.811098440010323e+123
9
-5.269798588618117e+155
-1.769171722317776e+149
-1.3870375139541522e+152

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02432
12830
done2830

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s8818×body80valid
255.0ms3008×body80nan