Details

Time bar (total: 13.3s)

sample34.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms96×body80nan

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done6
16
05

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize15.0ms

Local error

Found 1 expressions with local error:

19.9b
(sqrt (+ (* x x) y))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt sqrt-prod
2×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
1×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ add-log-exp
Counts
1 → 15
Calls
1 calls:
10.0ms
(sqrt (+ (* x x) y))

series58.0ms

Counts
1 → 3
Calls
1 calls:
58.0ms
(sqrt (+ (* x x) y))

simplify2.6s

Counts
18 → 18
Iterations
IterNodes
done5001
42254
3739
2276
1114
051

prune103.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 1 expressions with local error:

0.9b
(/ -1/2 (/ x y))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
43×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×associate-/r*
6×add-cbrt-cube add-exp-log
5×div-inv
3×cbrt-undiv div-exp associate-/l*
1×pow1 clear-num frac-2neg associate-/r/ add-log-exp
Counts
1 → 70
Calls
1 calls:
14.0ms
(/ -1/2 (/ x y))

series29.0ms

Counts
1 → 3
Calls
1 calls:
29.0ms
(/ -1/2 (/ x y))

simplify2.0s

Counts
73 → 73
Iterations
IterNodes
done5101
33102
2976
1371
0150

prune381.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 1/2 (/ y x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×associate-*r*
10×times-frac
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
3×pow1 associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative div-inv add-log-exp
Counts
1 → 32
Calls
1 calls:
11.0ms
(* 1/2 (/ y x))

series25.0ms

Counts
1 → 3
Calls
1 calls:
25.0ms
(* 1/2 (/ y x))

simplify1.7s

Counts
35 → 35
Iterations
IterNodes
done5003
31421
2508
1172
068

prune146.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

6.6b
(- (* (* x x) (* x x)) (* y y))
15.2b
(sqrt (- (* (* x x) (* x x)) (* y y)))
19.9b
(sqrt (- (* x x) y))
19.9b
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
49×add-sqr-sqrt times-frac
38×*-un-lft-identity add-cube-cbrt
19×difference-of-squares
8×sqrt-div
7×associate-/r* associate-/l*
6×pow1 add-cbrt-cube add-exp-log add-log-exp
5×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv sqrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
4 → 125
Calls
4 calls:
33.0ms
(- (* (* x x) (* x x)) (* y y))
67.0ms
(sqrt (- (* (* x x) (* x x)) (* y y)))
15.0ms
(sqrt (- (* x x) y))
81.0ms
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* (* x x) (* x x)) (* y y))
83.0ms
(sqrt (- (* (* x x) (* x x)) (* y y)))
58.0ms
(sqrt (- (* x x) y))
118.0ms
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

simplify3.5s

Counts
137 → 137
Iterations
IterNodes
done5012
34312
2933
1371
0183

prune715.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes414.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.1b

bsearch67.0ms

Steps
ItersRangePoint
7
7.706155067127394e+81
2.2700601279324915e+83
2.2470376765740678e+83
9
-2.466971418500489e+156
-3.577081875012498e+150
-1.3584562935631267e+154

simplify5.0ms

Iterations
IterNodes
done22
122
019

end0.0ms

sample838.0ms

Algorithm
intervals
Results
338.0ms8000×body80valid
91.0ms2696×body80nan