Details

Time bar (total: 11.8s)

sample29.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms96×body80nan

simplify2.0ms

Counts
1 → 1
Iterations
IterNodes
done6
16
05

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize8.0ms

Local error

Found 1 expressions with local error:

16.2b
(sqrt (+ (* x x) y))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt sqrt-prod
pow1 *-un-lft-identity sqrt-div add-cube-cbrt
rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
1 → 16
Calls
1 calls:
7.0ms
(sqrt (+ (* x x) y))

series62.0ms

Counts
1 → 3
Calls
1 calls:
62.0ms
(sqrt (+ (* x x) y))

simplify2.0s

Counts
19 → 19
Iterations
IterNodes
done5000
42302
3793
2279
1115
052

prune118.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×associate-*r*
10×*-un-lft-identity times-frac add-cube-cbrt
add-cbrt-cube add-exp-log
pow1 add-log-exp
associate-*l*
prod-exp cbrt-unprod insert-posit16 unswap-sqr
cbrt-undiv sub-neg flip3-- diff-log div-exp pow-prod-down associate-*r/ *-commutative div-inv flip--
Counts
2 → 46
Calls
2 calls:
8.0ms
(- (* -1/2 (/ y x)) x)
12.0ms
(* -1/2 (/ y x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(- (* -1/2 (/ y x)) x)
29.0ms
(* -1/2 (/ y x))

simplify1.4s

Counts
52 → 52
Iterations
IterNodes
done5000
31752
2641
1229
094

prune178.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×associate-*r*
10×*-un-lft-identity times-frac add-cube-cbrt
add-cbrt-cube add-exp-log
pow1 add-log-exp
associate-*l*
prod-exp cbrt-unprod insert-posit16 unswap-sqr
cbrt-undiv +-commutative sum-log flip3-+ div-exp pow-prod-down associate-*r/ *-commutative flip-+ div-inv
Counts
2 → 45
Calls
2 calls:
5.0ms
(+ x (* 1/2 (/ y x)))
8.0ms
(* 1/2 (/ y x))

series61.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(+ x (* 1/2 (/ y x)))
29.0ms
(* 1/2 (/ y x))

simplify2.0s

Counts
51 → 51
Iterations
IterNodes
done5003
32154
2712
1234
089

prune155.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

4.5b
(- (* (* x x) (* x x)) (* y y))
12.8b
(sqrt (- (* (* x x) (* x x)) (* y y)))
16.2b
(sqrt (- (* x x) y))
16.2b
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

rewrite217.0ms

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
sqrt-div
associate-/r* associate-/l*
pow1 add-cbrt-cube add-exp-log add-log-exp
flip3-- flip--
insert-posit16
rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
cbrt-undiv sqrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
4 → 129
Calls
4 calls:
51.0ms
(- (* (* x x) (* x x)) (* y y))
69.0ms
(sqrt (- (* (* x x) (* x x)) (* y y)))
16.0ms
(sqrt (- (* x x) y))
78.0ms
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (* (* x x) (* x x)) (* y y))
86.0ms
(sqrt (- (* (* x x) (* x x)) (* y y)))
53.0ms
(sqrt (- (* x x) y))
128.0ms
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

simplify3.1s

Counts
141 → 141
Iterations
IterNodes
done5023
34225
2941
1375
0187

prune551.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes259.0ms

Accuracy

97.9% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 19.7b

bsearch64.0ms

Steps
ItersRangePoint
8
1.514115744383235e+64
1.0077232000722927e+68
9.943288082924311e+67
9
-3.59454624536844e+155
-4.448318838164251e+147
-1.3262598264970426e+154

simplify5.0ms

Iterations
IterNodes
done22
122
018

end0.0ms

sample1.1s

Algorithm
intervals
Results
822.0ms8000×body80valid
106.0ms2731×body80nan