Details

Time bar (total: 15.9s)

sample88.0ms

Algorithm
intervals
Results
46.0ms290×body80valid
15.0ms103×body80nan

simplify109.0ms

Counts
1 → 1
Iterations
IterNodes
done106
6106
597
477
358
237
122
012

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.1b
(* (* x y) z)
9.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cube-cbrt
9×sqrt-prod
6×associate-/r* times-frac prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff *-commutative div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
18.0ms
(- (* z z) (* t a))
30.0ms
(* (* x y) z)
48.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
19.0ms
(sqrt (- (* z z) (* t a)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) z)
126.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
83.0ms
(sqrt (- (* z z) (* t a)))

simplify837.0ms

Counts
102 → 102
Iterations
IterNodes
done2009
21508
1385
0150

prune580.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
3.6b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×*-un-lft-identity add-cube-cbrt
33×sqrt-prod
25×associate-/r*
18×add-cbrt-cube add-exp-log
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u div-inv
3×flip3-- flip--
2×clear-num frac-2neg prod-exp cbrt-unprod associate-/l/
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 146
Calls
4 calls:
18.0ms
(/ (sqrt (- (* z z) (* t a))) z)
8.0ms
(- (* z z) (* t a))
16.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
10.0ms
(sqrt (- (* z z) (* t a)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (sqrt (- (* z z) (* t a))) z)
62.0ms
(- (* z z) (* t a))
104.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
158 → 158
Iterations
IterNodes
done2000
21959
1588
0226

prune818.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
3.6b
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
347×times-frac
149×add-sqr-sqrt
148×*-un-lft-identity add-cube-cbrt
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×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u associate-/l*
3×cbrt-unprod
2×clear-num frac-2neg
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 268
Calls
4 calls:
12.0ms
(/ z (sqrt (- (* z z) (* t a))))
8.0ms
(- (* z z) (* t a))
29.0ms
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ z (sqrt (- (* z z) (* t a))))
50.0ms
(- (* z z) (* t a))
111.0ms
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
75.0ms
(sqrt (- (* z z) (* t a)))

simplify1.0s

Counts
280 → 280
Iterations
IterNodes
done2006
11417
0491

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.0b
(/ y (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
2.0b
(* x (/ y (/ 1 (/ z (sqrt (- (* z z) (* t a)))))))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
1361×times-frac
641×add-sqr-sqrt
613×*-un-lft-identity
610×add-cube-cbrt
236×associate-*r*
194×sqrt-prod
77×associate-/r*
51×add-exp-log associate-/r/
44×sqrt-div
30×div-inv
28×div-exp
27×add-cbrt-cube
23×flip3-- flip--
12×cbrt-undiv
8×prod-exp unswap-sqr
7×pow1
6×add-log-exp
4×expm1-log1p-u rec-exp 1-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-*l* associate-/l*
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down associate-*r/ *-commutative
Counts
4 → 642
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
19.0ms
(/ y (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
81.0ms
(* x (/ y (/ 1 (/ z (sqrt (- (* z z) (* t a)))))))
20.0ms
(sqrt (- (* z z) (* t a)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* z z) (* t a))
71.0ms
(/ y (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
127.0ms
(* x (/ y (/ 1 (/ z (sqrt (- (* z z) (* t a)))))))
110.0ms
(sqrt (- (* z z) (* t a)))

simplify979.0ms

Counts
654 → 654
Iterations
IterNodes
done2000
0930

prune3.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.5b

regimes999.0ms

Accuracy

84.4% (3.1b remaining)

Error of 6.3b against oracle of 3.3b and baseline of 23.0b

bsearch143.0ms

Steps
ItersRangePoint
9
3.0793339614790758e+57
6.511477481037166e+66
4.1336262698551934e+63
8
-9.085603498737435e+154
-2.0214746804973124e+152
-1.3222627138699112e+154

simplify11.0ms

Iterations
IterNodes
done43
143
034

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.5s8878×body80valid
386.0ms2989×body80nan