Details

sample32.0ms

Algorithm

intervals

Results

15.0ms	93×	body	1280	valid
4.0ms	125×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	6×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	28	12
4	30	12
5	35	12
6	36	12
done	36	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.4b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(hypot 1.0 x)
11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(hypot 1.0 x)
76.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
89.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.5s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	106	904
1	203	828
2	472	778
3	1198	776
4	4103	774
done	5002	774

prune157.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.9b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/l*` `add-log-exp`
4×	`distribute-lft-out`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `associate-/r/` `flip--` `flip-+` `div-inv` `associate-/l/` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow1/2` `diff-log` `div-sub` `pow-prod-down` `sqrt-prod`

Counts

4 → 90

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
25.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series268.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
156.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
70.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
35.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify747.0ms

Counts

102 → 102

Iterations

Useful iterations: done (743.0ms)

Iter	Nodes	Cost
0	163	2352
1	385	2241
2	1282	2071
done	5001	1894

prune254.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.9b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

357×	`times-frac`
276×	`*-un-lft-identity`
210×	`sqrt-prod`
172×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`distribute-lft-out`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
11×	`flip3-+` `flip-+`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`associate-/r*`
6×	`add-log-exp`
4×	`sqrt-pow1` `associate-*r/`
3×	`cbrt-undiv` `div-exp`
2×	`pow1/2` `div-sub` `pow-prod-down` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `diff-log` `clear-num` `flip--` `associate-/l/`

Counts

4 → 281

Calls

4 calls:

44.0ms	(/ (/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
73.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
75.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
32.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.2s

Counts

293 → 293

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	338	19260
1	807	17128
2	2323	16260
done	5000	15353

prune491.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.9b	(log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.9b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`log-prod`
4×	`add-exp-log` `sqrt-pow1` `sqrt-div` `associate-*r/` `log-pow` `add-cbrt-cube`
3×	`exp-prod`
2×	`sub-neg` `flip3-+` `pow1/2` `exp-sum` `pow-prod-down` `sqrt-prod` `flip-+` `associate--r+`
1×	`distribute-rgt-in` `log-div` `flip3--` `distribute-lft-in` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 58

Calls

4 calls:

11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
8.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
32.0ms	(log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
33.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: 3 (550.0ms)

Iter	Nodes	Cost
0	95	1171
1	210	1065
2	641	953
3	2718	946
done	5002	946

prune220.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 16.3b

regimes125.0ms

Accuracy

0% (0.0b remaining)

Error of 14.7b against oracle of 14.7b and baseline of 14.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	43
1	19	43
done	19	43

end0.0ms

sample841.0ms

Algorithm

intervals

Results

470.0ms	2991×	body	1280	valid
114.0ms	3958×	body	80	valid
78.0ms	609×	body	640	valid
26.0ms	308×	body	320	valid
7.0ms	134×	body	160	valid