Details

sample77.0ms

Algorithm

intervals

Results

45.0ms	94×	body	1280	valid
8.0ms	124×	body	80	valid
5.0ms	16×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid

simplify64.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize20.0ms

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)))))
2.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite57.0ms

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)
37.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(hypot 1.0 x)
89.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
132.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.0s

Counts

73 → 73

Iterations

Useful iterations: 3 (887.0ms)

Iter	Nodes	Cost
0	106	904
1	218	828
2	714	778
3	4140	776
done	5001	776

prune252.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
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)))))))
2.3b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
6×	`add-log-exp`
4×	`pow1` `distribute-lft-out`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `diff-log` `div-sub` `flip-+`

Counts

4 → 104

Calls

4 calls:

9.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(/ 1.0 (hypot 1.0 x))
30.0ms	(/ (- (* 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)))))))
9.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
228.0ms	(/ (- (* 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)))))))
47.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.1s

Counts

116 → 116

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	141	2407
1	375	2331
2	1916	2145
done	5000	2112

prune453.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (/ 1.0 (hypot 1.0 x)))
0.2b	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
2.3b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

92×	`sqrt-prod`
84×	`add-sqr-sqrt`
62×	`times-frac`
50×	`add-cube-cbrt` `*-un-lft-identity`
21×	`pow1`
18×	`swap-sqr`
16×	`associate-r` `associate-l`
10×	`sqrt-pow1` `pow1/2`
9×	`unswap-sqr`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`rem-sqrt-square`
3×	`pow-prod-down` `pow-sqr`
2×	`associate--r+`
1×	`pow2` `distribute-rgt-in` `frac-times` `sub-neg` `flip3--` `distribute-lft-in` `pow-plus` `sqrt-unprod` `diff-log` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 151

Calls

4 calls:

7.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
13.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
32.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
8.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
72.0ms	(sqrt (/ 1.0 (hypot 1.0 x)))
94.0ms	(* (sqrt (/ 1.0 (hypot 1.0 x))) (sqrt (/ 1.0 (hypot 1.0 x))))
50.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.1s

Counts

163 → 163

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	170	2593
1	353	1908
2	1746	1767
done	5000	1740

prune607.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3b	(- (/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
23×	`times-frac`
22×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
7×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`div-inv`
4×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `flip-+`
3×	`distribute-rgt-out--` `frac-2neg` `clear-num`
2×	`associate-*r/` `associate-/l/` `distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--` `sub-div`

Counts

4 → 101

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
38.0ms	(/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
90.0ms	(- (/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series654.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(/ 1.0 (hypot 1.0 x))
241.0ms	(/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
392.0ms	(- (/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	161	2771
1	433	2622
2	2285	2385
done	5001	2368

prune463.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.6b

regimes193.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	86
1	27	86
done	27	86

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	2926×	body	1280	valid
555.0ms	602×	body	640	valid
196.0ms	3978×	body	80	valid
144.0ms	321×	body	320	valid
17.0ms	173×	body	160	valid