Details

sample76.0ms

Algorithm

intervals

Results

40.0ms	94×	body	1280	valid
10.0ms	126×	body	80	valid
8.0ms	23×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify88.0ms

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: 17.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
6×	`pow1`
5×	`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

3 → 54

Calls

3 calls:

9.0ms	(/ 1.0 (hypot 1.0 x))
20.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series277.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(/ 1.0 (hypot 1.0 x))
130.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
130.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.4s

Counts

63 → 63

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	105	855
1	202	779
2	471	735
3	1197	733
4	4096	731
done	5001	731

prune172.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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)))))))
1.5b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
61.0ms	(/ (- (* 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)))))))
14.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1.0 (hypot 1.0 x))
109.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
244.0ms	(/ (- (* 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)))))))
59.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	149	2415
1	354	2319
2	1206	2115
done	5000	1912

prune453.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 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	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
1.4b	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

294×	`times-frac`
225×	`add-sqr-sqrt`
219×	`*-un-lft-identity`
113×	`add-cube-cbrt`
96×	`difference-of-squares`
81×	`sqr-pow`
37×	`distribute-lft-out`
36×	`associate-/l*`
33×	`unpow-prod-down`
17×	`add-exp-log` `add-cbrt-cube`
16×	`distribute-lft-out--`
13×	`flip3-+` `flip-+`
12×	`pow1` `associate-/r/`
10×	`associate-*r/`
6×	`div-inv` `add-log-exp`
4×	`frac-times` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-r`
2×	`cube-div` `pow-pow` `div-sub` `associate-*l/` `pow-exp` `rem-cube-cbrt`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `cube-prod` `associate-l` `clear-num` `*-commutative` `flip--` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

94.0ms	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
107.0ms	(/ (/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 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)))))))
28.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
28.0ms	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

series1.0s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
566.0ms	(/ (/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 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)))))))
88.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
220.0ms	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

simplify1.1s

Counts

285 → 285

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	524	22781
1	1442	21876
done	5000	21289

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.4b

localize99.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
0.0b	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 6)
1.4b	(- (pow (pow 1.0 6) 3) (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
53×	`unpow-prod-down`
48×	`difference-of-squares`
45×	`sqr-pow`
40×	`cube-prod`
17×	`*-un-lft-identity`
13×	`pow1` `add-exp-log`
10×	`add-cbrt-cube`
9×	`pow-unpow`
7×	`add-cube-cbrt`
6×	`pow-pow` `pow-exp` `add-log-exp`
5×	`distribute-lft-out--`
4×	`cube-div` `associate-*r/` `rem-cube-cbrt`
3×	`pow-to-exp` `pow-prod-down` `prod-exp`
2×	`cube-mult` `flip3-+` `unpow3` `cbrt-unprod` `flip-+`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 131

Calls

4 calls:

15.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
14.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
19.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 6)
118.0ms	(- (pow (pow 1.0 6) 3) (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3))

series1.3s

Counts

4 → 12

Calls

4 calls:

123.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
109.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
140.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 6)
957.0ms	(- (pow (pow 1.0 6) 3) (pow (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) 3))

simplify1.3s

Counts

143 → 143

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	218	3983
1	561	3639
2	1820	3467
done	5000	3443

prune860.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.4b

regimes186.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	136
1	50	136
done	50	136

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s	2914×	body	1280	valid
264.0ms	4032×	body	80	valid
136.0ms	568×	body	640	valid
42.0ms	325×	body	320	valid
14.0ms	161×	body	160	valid