Details

sample54.0ms

Algorithm

intervals

Results

27.0ms	98×	body	1280	valid
6.0ms	123×	body	80	valid
4.0ms	18×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	22	12
2	31	12
3	37	12
done	37	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

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:

0.0ms	(hypot 1.0 x)
26.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
33.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(hypot 1.0 x)
113.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
15.0ms	(/ 1.0 (hypot 1.0 x))
121.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.2s

Counts

73 → 73

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	106	904
1	536	808
done	5000	776

prune272.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.8b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(/ 1.0 (hypot 1.0 x))
52.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.3s

Counts

92 → 92

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	109	1174
1	876	1112
done	5000	1005

prune366.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.7b

localize69.0ms

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 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (* (pow 1.0 3) 1.0) (* (* 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 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
1.7b	(- (pow (* 1.0 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`difference-of-squares`
39×	`times-frac`
34×	`*-un-lft-identity`
31×	`sqr-pow`
24×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`pow1`
11×	`unpow-prod-down` `cube-prod`
10×	`associate-*r/`
8×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`difference-cubes` `distribute-lft-out--`
4×	`frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`pow-unpow` `associate-r` `associate-/r*`
2×	`cube-div` `flip3--` `pow-pow` `associate-*l/` `pow-exp` `associate-/r/` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `div-exp` `associate-l` `clear-num` `*-commutative` `div-inv`

Counts

4 → 146

Calls

4 calls:

90.0ms	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
79.0ms	(/ (- (pow (* 1.0 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (* (pow 1.0 3) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
31.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
31.0ms	(- (pow (* 1.0 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

series865.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
466.0ms	(/ (- (pow (* 1.0 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (* (pow 1.0 3) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
95.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
190.0ms	(- (pow (* 1.0 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

simplify1.2s

Counts

158 → 158

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	274	8236
done	5000	7861

prune954.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.7b

localize75.0ms

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 3) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (pow (* 1.0 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))
1.7b	(- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `flip3-+` `flip-+`
6×	`pow-unpow` `associate-*r/` `add-log-exp`
5×	`associate-r` `pow-prod-down`
4×	`cube-div` `frac-times` `pow-pow` `pow-exp` `rem-cube-cbrt`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-*l/` `sqr-pow`
1×	`difference-cubes` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `sum-cubes` `*-commutative` `flip--` `distribute-lft-out` `difference-of-squares` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

16.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
22.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
146.0ms	(* (+ (* (pow 1.0 3) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (pow (* 1.0 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))
23.0ms	(- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
118.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
371.0ms	(* (+ (* (pow 1.0 3) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (pow (* 1.0 1.0) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))
556.0ms	(- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))

simplify4.0s

Counts

104 → 104

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	211	4241
1	2755	3585
done	5001	3235

prune689.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.7b

regimes432.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	42	186
1	60	184
2	61	182
done	61	182

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	2834×	body	1280	valid
283.0ms	4075×	body	80	valid
196.0ms	609×	body	640	valid
91.0ms	327×	body	320	valid
16.0ms	155×	body	160	valid