Details

sample48.0ms

Algorithm

intervals

Results

22.0ms	81×	body	1280	valid
8.0ms	148×	body	80	valid
4.0ms	19×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	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: 13.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (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))
1.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

20.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
25.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
103.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
15.0ms	(/ 1.0 (hypot 1.0 x))
120.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify4.7s

Counts

78 → 78

Iterations

Useful iterations: 4 (2.8s)

Iter	Nodes	Cost
0	112	1034
1	223	951
2	538	887
3	1394	885
4	4985	881
done	5000	881

prune261.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))
0.7b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

24.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series216.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
16.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(/ 1.0 (hypot 1.0 x))
54.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify2.3s

Counts

93 → 93

Iterations

Useful iterations: 3 (843.0ms)

Iter	Nodes	Cost
0	112	1111
1	244	1028
2	720	960
3	2865	953
done	5002	953

prune379.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 0.5 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.6b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 0.5 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
20.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(/ 0.5 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
49.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify2.2s

Counts

94 → 94

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	143	1026
1	275	955
2	604	905
3	1568	905
done	5000	901

prune366.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.0b	(* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
0.1b	(pow (/ 0.5 (hypot 1.0 x)) 3)
0.6b	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

300×	`add-sqr-sqrt`
167×	`times-frac`
120×	`difference-of-squares`
117×	`*-un-lft-identity`
103×	`unpow-prod-down` `cube-prod`
65×	`add-cube-cbrt`
51×	`sqr-pow`
33×	`associate-/l*`
25×	`distribute-lft-out--`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-l`
7×	`pow1`
6×	`add-log-exp`
5×	`difference-cubes`
4×	`associate-r` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `associate-/r*` `flip-+`
2×	`frac-times` `flip3--` `associate-*r/` `pow-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-div` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 279

Calls

4 calls:

211.0ms	(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
90.0ms	(* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
12.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
69.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

series510.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
72.0ms	(* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))
48.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
129.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

simplify3.2s

Counts

291 → 291

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	352	10626
1	978	10151
2	4013	9335
done	5002	9334

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.4b

regimes112.0ms

Accuracy

0% (0.3b remaining)

Error of 14.7b against oracle of 14.4b and baseline of 14.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	52
1	25	52
done	25	52

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	2825×	body	1280	valid
291.0ms	4098×	body	80	valid
183.0ms	619×	body	640	valid
53.0ms	311×	body	320	valid
16.0ms	147×	body	160	valid