Details

sample31.0ms

Algorithm

intervals

Results

6.0ms	286×	body	80	nan
5.0ms	59×	body	640	valid
5.0ms	41×	body	1280	valid
3.0ms	123×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	14	11
done	14	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
3.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
7.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
49.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
77.0ms	(/ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ 1.0 (sqrt x))
132.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.3s

Counts

145 → 145

Iterations

Useful iterations: 3 (700.0ms)

Iter	Nodes	Cost
0	215	1942
1	444	1778
2	1080	1696
3	2990	1673
done	5000	1673

prune313.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
3.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out` `distribute-lft-out--`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
31.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
15.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
26.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series416.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ x 1.0))
254.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
58.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify825.0ms

Counts

105 → 105

Iterations

Useful iterations: done (822.0ms)

Iter	Nodes	Cost
0	189	1624
1	511	1459
2	2085	1218
done	5001	1209

prune241.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.4b	(- (+ x 1.0) x)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
22×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`add-log-exp`
8×	`pow1` `cbrt-undiv` `add-cube-cbrt` `div-exp` `prod-exp` `cbrt-unprod`
7×	`associate-r`
6×	`associate-l` `distribute-lft-out`
5×	`associate-*r/`
4×	`sqrt-div` `unswap-sqr`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`sqrt-pow1` `pow1/2` `diff-log` `sum-log` `associate-/r/` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `times-frac` `sqrt-unprod` `associate--l+` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv` `associate-/l/` `associate-/l*` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

18.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
39.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
16.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
19.0ms	(- (+ x 1.0) x)

series605.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
479.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(- (+ x 1.0) x)

simplify988.0ms

Counts

104 → 104

Iterations

Useful iterations: done (985.0ms)

Iter	Nodes	Cost
0	226	1911
1	633	1740
2	2757	1377
done	5000	1370

prune246.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
0.3b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
31×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
21×	`distribute-lft-out`
19×	`add-cube-cbrt` `times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l*` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

18.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
26.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
26.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series757.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
142.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
55.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
493.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify1.2s

Counts

128 → 128

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	250	2311
1	671	2082
2	2602	1730
done	5000	1721

prune245.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	19	26
done	19	26

end0.0ms

sample817.0ms

Algorithm

intervals

Results

176.0ms	1796×	body	640	valid
164.0ms	8031×	body	80	nan
142.0ms	1162×	body	1280	valid
101.0ms	4077×	body	80	valid
45.0ms	609×	body	320	valid
17.0ms	356×	body	160	valid