Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	56×	body	640	valid
8.0ms	251×	body	80	nan
7.0ms	36×	body	1280	valid
5.0ms	134×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	11×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 17.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.3b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `hypot-def`

Counts

4 → 758

Calls

4 calls:

14.0ms	(sqrt (+ x 1.0))
25.0ms	(/ 1.0 (sqrt (+ x 1.0)))
12.0ms	(/ 1.0 (sqrt x))
136.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ x 1.0))
94.0ms	(/ 1.0 (sqrt (+ x 1.0)))
60.0ms	(/ 1.0 (sqrt x))
167.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.3s

Counts

770 → 770

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	701	40764
1	1531	35216
2	3012	26244
done	5001	20672

prune946.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 17.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
3.3b	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
11×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
9×	`pow1`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `times-frac` `pow1/2` `pow-prod-down` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `fma-neg` `sqrt-unprod` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r` `-commutative` `hypot-def` `div-inv`

Counts

4 → 98

Calls

4 calls:

8.0ms	(sqrt (+ x 1.0))
75.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
40.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series580.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ x 1.0))
345.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
81.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
116.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.5s

Counts

110 → 110

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	204	1790
1	557	1653
2	1868	1321
done	5000	1277

prune360.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
2.9b	(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
22×	`add-sqr-sqrt`
18×	`times-frac`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp` `associate-/l*`
11×	`sqrt-prod`
10×	`associate-*r/`
8×	`pow1` `associate-/r/`
7×	`associate-r` `prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`div-sub` `pow-prod-down` `associate-/l/`
2×	`flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate--l+` `clear-num` `associate-/r*` `flip--`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `*-commutative` `distribute-lft-out`

Counts

4 → 128

Calls

4 calls:

89.0ms	(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
96.0ms	(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
38.0ms	(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

series758.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
531.0ms	(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
65.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
3.0ms	(- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0)))

simplify1.7s

Counts

140 → 140

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	289	3978
1	840	3760
2	3829	2747
done	5000	2704

prune441.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
27×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
19×	`sqrt-prod`
18×	`times-frac`
16×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp` `associate-/l*`
10×	`associate-*r/`
8×	`pow1` `associate-/r/`
7×	`fma-def` `associate-r` `prod-exp` `cbrt-unprod`
6×	`flip3-+` `associate-l` `flip-+` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `div-inv` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r*`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

36.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
29.0ms	(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
56.0ms	(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
27.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series824.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms	(/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
542.0ms	(/ (/ 1.0 (* 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
69.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.2s

Counts

141 → 141

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	268	2572
1	716	2230
2	2805	1845
done	5000	1806

prune350.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	13	21
done	13	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

479.0ms	4096×	body	80	valid
307.0ms	1923×	body	640	valid
284.0ms	8028×	body	80	nan
277.0ms	1136×	body	1280	valid
90.0ms	564×	body	320	valid
19.0ms	281×	body	160	valid