Details

sample33.0ms

Algorithm

intervals

Results

6.0ms	62×	body	640	valid
6.0ms	275×	body	80	nan
4.0ms	140×	body	80	valid
3.0ms	27×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	13×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize8.0ms

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))
3.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite167.0ms

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:

4.0ms	(sqrt (+ x 1.0))
9.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
74.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1.0))
76.0ms	(/ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ 1.0 (sqrt x))
135.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts

770 → 770

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	701	40764
1	1536	36194
2	4134	26234
done	5000	26138

prune994.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
62×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
42×	`prod-diff`
37×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out`
9×	`pow1`
7×	`fma-neg` `associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `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` `hypot-def` `div-inv` `associate-/l*`

Counts

4 → 151

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
55.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
34.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series439.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
276.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
57.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.1s

Counts

163 → 163

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	241	3181
1	655	2542
2	2848	1975
done	5000	1965

prune327.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x)))
0.3b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.5b	(* (sqrt x) (sqrt x))
2.9b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`sqrt-prod`
36×	`*-un-lft-identity`
34×	`pow1`
22×	`add-cube-cbrt`
19×	`swap-sqr`
16×	`sqrt-pow1` `pow1/2` `sqrt-div`
13×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
11×	`flip3-+` `flip-+`
10×	`associate-*l/` `pow-prod-up`
8×	`unswap-sqr`
6×	`pow-prod-down` `associate-/r/` `pow-sqr` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `frac-add` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `pow2` `flip3--` `pow-plus` `sqrt-unprod` `div-exp` `rem-square-sqrt` `*-commutative` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 163

Calls

4 calls:

33.0ms	(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x)))
20.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
7.0ms	(* (sqrt x) (sqrt x))
12.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x)))
16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
15.0ms	(* (sqrt x) (sqrt x))
14.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

simplify1.5s

Counts

175 → 175

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	274	3202
1	722	1874
2	3585	1676
done	5000	1672

prune545.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x))
0.1b	(* (sqrt (+ x 1.0)) x)
0.1b	(* (+ x 1.0) (sqrt x))
0.4b	(/ (* 1.0 1.0) (+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

10.0ms	(+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x))
11.0ms	(* (sqrt (+ x 1.0)) x)
11.0ms	(* (+ x 1.0) (sqrt x))
12.0ms	(/ (* 1.0 1.0) (+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x))
69.0ms	(* (sqrt (+ x 1.0)) x)
56.0ms	(* (+ x 1.0) (sqrt x))
269.0ms	(/ (* 1.0 1.0) (+ (* (+ x 1.0) (sqrt x)) (* (sqrt (+ x 1.0)) x)))

simplify944.0ms

Counts

113 → 113

Iterations

Useful iterations: done (937.0ms)

Iter	Nodes	Cost
0	238	2097
1	662	1887
2	2845	1709
done	5000	1700

prune281.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

regimes49.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	14	17
done	14	17

end0.0ms

sample800.0ms

Algorithm

intervals

Results

167.0ms	1782×	body	640	valid
161.0ms	7968×	body	80	nan
140.0ms	1174×	body	1280	valid
101.0ms	4128×	body	80	valid
41.0ms	607×	body	320	valid
14.0ms	309×	body	160	valid