Details

sample58.0ms

Algorithm

intervals

Results

11.0ms	59×	body	640	valid
11.0ms	44×	body	1280	valid
9.0ms	241×	body	80	nan
6.0ms	123×	body	80	valid
3.0ms	24×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

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

localize32.0ms

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))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite309.0ms

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:

11.0ms	(sqrt (+ x 1.0))
24.0ms	(/ 1.0 (sqrt (+ x 1.0)))
12.0ms	(/ 1.0 (sqrt x))
150.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series869.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (+ x 1.0))
136.0ms	(/ 1.0 (sqrt (+ x 1.0)))
496.0ms	(/ 1.0 (sqrt x))
186.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.9s

Counts

770 → 770

Iterations

Useful iterations: done (2.8s)

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

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 17.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.2b	(* (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))) (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

2210×	`times-frac`
1853×	`*-un-lft-identity`
1727×	`add-sqr-sqrt`
1415×	`add-cube-cbrt`
1350×	`sqrt-prod`
1188×	`prod-diff`
156×	`distribute-lft-out`
113×	`div-inv`
112×	`sqrt-div`
88×	`associate-/r/`
86×	`difference-of-squares`
80×	`distribute-lft-out--`
52×	`swap-sqr`
44×	`flip3-+` `fma-neg` `flip-+`
26×	`associate-r` `associate-l`
19×	`pow1`
10×	`flip3--` `frac-sub` `flip--`
9×	`frac-times`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `associate-/l*`
2×	`sub-neg` `diff-log`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 1493

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt x))
652.0ms	(* (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))) (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
122.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
92.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series646.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1.0 (sqrt x))
212.0ms	(* (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))) (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
193.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
178.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.3s

Counts

1505 → 1505

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	800	85255
1	1642	70722
2	3496	54179
done	5000	54034

prune3.3s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 17.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite819.0ms

Algorithm

rewrite-expression-head

Rules

3984×	`times-frac`
3336×	`*-un-lft-identity`
2836×	`add-sqr-sqrt`
2716×	`add-cube-cbrt`
2376×	`prod-diff`
2136×	`sqrt-prod`
276×	`distribute-lft-out`
208×	`div-inv`
176×	`sqrt-div` `associate-/r/`
88×	`flip3-+` `fma-neg` `flip-+`
44×	`distribute-lft-out--`
36×	`difference-of-squares`
12×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 2604

Calls

4 calls:

106.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
111.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
95.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
87.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
166.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
157.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
183.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.3s

Counts

2616 → 2616

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	650	158056
1	1433	136480
2	2775	100780
done	5000	78492

prune3.1s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 17.4b

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
2.3b	(expm1 (log1p (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

rewrite529.0ms

Algorithm

rewrite-expression-head

Rules

2988×	`times-frac`
2503×	`*-un-lft-identity`
2128×	`add-sqr-sqrt`
2038×	`add-cube-cbrt`
1782×	`prod-diff`
1602×	`sqrt-prod`
207×	`distribute-lft-out`
156×	`div-inv`
132×	`sqrt-div` `associate-/r/`
66×	`flip3-+` `fma-neg` `flip-+`
33×	`distribute-lft-out--`
27×	`difference-of-squares`
10×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 1964

Calls

4 calls:

88.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
85.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
97.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
0.0ms	(expm1 (log1p (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
135.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
136.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
930.0ms	(expm1 (log1p (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))

simplify2.0s

Counts

1976 → 1976

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	714	118953
1	1612	102336
2	3372	75922
done	5001	65861

prune2.8s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 17.4b

regimes231.0ms

Accuracy

0% (0.8b remaining)

Error of 19.8b against oracle of 19.0b and baseline of 19.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	11	25
done	11	25

end0.0ms

sample1.8s

Algorithm

intervals

Results

612.0ms	8200×	body	80	nan
390.0ms	1792×	body	640	valid
218.0ms	1096×	body	1280	valid
149.0ms	4115×	body	80	valid
104.0ms	688×	body	320	valid
21.0ms	309×	body	160	valid