Details

sample79.0ms

Algorithm

intervals

Results

18.0ms	72×	body	640	valid
15.0ms	286×	body	80	nan
9.0ms	30×	body	1280	valid
8.0ms	122×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite365.0ms

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:

13.0ms	(sqrt (+ x 1.0))
22.0ms	(/ 1.0 (sqrt (+ x 1.0)))
11.0ms	(/ 1.0 (sqrt x))
180.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ x 1.0))
131.0ms	(/ 1.0 (sqrt (+ x 1.0)))
67.0ms	(/ 1.0 (sqrt x))
240.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify3.7s

Counts

770 → 770

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	701	40764
1	1585	35304
2	4978	27512
done	5000	27512

prune2.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt x) (sqrt 1.0))
0.2b	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

490×	`times-frac`
384×	`add-sqr-sqrt`
373×	`*-un-lft-identity`
365×	`add-cube-cbrt`
286×	`prod-diff`
140×	`sqrt-prod`
40×	`div-inv`
22×	`fma-neg`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp` `difference-of-squares`
5×	`distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `hypot-udef` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 414

Calls

4 calls:

1.0ms	(hypot (sqrt x) (sqrt 1.0))
12.0ms	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
11.0ms	(/ 1.0 (sqrt x))
95.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

series2.3s

Counts

4 → 12

Calls

4 calls:

427.0ms	(hypot (sqrt x) (sqrt 1.0))
756.0ms	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
74.0ms	(/ 1.0 (sqrt x))
1.1s	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

simplify2.7s

Counts

426 → 426

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	544	22119
1	1302	19334
2	4516	14596
done	5000	14596

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.4b	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

503×	`times-frac`
407×	`add-sqr-sqrt`
385×	`*-un-lft-identity`
369×	`add-cube-cbrt`
286×	`prod-diff`
142×	`sqrt-prod`
42×	`div-inv`
22×	`fma-neg`
14×	`log-prod` `exp-sum`
12×	`difference-of-squares`
10×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`log-div` `exp-diff`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

4 → 435

Calls

4 calls:

8.0ms	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
14.0ms	(/ 1.0 (sqrt x))
50.0ms	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))))
93.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

series2.5s

Counts

4 → 12

Calls

4 calls:

526.0ms	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
70.0ms	(/ 1.0 (sqrt x))
952.0ms	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))))
924.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

simplify2.6s

Counts

447 → 447

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	587	22847
1	1329	20027
2	4441	15197
done	5000	15197

prune1.9s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 22.1b

localize71.0ms

Local error

Found 4 expressions with local error:

2.4b	(pow (exp (* (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

1389×	`times-frac`
1078×	`add-sqr-sqrt`
1045×	`*-un-lft-identity`
1021×	`add-cube-cbrt`
858×	`prod-diff`
384×	`sqrt-prod`
114×	`div-inv`
66×	`fma-neg`
18×	`difference-of-squares`
15×	`distribute-lft-out--`
11×	`add-log-exp`
7×	`pow-unpow`
6×	`pow1`
4×	`add-exp-log` `cbrt-prod` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `unpow-prod-down` `flip3--` `pow-pow` `diff-log` `frac-sub` `flip--`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `log-pow` `sqr-pow`

Counts

4 → 1027

Calls

4 calls:

9.0ms	(pow (exp (* (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))))
63.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))
59.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))
86.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

series23.2s

Counts

4 → 12

Calls

4 calls:

21.0s	(pow (exp (* (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))))) (cbrt (log (- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0)))))))
609.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))
938.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))
687.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

simplify1.2s

Counts

1039 → 1039

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	797	66170
1	2213	58146
done	5001	44795

prune4.0s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 22.1b

regimes142.0ms

Accuracy

0% (0.5b remaining)

Error of 19.8b against oracle of 19.3b and baseline of 19.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
done	8	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

689.0ms	1859×	body	640	valid
333.0ms	7916×	body	80	nan
254.0ms	1156×	body	1280	valid
179.0ms	4044×	body	80	valid
108.0ms	615×	body	320	valid
22.0ms	326×	body	160	valid