Details

sample37.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
8.0ms	251×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	19	6
2	21	6
3	21	6

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

localize201.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 91

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
8.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))

series18.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
5.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify38.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	354	753
1	1071	709
2	5001	688

prune181.0ms

Filtered

70 candidates to 100 candidates (-42.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	2	101

Merged error: 0b

Counts

101 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
0.0b	(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
0.0b	(/ (- 1.0 x) (sqrt (+ 1.0 x)))
0.0b	(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

1144×	`times-frac`
1015×	`*-un-lft-identity`
954×	`sqrt-prod`
704×	`add-sqr-sqrt`
461×	`add-cube-cbrt`
164×	`distribute-lft-out`
113×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-/l*`
37×	`sqrt-div`
36×	`associate-/r/`
18×	`flip3-+` `flip-+` `div-inv`
14×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
7×	`rem-sqrt-square`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 734

Calls

4 calls:

1.0ms	(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
44.0ms	(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
9.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))
23.0ms	(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
5.0ms	(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
8.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))
3.0ms	(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

simplify175.0ms

Algorithm

egg-herbie

Counts

746 → 746

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1239	12138
1	4185	10880
2	5001	10724

prune943.0ms

Filtered

228 candidates to 746 candidates (-227.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	746	0	746
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	746	2	748

Merged error: 0b

Counts

748 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (sqrt (+ 1.0 (* 2.0 (- (pow x 2) x)))))
0.0b	(sqrt (+ 1.0 (* 2.0 (- (pow x 2) x))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (sqrt (+ 1.0 (* 2.0 (- (pow x 2) x)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (- (pow x 2) x))))

series8.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (sqrt (+ 1.0 (* 2.0 (- (pow x 2) x)))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (- (pow x 2) x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	187	261
1	543	239
2	2840	229
3	5001	228

prune59.0ms

Filtered

22 candidates to 28 candidates (-27.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	28	2	30

Merged error: 0b

Counts

30 → 2

regimes28.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	10
1	13	10

end0.0ms

sample894.0ms

Algorithm

intervals

Results

380.0ms	8000×	body	80	valid
268.0ms	8044×	body	80	nan

Details

sample37.0ms

simplify11.0ms

prune4.0ms

localize201.0ms

rewrite24.0ms

series18.0ms

simplify38.0ms

prune181.0ms

localize13.0ms

rewrite143.0ms

series17.0ms

simplify175.0ms

prune943.0ms

localize10.0ms

rewrite4.0ms

series8.0ms

simplify75.0ms

prune59.0ms

regimes28.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample894.0ms

Profiling