Details

sample286.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
11.0ms	294×	body	80	nan

simplify13.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(atan (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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 97

Calls

3 calls:

7.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))

series150.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
55.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	370	779
1	1128	734
2	5001	719

prune218.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 0b

Counts

107 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

582×	`*-un-lft-identity`
484×	`times-frac`
332×	`add-sqr-sqrt`
324×	`prod-diff`
320×	`add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/r/`
41×	`flip3-+` `flip-+` `div-inv`
18×	`fma-neg`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 451

Calls

4 calls:

1.0ms	(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
5.0ms	(/ x (+ x 1.0))
32.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))
5.0ms	(/ 1.0 (+ x 1.0))

series120.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
33.0ms	(/ x (+ x 1.0))
59.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))
25.0ms	(/ 1.0 (+ x 1.0))

simplify153.0ms

Algorithm

egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	1032	11091
1	3079	8021
2	5001	7159

prune500.0ms

Filtered

463 candidates to 161 candidates (34.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	463	0	463
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	463	2	465

Merged error: 0b

Counts

465 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(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)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

602×	`times-frac`
562×	`*-un-lft-identity`
388×	`add-sqr-sqrt`
360×	`sqrt-prod`
254×	`add-cube-cbrt`
90×	`distribute-lft-out`
64×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `hypot-def`
1×	`flip3--` `flip--`

Counts

4 → 459

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 x))
3.0ms	(sqrt (+ 1.0 x))
13.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))
22.0ms	(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

series188.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ 1.0 x))
30.0ms	(sqrt (+ 1.0 x))
89.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))
40.0ms	(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

simplify119.0ms

Algorithm

egg-herbie

Counts

471 → 471

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	935	6225
1	3542	5496
2	5001	5489

prune587.0ms

Filtered

471 candidates to 179 candidates (38.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	471	0	471
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	471	2	473

Merged error: 0b

Counts

473 → 2

regimes13.0ms

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	12	8
1	12	8

end0.0ms

sample893.0ms

Algorithm

intervals

Results

406.0ms	8000×	body	80	valid
284.0ms	7922×	body	80	nan

Details

sample286.0ms

simplify13.0ms

prune4.0ms

localize11.0ms

rewrite24.0ms

series150.0ms

simplify42.0ms

prune218.0ms

localize9.0ms

rewrite86.0ms

series120.0ms

simplify153.0ms

prune500.0ms

localize10.0ms

rewrite76.0ms

series188.0ms

simplify119.0ms

prune587.0ms

regimes13.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample893.0ms

Profiling