Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample27.0ms

Algorithm

intervals

Results

8.0ms	61×	body	1280	valid
8.0ms	45×	body	640	valid
3.0ms	123×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune3.0ms

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: 31.6b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 34

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series14.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune71.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.1b

Counts

41 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify25.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5038	1051

prune138.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	76	7	83

Merged error: 0.0b

Counts

83 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
0.3b	(cbrt (+ 1.0 x))
0.3b	(cbrt (+ 1.0 x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
8.0ms	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
3.0ms	(cbrt (+ 1.0 x))
3.0ms	(cbrt (+ 1.0 x))

series66.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
11.0ms	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
6.0ms	(cbrt (+ 1.0 x))
6.0ms	(cbrt (+ 1.0 x))

simplify55.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5760	2085

prune299.0ms

Filtered

80 candidates to 98 candidates (-22.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	98	7	105

Merged error: 0.0b

Counts

105 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

10.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
37.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
16.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4952	4249
1	4952	4249

prune443.0ms

Filtered

143 candidates to 262 candidates (-83.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	261	8	269

Merged error: 0.0b

Counts

269 → 8

regimes55.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

end0.0ms

sample596.0ms

Algorithm

intervals

Results

214.0ms	1699×	body	1280	valid
127.0ms	1287×	body	640	valid
108.0ms	4130×	body	80	valid
44.0ms	576×	body	320	valid
15.0ms	308×	body	160	valid
0.0ms	7×	body	80	nan

Details

analyze3.0ms

sample27.0ms

simplify4.0ms

prune3.0ms

localize5.0ms

rewrite13.0ms

series14.0ms

simplify46.0ms

prune71.0ms

localize6.0ms

rewrite24.0ms

series18.0ms

simplify25.0ms

prune138.0ms

localize10.0ms

rewrite26.0ms

series66.0ms

simplify55.0ms

prune299.0ms

localize9.0ms

rewrite81.0ms

series53.0ms

simplify87.0ms

prune443.0ms

regimes55.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample596.0ms

Profiling