Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	66×	body	1280	valid
7.0ms	249×	body	80	nan
4.0ms	37×	body	640	valid
4.0ms	123×	body	80	valid
2.0ms	25×	body	320	valid
0.0ms	5×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	7
1	10	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: 32.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.7b	(- (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 → 35

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series15.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify26.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5031	521

prune85.0ms

Filtered

30 candidates to 41 candidates (-36.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.1b

Counts

42 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

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

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
4.0ms	(sqrt (+ x 1.0))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series20.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
4.0ms	(sqrt (+ x 1.0))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5621	1039

prune159.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 0.0b

Counts

84 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ 1.0 x)))
5.0ms	(sqrt (sqrt (+ 1.0 x)))
20.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
16.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (sqrt (+ 1.0 x)))
7.0ms	(sqrt (sqrt (+ 1.0 x)))
10.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
4.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify55.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4928	1732
1	4928	1732

prune255.0ms

Filtered

91 candidates to 173 candidates (-90.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	173	9	182

Merged error: 0.0b

Counts

182 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
74×	`*-un-lft-identity`
32×	`distribute-lft-out`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
21×	`pow1`
16×	`add-cube-cbrt`
15×	`swap-sqr`
14×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
8×	`frac-times` `associate-/r/`
5×	`pow-prod-up`
4×	`associate-r/` `associate-l/` `add-log-exp` `unswap-sqr`
3×	`times-frac` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv`

Counts

4 → 135

Calls

4 calls:

8.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
22.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
25.0ms	(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
16.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
6.0ms	(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify43.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4956	2084
1	4956	2084

prune232.0ms

Filtered

84 candidates to 147 candidates (-75.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	147	9	156

Merged error: 0.0b

Counts

156 → 9

regimes113.0ms

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

sample1.3s

Algorithm

intervals

Results

246.0ms	1738×	body	1280	valid
231.0ms	8058×	body	80	nan
139.0ms	1221×	body	640	valid
123.0ms	4125×	body	80	valid
56.0ms	625×	body	320	valid
18.0ms	291×	body	160	valid

Details

sample38.0ms

simplify2.0ms

prune3.0ms

localize6.0ms

rewrite13.0ms

series15.0ms

simplify26.0ms

prune85.0ms

localize6.0ms

rewrite24.0ms

series20.0ms

simplify37.0ms

prune159.0ms

localize9.0ms

rewrite53.0ms

series28.0ms

simplify55.0ms

prune255.0ms

localize9.0ms

rewrite70.0ms

series44.0ms

simplify43.0ms

prune232.0ms

regimes113.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling