Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample28.0ms

Algorithm

intervals

Results

9.0ms	64×	body	640	valid
5.0ms	29×	body	1280	valid
5.0ms	134×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	13×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	9	11

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 19.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.4b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
69×	`times-frac`
46×	`sqrt-prod`
40×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+`

Counts

3 → 116

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
37.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series27.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ 1.0 (sqrt x))
13.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4975	1654
1	4975	1654

prune220.0ms

Filtered

87 candidates to 125 candidates (-43.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	13	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	13	126

Merged error: 18.6b

Counts

126 → 13

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.2b	(* (sqrt x) (sqrt (+ 1.0 x)))
3.4b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
17×	`add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt` `associate-r`
6×	`associate-r/` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`pow-prod-down` `distribute-lft-out--`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

3 → 76

Calls

3 calls:

17.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
8.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series49.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
10.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify35.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5302	1342

prune149.0ms

Filtered

61 candidates to 85 candidates (-39.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	92	6	98

Merged error: 0.3b

Counts

98 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.2b	(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`distribute-lft-out`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `associate-r/` `flip-+` `associate-/l`
4×	`sqrt-div` `associate-/r/` `unswap-sqr`
3×	`pow-prod-down` `associate-/l/`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative`

Counts

4 → 125

Calls

4 calls:

8.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
20.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
35.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
7.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4962	2089
1	4962	2089

prune247.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	128	9	137
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	132	11	143

Merged error: 0.0b

Counts

143 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
0.1b	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
0.3b	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
72×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
55×	`sqrt-prod`
48×	`add-cube-cbrt`
23×	`distribute-lft-out`
20×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
11×	`associate-/r` `associate-/l`
10×	`div-inv`
8×	`pow1`
7×	`cbrt-undiv` `div-exp` `associate-r`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

3.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
15.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
6.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
27.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
11.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4978	4286
1	4978	4286

prune346.0ms

Filtered

129 candidates to 188 candidates (-45.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	189	10	199

Merged error: 0.0b

Counts

199 → 10

regimes56.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	18	25

end0.0ms

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample824.0ms

Algorithm

intervals

Results

277.0ms	1846×	body	640	valid
209.0ms	1135×	body	1280	valid
157.0ms	4080×	body	80	valid
68.0ms	630×	body	320	valid
24.0ms	309×	body	160	valid

Details

analyze1.0ms

sample28.0ms

simplify3.0ms

prune5.0ms

localize7.0ms

rewrite52.0ms

series27.0ms

simplify48.0ms

prune220.0ms

localize8.0ms

rewrite36.0ms

series49.0ms

simplify35.0ms

prune149.0ms

localize10.0ms

rewrite55.0ms

series57.0ms

simplify44.0ms

prune247.0ms

localize11.0ms

rewrite39.0ms

series50.0ms

simplify90.0ms

prune346.0ms

regimes56.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample824.0ms

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