Details

analyze1.0ms

Algorithm

Search

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

sample29.0ms

Algorithm

intervals

Results

10.0ms	69×	body	640	valid
7.0ms	38×	body	1280	valid
4.0ms	122×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	265	11
1	265	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: 20.7b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
2.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 132

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
34.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
13.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5076	1839

prune254.0ms

Filtered

103 candidates to 144 candidates (-39.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	134	10	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	10	145

Merged error: 20.1b

Counts

145 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.1b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))
2.0b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
19.0ms	(/ (* 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))

series47.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
28.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
9.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify40.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5212	1577

prune185.0ms

Filtered

76 candidates to 104 candidates (-36.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 0.2b

Counts

114 → 5

localize11.0ms

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))))
0.3b	(* (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))
14.0ms	(/ (+ 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)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
31.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5523	2087

prune254.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	133	9	142

Merged error: 0.0b

Counts

142 → 9

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

rewrite35.0ms

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))))
6.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
12.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
10.0ms	(/ (* 1.0 1.0) (+ 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)))

simplify83.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4975	4295
1	4975	4295

prune338.0ms

Filtered

127 candidates to 188 candidates (-48.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	182	6	188
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	188	9	197

Merged error: 0b

Counts

197 → 9

regimes52.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	13	18

end0.0ms

sample797.0ms

Algorithm

intervals

Results

265.0ms	1858×	body	640	valid
207.0ms	1133×	body	1280	valid
152.0ms	4121×	body	80	valid
59.0ms	577×	body	320	valid
22.0ms	311×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify12.0ms

prune5.0ms

localize7.0ms

rewrite52.0ms

series30.0ms

simplify33.0ms

prune254.0ms

localize8.0ms

rewrite41.0ms

series47.0ms

simplify40.0ms

prune185.0ms

localize11.0ms

rewrite55.0ms

series52.0ms

simplify62.0ms

prune254.0ms

localize11.0ms

rewrite35.0ms

series48.0ms

simplify83.0ms

prune338.0ms

regimes52.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample797.0ms

Profiling