Details

analyze2.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 50.024414%

Guaranteed chance to sample good point: 100%

sample26.0ms

Algorithm

intervals

Results

7.0ms	49×	body	640	valid
6.0ms	32×	body	1280	valid
5.0ms	136×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	14×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

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: 20.6b

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))
4.7b	(- (/ 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 → 133

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:

4.0ms	(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))))

simplify61.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	610	1151
1	2301	1116
2	5001	1086

prune266.0ms

Filtered

100 candidates to 145 candidates (-45.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	133	12	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	12	146

Merged error: 19.9b

Counts

146 → 12

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
4.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite39.0ms

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 → 93

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
16.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
31.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify99.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	835	1032
1	4250	935
2	5001	927

prune211.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Merged error: 19.4b

Counts

117 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
4.1b	(+ x (- 1.0 x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

14.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
5.0ms	(+ x (- 1.0 x))

series48.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify39.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	938	1674
1	5002	1471

prune263.0ms

Filtered

91 candidates to 148 candidates (-62.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	5	148
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	150	10	160

Merged error: 0.3b

Counts

160 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
18.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
10.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
11.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	935	1330
1	5001	1177

prune232.0ms

Filtered

91 candidates to 130 candidates (-42.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	117	13	130
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	124	16	140

Merged error: 0.0b

Counts

140 → 16

regimes84.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

analyze1.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 50.024414%

Guaranteed chance to sample good point: 100%

sample779.0ms

Algorithm

intervals

Results

260.0ms	1855×	body	640	valid
191.0ms	1096×	body	1280	valid
153.0ms	4051×	body	80	valid
63.0ms	626×	body	320	valid
25.0ms	372×	body	160	valid

Details

analyze2.0ms

sample26.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite52.0ms

series30.0ms

simplify61.0ms

prune266.0ms

localize8.0ms

rewrite39.0ms

series50.0ms

simplify99.0ms

prune211.0ms

localize11.0ms

rewrite56.0ms

series48.0ms

simplify39.0ms

prune263.0ms

localize9.0ms

rewrite44.0ms

series53.0ms

simplify37.0ms

prune232.0ms

regimes84.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample779.0ms

Profiling