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

8.0ms	54×	body	640	valid
7.0ms	36×	body	1280	valid
5.0ms	135×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	15×	body	160	valid

simplify11.0ms

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: 18.3b

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)))
0.3b	(/ 1.0 (sqrt x))
3.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite51.0ms

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))))

series29.0ms

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

prune259.0ms

Filtered

103 candidates to 144 candidates (-39.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	131	13	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	13	145

Merged error: 17.6b

Counts

145 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.2b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.2b	(* (sqrt x) (sqrt (+ 1.0 x)))
2.9b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite40.0ms

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 x))
30.0ms	(/ (* 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))

simplify37.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5212	1577

prune186.0ms

Filtered

76 candidates to 104 candidates (-36.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	111	6	117

Merged error: 0.2b

Counts

117 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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:

7.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
22.0ms	(/ (* 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)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
32.0ms	(/ (* 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 (49.0ms)

Iter	Nodes	Cost
0	5523	2087

prune252.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	133	10	143

Merged error: 0.0b

Counts

143 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt x) (fabs (cbrt (+ x 1.0))))
0.2b	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (* (sqrt x) (fabs (cbrt (+ x 1.0)))) (sqrt (cbrt (+ 1.0 x)))))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ 1.0 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (sqrt x) (fabs (cbrt (+ x 1.0))))
23.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (* (sqrt x) (fabs (cbrt (+ x 1.0)))) (sqrt (cbrt (+ 1.0 x)))))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ 1.0 x))

series99.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt x) (fabs (cbrt (+ x 1.0))))
79.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (* (sqrt x) (fabs (cbrt (+ x 1.0)))) (sqrt (cbrt (+ 1.0 x)))))
8.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ 1.0 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4969	2196
1	4969	2196

prune252.0ms

Filtered

71 candidates to 96 candidates (-35.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Merged error: 0.0b

Counts

106 → 10

regimes61.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	26
1	22	26

end0.0ms

sample830.0ms

Algorithm

intervals

Results

261.0ms	1763×	body	640	valid
216.0ms	1149×	body	1280	valid
166.0ms	4168×	body	80	valid
68.0ms	604×	body	320	valid
23.0ms	316×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify11.0ms

prune5.0ms

localize7.0ms

rewrite51.0ms

series29.0ms

simplify33.0ms

prune259.0ms

localize9.0ms

rewrite40.0ms

series49.0ms

simplify37.0ms

prune186.0ms

localize11.0ms

rewrite54.0ms

series55.0ms

simplify62.0ms

prune252.0ms

localize17.0ms

rewrite36.0ms

series99.0ms

simplify48.0ms

prune252.0ms

regimes61.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample830.0ms

Profiling