Details

sample46.0ms

Algorithm

intervals

Results

12.0ms	55×	body	1280	valid
9.0ms	64×	body	640	valid
8.0ms	246×	body	80	nan
5.0ms	118×	body	80	valid
2.0ms	15×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 20.7b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.1b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite50.0ms

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:

6.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
29.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series649.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (+ x 1.0))
121.0ms	(/ 1.0 (sqrt (+ x 1.0)))
215.0ms	(/ 1.0 (sqrt x))
263.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify65.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (52.0ms)

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

prune312.0ms

Filtered

145 candidates to 100 candidates (69.0%)

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: 20.3b

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)))
2.1b	(- (sqrt (+ x 1.0)) (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 → 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)))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series1.1s

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ x 1.0))
694.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
117.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
184.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify102.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	835	1033
1	4245	935
2	5002	927

prune251.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Merged error: 20.1b

Counts

117 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 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)))
1.9b	(+ x (- 1.0 x))

rewrite57.0ms

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)))
21.0ms	(/ (* 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)))
6.0ms	(+ x (- 1.0 x))

series1.2s

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
855.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
118.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify41.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	938	1674
1	5002	1471

prune339.0ms

Filtered

148 candidates to 91 candidates (61.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	151	10	161

Merged error: 0.2b

Counts

161 → 10

localize10.0ms

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)))

rewrite41.0ms

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

series1.2s

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (+ x 1.0))
215.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
852.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
125.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	935	1330
1	5001	1177

prune285.0ms

Filtered

130 candidates to 91 candidates (70.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	120	10	130
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	126	14	140

Merged error: 0.0b

Counts

140 → 14

regimes51.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

285.0ms	8240×	body	80	nan
263.0ms	1853×	body	640	valid
208.0ms	1165×	body	1280	valid
150.0ms	4049×	body	80	valid
61.0ms	596×	body	320	valid
23.0ms	337×	body	160	valid

Details

sample46.0ms

simplify5.0ms

prune2.0ms

localize7.0ms

rewrite50.0ms

series649.0ms

simplify65.0ms

prune312.0ms

localize8.0ms

rewrite41.0ms

series1.1s

simplify102.0ms

prune251.0ms

localize12.0ms

rewrite57.0ms

series1.2s

simplify41.0ms

prune339.0ms

localize10.0ms

rewrite41.0ms

series1.2s

simplify48.0ms

prune285.0ms

regimes51.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling