Details

sample47.0ms

Algorithm

intervals

Results

9.0ms	267×	body	80	nan
8.0ms	56×	body	640	valid
7.0ms	37×	body	1280	valid
5.0ms	128×	body	80	valid
2.0ms	21×	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

Filtered

1 candidates to 0 candidates (100.0%)

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: 20.1b

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)))
0.2b	(/ 1.0 (sqrt x))
3.7b	(- (/ 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 → 133

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
32.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ 1.0 (sqrt x))
16.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify62.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (48.0ms)

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

prune277.0ms

Filtered

145 candidates to 100 candidates (31.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	131	14	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	14	146

Merged error: 19.6b

Counts

146 → 14

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))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
3.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite42.0ms

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))
19.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series50.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
30.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
7.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify102.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	835	1032
1	4250	935
2	5001	933

prune224.0ms

Filtered

105 candidates to 78 candidates (25.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	106	13	119

Merged error: 18.6b

Counts

119 → 13

localize12.0ms

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))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
2.7b	(+ x (- 1.0 x))

rewrite58.0ms

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:

15.0ms	(/ (+ 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)))
6.0ms	(+ x (- 1.0 x))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
33.0ms	(/ (* 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)))
1.0ms	(+ x (- 1.0 x))

simplify40.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	938	1674
1	5002	1471

prune260.0ms

Filtered

148 candidates to 91 candidates (38.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	152	9	161

Merged error: 0.2b

Counts

161 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ 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))))
9.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
33.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	935	1360
1	5002	1197

prune236.0ms

Filtered

128 candidates to 89 candidates (30.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	124	13	137

Merged error: 0.0b

Counts

137 → 13

regimes72.0ms

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

sample1.3s

Algorithm

intervals

Results

287.0ms	8182×	body	80	nan
273.0ms	1859×	body	640	valid
221.0ms	1183×	body	1280	valid
159.0ms	4058×	body	80	valid
62.0ms	578×	body	320	valid
23.0ms	322×	body	160	valid

Details

sample47.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite51.0ms

series33.0ms

simplify62.0ms

prune277.0ms

localize8.0ms

rewrite42.0ms

series50.0ms

simplify102.0ms

prune224.0ms

localize12.0ms

rewrite58.0ms

series52.0ms

simplify40.0ms

prune260.0ms

localize10.0ms

rewrite51.0ms

series54.0ms

simplify40.0ms

prune236.0ms

regimes72.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling