Details

sample30.0ms

Algorithm

intervals

Results

5.0ms	43×	body	1280	valid
5.0ms	229×	body	80	nan
5.0ms	52×	body	640	valid
3.0ms	127×	body	80	valid
1.0ms	21×	body	320	valid
1.0ms	13×	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: 21.2b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
4.8b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
875×	`*-un-lft-identity`
742×	`add-sqr-sqrt`
712×	`add-cube-cbrt`
594×	`prod-diff`
562×	`sqrt-prod`
73×	`distribute-lft-out`
54×	`div-inv`
46×	`sqrt-div` `associate-/r/`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 739

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
52.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series245.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ 1.0 (sqrt (+ x 1.0)))
37.0ms	(/ 1.0 (sqrt x))
135.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify264.0ms

Algorithm

egg-herbie

Counts

748 → 748

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1517	24924
1	4197	18301
2	5001	18266

prune1.2s

Filtered

748 candidates to 285 candidates (38.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	730	18	748
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	731	18	749

Merged error: 20.5b

Counts

749 → 18

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
4.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

68×	`sqrt-prod`
58×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
42×	`prod-diff`
35×	`add-cube-cbrt`
17×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out`
7×	`pow1` `fma-neg` `associate-r`
6×	`associate-r/` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `distribute-lft-out--`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

3 → 132

Calls

3 calls:

22.0ms	(/ (* 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))

series393.0ms

Counts

3 → 9

Calls

3 calls:

260.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify85.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	614	1715
1	2883	1280
2	5002	1185

prune302.0ms

Filtered

141 candidates to 76 candidates (53.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	140	19	159

Merged error: 19.8b

Counts

159 → 19

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)))
4.4b	(+ x (- 1.0 x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

112×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt`
35×	`sqrt-prod`
31×	`times-frac`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-cube-cbrt`
11×	`associate-+r+`
9×	`cbrt-undiv` `div-exp` `prod-diff` `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×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `associate-/l/`
2×	`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 → 156

Calls

4 calls:

15.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms	(/ (* 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)))
7.0ms	(+ x (- 1.0 x))

series698.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
500.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
57.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify114.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	799	1711
1	4236	1448
2	5001	1435

prune405.0ms

Filtered

168 candidates to 106 candidates (63.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	11	7	18
Picked	1	0	1
Done	0	0	0
Total	177	10	187

Merged error: 0.2b

Counts

187 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 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)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
35×	`sqrt-prod`
29×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
22×	`distribute-lft-out`
21×	`add-cube-cbrt`
19×	`times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`fma-def` `associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `associate-/r/` `flip-+` `log1p-expm1-u` `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 → 131

Calls

4 calls:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
19.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series781.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
144.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
492.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	704	1320
1	3636	1120
2	5002	1050

prune308.0ms

Filtered

143 candidates to 94 candidates (65.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	132	11	143
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	139	14	153

Merged error: 0.0b

Counts

153 → 14

regimes51.0ms

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	13	11
1	13	11

end0.0ms

sample847.0ms

Algorithm

intervals

Results

185.0ms	1936×	body	640	valid
176.0ms	7833×	body	80	nan
139.0ms	1128×	body	1280	valid
101.0ms	4028×	body	80	valid
43.0ms	589×	body	320	valid
15.0ms	319×	body	160	valid