Details

sample433.0ms

Algorithm

intervals

Results

253.0ms	3971×	body	80	nan
46.0ms	173×	body	640	valid
10.0ms	51×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	4×	body	1280	valid
1.0ms	15×	body	80	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune5.0ms

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: 4.5b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))
3.6b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

228×	`sqrt-prod`
200×	`*-un-lft-identity`
168×	`prod-diff`
148×	`add-sqr-sqrt`
116×	`add-cube-cbrt`
32×	`distribute-lft-out`
28×	`fma-neg`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 280

Calls

4 calls:

9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series274.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
65.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify112.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	945	4262
1	2912	2932
2	5002	2860

prune964.0ms

Filtered

292 candidates to 132 candidates (45.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	279	13	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	280	13	293

Merged error: 3.5b

Counts

293 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (+ x 1.0)) (sqrt x))
2.2b	(+ z (- 1.0 z))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
3.6b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

171×	`sqrt-prod`
163×	`*-un-lft-identity`
135×	`prod-diff`
119×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
26×	`distribute-lft-out`
21×	`fma-neg`
15×	`add-log-exp`
12×	`difference-of-squares`
11×	`associate-+r+`
10×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `diff-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `fma-def` `flip--`
2×	`sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 241

Calls

4 calls:

10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
7.0ms	(+ z (- 1.0 z))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series211.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(+ z (- 1.0 z))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify98.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	848	3327
1	2686	2292
2	5002	2082

prune815.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	245	8	253
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	254	12	266

Merged error: 2.9b

Counts

266 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.7b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
3.6b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

190×	`*-un-lft-identity`
187×	`sqrt-prod`
126×	`prod-diff`
123×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
40×	`distribute-lft-out`
21×	`fma-neg`
18×	`times-frac`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 253

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series352.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify116.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	948	3617
1	3148	2584
2	5001	2530

prune1.0s

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	255	10	265
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	264	13	277

Merged error: 2.9b

Counts

277 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.7b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.9b	(+ y (- 1.0 y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

153×	`*-un-lft-identity`
130×	`sqrt-prod`
94×	`add-sqr-sqrt`
93×	`prod-diff`
78×	`add-cube-cbrt`
34×	`distribute-lft-out`
18×	`times-frac`
14×	`fma-neg`
13×	`add-log-exp`
11×	`associate-+r+`
8×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-def` `diff-log` `associate-/l*`
2×	`flip3--` `flip3-+` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 214

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
7.0ms	(+ y (- 1.0 y))

series284.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
1.0ms	(+ y (- 1.0 y))

simplify100.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	856	2684
1	2955	1944
2	5001	1788

prune802.0ms

Filtered

226 candidates to 106 candidates (46.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	221	5	226
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	230	9	239

Merged error: 1.9b

Counts

239 → 9

regimes742.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample854.0ms

Algorithm

intervals

Results

511.0ms	8285×	body	80	nan
82.0ms	318×	body	640	valid
23.0ms	119×	body	320	valid
4.0ms	32×	body	160	valid
3.0ms	10×	body	1280	valid
2.0ms	37×	body	80	valid