Details

sample414.0ms

Algorithm

intervals

Results

235.0ms	3828×	body	80	nan
37.0ms	146×	body	640	valid
12.0ms	60×	body	320	valid
3.0ms	21×	body	160	valid
2.0ms	25×	body	80	valid
1.0ms	4×	body	1280	valid

simplify39.0ms

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: 4.6b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ z 1.0)) (sqrt z))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite57.0ms

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:

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

series289.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify102.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (70.0ms)

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

prune1.1s

Filtered

292 candidates to 132 candidates (45.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	274	18	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	275	18	293

Merged error: 3.5b

Counts

293 → 18

localize31.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.2b	(+ z (- 1.0 z))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite52.0ms

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:

11.0ms	(- (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))

series418.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(+ z (- 1.0 z))
70.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
278.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify94.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (68.0ms)

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

prune836.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	250	3	253
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	256	15	271

Merged error: 2.4b

Counts

271 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite57.0ms

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))
12.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series345.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
70.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify109.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (75.0ms)

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

prune1.0s

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	260	5	265
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	264	16	280

Merged error: 2.4b

Counts

280 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.7b	(+ x (- 1.0 x))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite51.0ms

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:

12.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
7.0ms	(+ x (- 1.0 x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series269.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.0ms	(+ x (- 1.0 x))
65.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify87.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	857	2684
1	2956	1944
2	5001	1788

prune711.0ms

Filtered

226 candidates to 106 candidates (46.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	228	14	242

Merged error: 2.1b

Counts

242 → 14

regimes1.4s

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample526.0ms

Algorithm

intervals

Results

309.0ms	5290×	body	80	nan
51.0ms	202×	body	640	valid
11.0ms	62×	body	320	valid
2.0ms	8×	body	1280	valid
2.0ms	34×	body	80	valid
2.0ms	14×	body	160	valid