Details

sample605.0ms

Algorithm

intervals

Results

388.0ms	4117×	body	80	nan
65.0ms	168×	body	640	valid
13.0ms	48×	body	320	valid
3.0ms	16×	body	160	valid
2.0ms	5×	body	1280	valid
2.0ms	19×	body	80	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 5.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ y 1.0)) (sqrt y))
4.8b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite51.0ms

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

series277.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
68.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
73.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify99.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (68.0ms)

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

prune884.0ms

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: 3.8b

Counts

293 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))
3.2b	(+ z (- 1.0 z))
3.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite48.0ms

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:

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

series204.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(+ z (- 1.0 z))
66.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify95.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	848	3327
1	2686	2292
2	5001	2082

prune710.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	257	14	271

Merged error: 2.9b

Counts

271 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite49.0ms

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:

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

series338.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
68.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify101.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (71.0ms)

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

prune919.0ms

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	261	4	265
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	263	16	279

Merged error: 2.9b

Counts

279 → 16

localize31.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
2.5b	(log (exp (- (sqrt (+ y 1.0)) (sqrt y))))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

224×	`sqrt-prod`
198×	`*-un-lft-identity`
168×	`prod-diff`
148×	`add-sqr-sqrt`
116×	`add-cube-cbrt`
47×	`log-prod`
44×	`exp-sum`
31×	`distribute-lft-out`
21×	`fma-neg`
16×	`difference-of-squares`
12×	`distribute-lft-out--`
11×	`log-pow`
10×	`exp-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 279

Calls

4 calls:

9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
13.0ms	(log (exp (- (sqrt (+ y 1.0)) (sqrt y))))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series290.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(log (exp (- (sqrt (+ y 1.0)) (sqrt y))))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify87.0ms

Algorithm

egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	811	4251
1	2398	2921
2	5001	2359

prune706.0ms

Filtered

291 candidates to 106 candidates (36.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	286	5	291
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	290	17	307

Merged error: 2.5b

Counts

307 → 17

regimes1.3s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	27
1	35	27

end0.0ms

sample672.0ms

Algorithm

intervals

Results

432.0ms	4594×	body	80	nan
75.0ms	191×	body	640	valid
18.0ms	53×	body	320	valid
3.0ms	17×	body	160	valid
3.0ms	6×	body	1280	valid
2.0ms	20×	body	80	valid

Details

sample605.0ms

simplify26.0ms

prune5.0ms

localize24.0ms

rewrite51.0ms

series277.0ms

simplify99.0ms

prune884.0ms

localize25.0ms

rewrite48.0ms

series204.0ms

simplify95.0ms

prune710.0ms

localize26.0ms

rewrite49.0ms

series338.0ms

simplify101.0ms

prune919.0ms

localize31.0ms

rewrite57.0ms

series290.0ms

simplify87.0ms

prune706.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample672.0ms

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