Details

sample386.0ms

Algorithm

intervals

Results

219.0ms	3556×	body	80	nan
44.0ms	164×	body	640	valid
11.0ms	51×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	21×	body	80	valid
1.0ms	2×	body	1280	valid

simplify29.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (sqrt (+ x 1.0)) (sqrt x))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))
4.6b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite126.0ms

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:

27.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
28.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
27.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
29.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series280.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
68.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify96.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (67.0ms)

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

prune975.0ms

Filtered

292 candidates to 132 candidates (45.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.2b

localize27.0ms

Local error

Found 4 expressions with local error:

1.9b	(+ y (- 1.0 y))
2.7b	(- (sqrt (+ x 1.0)) (sqrt x))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))
4.6b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite106.0ms

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	(+ y (- 1.0 y))
26.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
27.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
30.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series214.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(+ y (- 1.0 y))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
66.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
75.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify105.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	855	3329
1	2715	2292
2	5002	2082

prune815.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.9b	(+ y (- 1.0 y))
2.7b	(- (sqrt (+ x 1.0)) (sqrt x))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))
3.6b	(+ t (- 1.0 t))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
114×	`sqrt-prod`
102×	`prod-diff`
90×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
22×	`associate-+r+`
20×	`distribute-lft-out`
18×	`add-log-exp`
14×	`fma-neg`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`fma-def`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u`
2×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+`

Counts

4 → 202

Calls

4 calls:

9.0ms	(+ y (- 1.0 y))
30.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
27.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(+ t (- 1.0 t))

series150.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(+ y (- 1.0 y))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ t (- 1.0 t))

simplify84.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	761	2396
1	2505	1652
2	5002	1512

prune834.0ms

Filtered

214 candidates to 103 candidates (48.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.9b	(+ y (- 1.0 y))
2.7b	(- (sqrt (+ x 1.0)) (sqrt x))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite97.0ms

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:

26.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
8.0ms	(+ y (- 1.0 y))
26.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
27.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series284.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.0ms	(+ y (- 1.0 y))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify95.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	864	2686
1	2981	1944
2	5001	1788

prune772.0ms

Filtered

226 candidates to 106 candidates (46.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.5b

regimes931.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	43	26

end0.0ms

sample595.0ms

Algorithm

intervals

Results

345.0ms	5720×	body	80	nan
70.0ms	256×	body	640	valid
15.0ms	82×	body	320	valid
3.0ms	23×	body	160	valid
2.0ms	26×	body	80	valid
1.0ms	4×	body	1280	valid