Details

sample449.0ms

Algorithm

intervals

Results

232.0ms	3848×	body	80	nan
43.0ms	169×	body	640	valid
10.0ms	53×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	19×	body	80	valid
1.0ms	3×	body	1280	valid

simplify25.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (+ x 1.0)) (sqrt x))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
3.7b	(- (sqrt (+ z 1.0)) (sqrt z))
4.1b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite215.0ms

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:

50.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
50.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
50.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
49.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series273.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
59.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
74.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
75.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify103.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (67.0ms)

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

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize32.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (+ x 1.0)) (sqrt x))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(+ z (- 1.0 z))
4.1b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite183.0ms

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:

50.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
51.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
19.0ms	(+ z (- 1.0 z))
49.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series197.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
68.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
1.0ms	(+ z (- 1.0 z))
60.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify88.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (63.0ms)

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

prune852.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
4.1b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite214.0ms

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:

44.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
51.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
52.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
54.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series335.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
61.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
68.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify100.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (71.0ms)

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

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
3.4b	(+ t (- 1.0 t))

rewrite185.0ms

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:

43.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
62.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
50.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
20.0ms	(+ t (- 1.0 t))

series264.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
67.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
1.0ms	(+ t (- 1.0 t))

simplify89.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	857	2684
1	2953	1944
2	5001	1788

prune936.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.5b

regimes962.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

591.0ms	10124×	body	80	nan
99.0ms	420×	body	640	valid
23.0ms	130×	body	320	valid
6.0ms	42×	body	160	valid
3.0ms	11×	body	1280	valid
3.0ms	53×	body	80	valid