Details

sample442.0ms

Algorithm

intervals

Results

258.0ms	4011×	body	80	nan
45.0ms	165×	body	640	valid
8.0ms	43×	body	320	valid
3.0ms	8×	body	1280	valid
2.0ms	15×	body	160	valid
2.0ms	25×	body	80	valid

simplify28.0ms

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: 5.7b

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ y 1.0)) (sqrt y))
3.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite132.0ms

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:

28.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
31.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
28.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
29.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series282.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify100.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (70.0ms)

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

prune1.0s

Filtered

292 candidates to 132 candidates (45.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.4b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

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:

31.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(+ z (- 1.0 z))
28.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
31.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
1.0ms	(+ z (- 1.0 z))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify96.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (68.0ms)

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

prune887.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize24.0ms

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 (+ y 1.0)) (sqrt y))
3.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite132.0ms

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:

26.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
31.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
30.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
33.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series367.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify103.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (71.0ms)

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

prune1.1s

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.5b	(+ t (- 1.0 t))
3.0b	(- (sqrt (+ y 1.0)) (sqrt y))
3.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite107.0ms

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:

27.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
9.0ms	(+ t (- 1.0 t))
28.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
32.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series280.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.0ms	(+ t (- 1.0 t))
67.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify93.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (72.0ms)

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

prune829.0ms

Filtered

226 candidates to 106 candidates (46.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

regimes854.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s	15973×	body	80	nan
180.0ms	685×	body	640	valid
40.0ms	208×	body	320	valid
9.0ms	71×	body	160	valid
8.0ms	25×	body	1280	valid
6.0ms	89×	body	80	valid