Details

sample31.0ms

Algorithm

intervals

Results

6.0ms	64×	body	640	valid
6.0ms	259×	body	80	nan
4.0ms	130×	body	80	valid
3.0ms	25×	body	1280	valid
2.0ms	23×	body	320	valid
1.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

prune2.0ms

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: 20.3b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.3b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

175×	`associate-/r*`
174×	`*-un-lft-identity`
156×	`frac-sub`
148×	`add-sqr-sqrt`
137×	`sqrt-prod`
117×	`add-cube-cbrt`
81×	`associate-/l*`
69×	`times-frac`
27×	`frac-2neg` `clear-num`
20×	`distribute-lft-out`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--`

Counts

4 → 288

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
42.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
80.0ms	(/ 1.0 (sqrt (+ x 1.0)))
45.0ms	(/ 1.0 (sqrt x))
137.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify73.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1402	3847
1	5001	3760

prune512.0ms

Filtered

300 candidates to 185 candidates (61.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	279	21	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	280	21	301

Merged error: 19.6b

Counts

301 → 21

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* (sqrt 1.0) (- (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))) (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))))
0.3b	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
3.4b	(- (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

26298×	`times-frac`
24820×	`add-sqr-sqrt`
21051×	`sqrt-prod`
13913×	`*-un-lft-identity`
9492×	`associate-r`
6097×	`add-cube-cbrt`
3462×	`associate-l`
2950×	`distribute-lft-out--` `difference-of-squares`
1959×	`unswap-sqr`
1421×	`distribute-lft-out`
980×	`associate-/r*`
947×	`associate-/l*`
540×	`frac-times` `frac-sub`
412×	`associate-/l/`
375×	`div-inv`
324×	`associate-*r/`
305×	`associate-/r/`
186×	`*-commutative`
141×	`frac-2neg`
139×	`clear-num`
126×	`sqrt-div`
118×	`distribute-rgt-out--`
63×	`flip3-+` `flip-+`
57×	`add-exp-log` `add-cbrt-cube`
32×	`sub-div`
30×	`associate-*l/`
22×	`cbrt-undiv` `div-exp`
17×	`prod-exp` `cbrt-unprod`
7×	`pow1`
6×	`add-log-exp`
4×	`un-div-inv`
2×	`sqrt-undiv` `flip3--` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-unprod` `diff-log` `pow-prod-down`

Counts

4 → 9377

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
365.0ms	(/ (* (sqrt 1.0) (- (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))) (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))))
49.0ms	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
87.0ms	(- (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1.0))
579.0ms	(/ (* (sqrt 1.0) (- (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))) (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))))
174.0ms	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
221.0ms	(- (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))

simplify2.9s

Algorithm

egg-herbie

Counts

9389 → 9389

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5001	322513

prune11.6s

Filtered

9389 candidates to 2710 candidates (28.9%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	9367	22	9389
Fresh	9	11	20
Picked	1	0	1
Done	0	0	0
Total	9377	33	9410

Merged error: 19.4b

Counts

9410 → 33

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
0.3b	(* (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
0.5b	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))
2.7b	(- (* (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0))))

rewrite22.5s

Algorithm

rewrite-expression-head

Rules

166049×	`frac-times`
146729×	`sqrt-prod`
139172×	`associate-/l*`
129594×	`associate-/r*`
107534×	`*-un-lft-identity`
101296×	`add-sqr-sqrt`
93034×	`frac-sub`
86320×	`add-cube-cbrt`
22077×	`clear-num`
21527×	`frac-2neg`
19640×	`sqrt-div` `associate-/l/`
10171×	`associate-*r/`
10168×	`associate-*l/`
9958×	`distribute-lft-out`
9820×	`flip3-+` `flip-+`
7586×	`times-frac`
2325×	`unswap-sqr`
2025×	`difference-of-squares`
1894×	`swap-sqr`
1244×	`un-div-inv`
320×	`sub-div`
178×	`associate-l`
134×	`associate-r`
129×	`distribute-lft-out--`
93×	`*-commutative`
40×	`add-exp-log` `add-cbrt-cube`
20×	`pow1`
16×	`div-inv`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
10×	`sqrt-undiv`
6×	`add-log-exp`
3×	`sqrt-unprod` `pow-prod-down`
2×	`pow2` `distribute-rgt-out--` `pow-plus` `rem-square-sqrt` `pow-sqr` `pow-prod-up`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 97003

Calls

4 calls:

47.0ms	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
54.0ms	(* (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
45.0ms	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))
4.6s	(- (* (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
103.0ms	(* (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
94.0ms	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))
148.0ms	(- (* (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0))))

simplify42.5s

Algorithm

egg-herbie

Counts

97015 → 97015

Iterations

Useful iterations: 0 (4.0s)

Iter	Nodes	Cost
0	93882	4306236

prune4.5m

Filtered

97015 candidates to 39196 candidates (40.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97012	3	97015
Fresh	27	5	32
Picked	1	0	1
Done	0	0	0
Total	97040	8	97048

Merged error: 0.7b

Counts

97048 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))
0.1b	(* (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0))))
0.3b	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
0.7b	(/ (* (sqrt 1.0) (/ 1.0 (pow (sqrt 1.0) 2))) (* (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))))

rewrite39.8s

Algorithm

rewrite-expression-head

Rules

313610×	`frac-times`
271365×	`sqrt-prod`
254802×	`associate-/l*`
236431×	`associate-/r*`
206821×	`*-un-lft-identity`
184959×	`add-sqr-sqrt`
165969×	`add-cube-cbrt`
165510×	`frac-add`
83537×	`associate-/r/`
39924×	`clear-num`
39376×	`frac-2neg`
35913×	`associate-/l/`
35894×	`sqrt-div`
31109×	`times-frac`
20404×	`distribute-lft-out`
18560×	`flip3-+` `flip-+`
11245×	`associate-r`
10774×	`associate-l`
10407×	`associate-*r/`
8815×	`associate-*l/`
6861×	`unswap-sqr`
3900×	`unpow-prod-down`
1096×	`un-div-inv`
886×	`unpow2` `sqr-pow`
430×	`div-inv`
302×	`*-commutative`
195×	`add-exp-log`
127×	`add-cbrt-cube`
82×	`prod-exp`
76×	`div-exp`
63×	`distribute-rgt-out`
52×	`cbrt-unprod`
44×	`cbrt-undiv`
11×	`pow1`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow-prod-down`
3×	`+-commutative`
2×	`distribute-rgt-in` `sqrt-undiv` `distribute-lft-in`
1×	`sqrt-unprod` `sum-log`

Counts

4 → 178883

Calls

4 calls:

75.0ms	(+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))
1.7s	(* (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0))))
59.0ms	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
5.5s	(/ (* (sqrt 1.0) (/ 1.0 (pow (sqrt 1.0) 2))) (* (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

191.0ms	(+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))
604.0ms	(* (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0))))
160.0ms	(* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0)))
701.0ms	(/ (* (sqrt 1.0) (/ 1.0 (pow (sqrt 1.0) 2))) (* (* (/ (sqrt x) (sqrt 1.0)) (/ (sqrt (+ x 1.0)) (sqrt 1.0))) (+ (/ (sqrt (+ x 1.0)) (sqrt 1.0)) (/ (sqrt x) (sqrt 1.0)))))

simplify1.0m

Algorithm

egg-herbie

Counts

178895 → 178895

Iterations

Useful iterations: 0 (3.8s)

Iter	Nodes	Cost
0	86669	6162653

prune2.4m

Filtered: 178895 candidates to 72085 candidates (40.3%)