Details

analyze12.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample211.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify467.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	786	11
1	786	11

prune4.0ms

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: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 91

Calls

3 calls:

7.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

series37.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify36.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5097	1256

prune170.0ms

Filtered

68 candidates to 100 candidates (-47.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0b

Counts

101 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
0.0b	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
100×	`times-frac`
99×	`add-sqr-sqrt`
58×	`cbrt-prod`
57×	`add-cube-cbrt`
52×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`associate-/r*` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `clear-num` `flip--` `rem-cbrt-cube`

Counts

4 → 193

Calls

4 calls:

1.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
8.0ms	(/ (- 1.0 x) (+ 1.0 x))
11.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
10.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

series14.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
3.0ms	(/ (- 1.0 x) (+ 1.0 x))
6.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
4.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

simplify43.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5105	2713

prune238.0ms

Filtered

94 candidates to 205 candidates (-118.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	205	4	209

Merged error: 0b

Counts

209 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ 1.0 x))
0.0b	(/ 1.0 (+ 1.0 x))
0.0b	(atan (sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
0.0b	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`times-frac`
36×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
12×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*` `associate-/r/` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `div-inv` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 100

Calls

4 calls:

5.0ms	(/ x (+ 1.0 x))
5.0ms	(/ 1.0 (+ 1.0 x))
1.0ms	(atan (sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
23.0ms	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

series12.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ 1.0 x))
2.0ms	(/ 1.0 (+ 1.0 x))
2.0ms	(atan (sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))
5.0ms	(- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4971	1265
1	4971	1265

prune183.0ms

Filtered

83 candidates to 112 candidates (-34.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	112	4	116

Merged error: 0b

Counts

116 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
0.0b	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

155×	`*-un-lft-identity`
104×	`sqrt-prod`
103×	`add-sqr-sqrt`
100×	`times-frac`
64×	`cbrt-prod`
61×	`add-cube-cbrt`
58×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`associate-/r*` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`cube-div` `cube-mult` `sqrt-div` `unpow3` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 206

Calls

4 calls:

3.0ms	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)))
8.0ms	(/ (- 1.0 x) (+ 1.0 x))
13.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
12.0ms	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)))
3.0ms	(/ (- 1.0 x) (+ 1.0 x))
5.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
8.0ms	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

simplify65.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4969	3265
1	4969	3265

prune262.0ms

Filtered

100 candidates to 218 candidates (-118.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	218	4	222

Merged error: 0b

Counts

222 → 4

regimes94.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample507.0ms

Algorithm

intervals

Results

395.0ms

8000×

body

valid

Details

analyze12.0ms

sample211.0ms

simplify467.0ms

prune4.0ms

localize10.0ms

rewrite22.0ms

series37.0ms

simplify36.0ms

prune170.0ms

localize11.0ms

rewrite39.0ms

series14.0ms

simplify43.0ms

prune238.0ms

localize9.0ms

rewrite40.0ms

series12.0ms

simplify52.0ms

prune183.0ms

localize11.0ms

rewrite45.0ms

series17.0ms

simplify65.0ms

prune262.0ms

regimes94.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample507.0ms

Profiling