Details

sample35.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 50.021362%

Guaranteed chance to sample good point: 99.981682%

Results

13.0ms

256×

body

valid

simplify568.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	19	6
2	21	6
3	21	6

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

rewrite31.0ms

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	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
9.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series17.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(/ (- 1.0 x) (+ 1.0 x))
2.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
12.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	354	753
1	1071	709
2	5001	688

prune167.0ms

Filtered

70 candidates to 100 candidates (-42.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Merged error: 0b

Counts

101 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
56×	`times-frac`
40×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`sqrt-div` `associate-/l*`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 128

Calls

4 calls:

3.0ms	(sqrt (- 1.0 x))
3.0ms	(sqrt (+ 1.0 x))
3.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
9.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (- 1.0 x))
4.0ms	(sqrt (+ 1.0 x))
1.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
4.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	387	1280
1	1221	1220
2	5001	1157

prune205.0ms

Filtered

82 candidates to 140 candidates (-70.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Merged error: 0b

Counts

143 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 x) (+ x 1.0))
0.0b	(sqrt (/ (- 1.0 x) (+ x 1.0)))
0.0b	(log (exp (sqrt (/ (- 1.0 x) (+ x 1.0)))))
0.0b	(exp (sqrt (/ (- 1.0 x) (+ x 1.0))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
85×	`add-sqr-sqrt`
81×	`times-frac`
78×	`sqrt-prod`
58×	`exp-prod`
48×	`add-cube-cbrt`
30×	`log-pow`
21×	`distribute-lft-out`
17×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-/l*` `add-log-exp`
4×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
3×	`log-prod`
2×	`rem-sqrt-square` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 162

Calls

4 calls:

7.0ms	(/ (- 1.0 x) (+ x 1.0))
7.0ms	(sqrt (/ (- 1.0 x) (+ x 1.0)))
12.0ms	(log (exp (sqrt (/ (- 1.0 x) (+ x 1.0)))))
9.0ms	(exp (sqrt (/ (- 1.0 x) (+ x 1.0))))

series19.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ (- 1.0 x) (+ x 1.0))
5.0ms	(sqrt (/ (- 1.0 x) (+ x 1.0)))
4.0ms	(log (exp (sqrt (/ (- 1.0 x) (+ x 1.0)))))
8.0ms	(exp (sqrt (/ (- 1.0 x) (+ x 1.0))))

simplify51.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	506	1319
1	1554	1244
2	5002	1184

prune312.0ms

Filtered

116 candidates to 174 candidates (-50.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	174	3	177

Merged error: 0b

Counts

177 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))
0.0b	(sqrt (/ (- 1.0 x) (+ x 1.0)))
0.0b	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
0.1b	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
130×	`sqrt-prod`
103×	`add-sqr-sqrt`
101×	`times-frac`
64×	`cbrt-prod`
60×	`add-cube-cbrt`
58×	`unpow-prod-down` `cube-prod`
25×	`distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
7×	`pow1`
5×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv`
4×	`add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-div`
2×	`cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 198

Calls

4 calls:

1.0ms	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))
7.0ms	(sqrt (/ (- 1.0 x) (+ x 1.0)))
11.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
10.0ms	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

series21.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))
8.0ms	(sqrt (/ (- 1.0 x) (+ x 1.0)))
4.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
7.0ms	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

simplify63.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	611	2028
1	1904	1880
2	5003	1838

prune245.0ms

Filtered

94 candidates to 210 candidates (-123.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	210	3	213

Merged error: 0b

Counts

213 → 3

regimes32.0ms

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	12	7
1	12	7

end0.0ms

sample524.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 50.021362%

Guaranteed chance to sample good point: 99.981682%

Results

381.0ms

8000×

body

valid

Details

sample35.0ms

simplify568.0ms

prune4.0ms

localize10.0ms

rewrite31.0ms

series17.0ms

simplify41.0ms

prune167.0ms

localize9.0ms

rewrite23.0ms

series13.0ms

simplify48.0ms

prune205.0ms

localize11.0ms

rewrite43.0ms

series19.0ms

simplify51.0ms

prune312.0ms

localize10.0ms

rewrite39.0ms

series21.0ms

simplify63.0ms

prune245.0ms

regimes32.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample524.0ms

Profiling