Details

sample305.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
7.0ms	244×	body	80	nan

simplify12.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 104

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
9.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

series157.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
94.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
60.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	372	833
1	1088	797
2	5001	775

prune199.0ms

Filtered

113 candidates to 79 candidates (30.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Merged error: 0b

Counts

114 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 112

Calls

3 calls:

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

series130.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(sqrt (- 1.0 x))
2.0ms	(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
94.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	334	1178
1	1019	1111
2	5002	1052

prune201.0ms

Filtered

121 candidates to 66 candidates (45.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	122	1	123

Merged error: 0b

Counts

123 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

131×	`*-un-lft-identity`
118×	`sqrt-prod`
117×	`cbrt-prod`
112×	`times-frac`
96×	`add-sqr-sqrt`
80×	`unpow-prod-down`
76×	`add-cube-cbrt`
17×	`distribute-lft-out`
16×	`associate-/l*`
10×	`unpow3` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
8×	`add-cbrt-cube`
7×	`add-exp-log` `associate-/r*`
6×	`pow1`
4×	`pow-unpow` `add-log-exp`
3×	`pow-pow`
2×	`cbrt-undiv` `sqrt-div` `associate-/r/` `rem-cbrt-cube`
1×	`pow-to-exp` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 207

Calls

4 calls:

1.0ms	(atan (fabs (/ (cbrt (pow (sqrt (- 1.0 x)) 3)) (sqrt (+ 1.0 x)))))
13.0ms	(/ (cbrt (pow (sqrt (- 1.0 x)) 3)) (sqrt (+ 1.0 x)))
5.0ms	(pow (sqrt (- 1.0 x)) 3)
5.0ms	(cbrt (pow (sqrt (- 1.0 x)) 3))

series202.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (fabs (/ (cbrt (pow (sqrt (- 1.0 x)) 3)) (sqrt (+ 1.0 x)))))
91.0ms	(/ (cbrt (pow (sqrt (- 1.0 x)) 3)) (sqrt (+ 1.0 x)))
72.0ms	(pow (sqrt (- 1.0 x)) 3)
37.0ms	(cbrt (pow (sqrt (- 1.0 x)) 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	514	2525
1	1805	2015
2	5001	1965

prune316.0ms

Filtered

219 candidates to 93 candidates (57.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	219	1	220

Merged error: 0b

Counts

220 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	10
1	16	10

end0.0ms

sample703.0ms

Algorithm

intervals

Results

313.0ms	8000×	body	80	valid
200.0ms	7941×	body	80	nan