Details

sample275.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
7.0ms	249×	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 (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: 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))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

5×	`sqrt-div`
4×	`associate-/r/` `associate-/l/`
3×	`sqrt-prod`
2×	`flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv`
1×	`pow1/2` `div-sub`

Counts

3 → 17

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
4.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
7.0ms	(/ (- 1.0 x) (+ 1.0 x))

series154.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
95.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
56.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify82.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	216	174
1	640	171
2	2895	161
3	5001	157

prune72.0ms

Filtered

26 candidates to 22 candidates (84.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	25	1	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	1	27

Merged error: 0.0b

Counts

27 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

24×	`frac-times`
20×	`sqrt-div`
18×	`associate-+r+`
17×	`flip3-+` `flip-+`
15×	`*-commutative`
12×	`prod-diff` `associate-*l/` `associate-/l/`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`flip3--` `frac-2neg` `associate-l` `clear-num` `associate-/r*` `sum-cubes` `flip--`
5×	`sqrt-prod`
4×	`associate-*r/` `associate-/r/`
3×	`+-commutative` `sub-neg`
2×	`fma-def` `div-inv`
1×	`associate-+r-` `pow1/2`

Counts

4 → 78

Calls

4 calls:

1.0ms	(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
8.0ms	(+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))
19.0ms	(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
15.0ms	(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
21.0ms	(+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))
134.0ms	(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
74.0ms	(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify88.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	634	1449
1	2851	1387
2	5002	1358

prune319.0ms

Filtered

90 candidates to 68 candidates (75.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	1	91

Merged error: 0.0b

Counts

91 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 1.0 (- (* x x) (* 1.0 x)))
0.0b	(sqrt (* (/ (- 1.0 x) (- (* (pow 1.0 3) (pow 1.0 3)) (* (pow x 3) (pow x 3)))) (* (fma 1.0 1.0 (- (* x x) (* 1.0 x))) (- (pow 1.0 3) (pow x 3)))))
0.0b	(* (/ (- 1.0 x) (- (* (pow 1.0 3) (pow 1.0 3)) (* (pow x 3) (pow x 3)))) (* (fma 1.0 1.0 (- (* x x) (* 1.0 x))) (- (pow 1.0 3) (pow x 3))))
0.1b	(* (pow x 3) (pow x 3))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

218×	`sqr-pow`
102×	`associate-/r*`
98×	`difference-of-squares`
96×	`associate-*r/`
88×	`frac-times`
68×	`sqrt-div`
54×	`flip3--` `flip--`
53×	`*-commutative`
50×	`swap-sqr`
49×	`unswap-sqr`
44×	`associate-*l/`
24×	`distribute-rgt-in` `distribute-lft-in`
20×	`unpow3`
16×	`prod-diff`
14×	`associate-r`
13×	`pow-prod-down`
12×	`associate-/l/`
9×	`sqrt-prod`
8×	`difference-cubes` `associate-l`
6×	`frac-2neg` `clear-num`
4×	`sub-neg` `associate-/r/`
2×	`pow-to-exp` `div-inv`
1×	`pow2` `pow1/2` `prod-exp` `pow-sqr` `pow-prod-up` `fma-udef`

Counts

4 → 192

Calls

4 calls:

1.0ms	(fma 1.0 1.0 (- (* x x) (* 1.0 x)))
32.0ms	(sqrt (* (/ (- 1.0 x) (- (* (pow 1.0 3) (pow 1.0 3)) (* (pow x 3) (pow x 3)))) (* (fma 1.0 1.0 (- (* x x) (* 1.0 x))) (- (pow 1.0 3) (pow x 3)))))
26.0ms	(* (/ (- 1.0 x) (- (* (pow 1.0 3) (pow 1.0 3)) (* (pow x 3) (pow x 3)))) (* (fma 1.0 1.0 (- (* x x) (* 1.0 x))) (- (pow 1.0 3) (pow x 3))))
5.0ms	(* (pow x 3) (pow x 3))

series357.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(fma 1.0 1.0 (- (* x x) (* 1.0 x)))
180.0ms	(sqrt (* (/ (- 1.0 x) (- (* (pow 1.0 3) (pow 1.0 3)) (* (pow x 3) (pow x 3)))) (* (fma 1.0 1.0 (- (* x x) (* 1.0 x))) (- (pow 1.0 3) (pow x 3)))))
110.0ms	(* (/ (- 1.0 x) (- (* (pow 1.0 3) (pow 1.0 3)) (* (pow x 3) (pow x 3)))) (* (fma 1.0 1.0 (- (* x x) (* 1.0 x))) (- (pow 1.0 3) (pow x 3))))
44.0ms	(* (pow x 3) (pow x 3))

simplify150.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	982	4684
1	4452	4369
2	5001	4353

prune466.0ms

Filtered

204 candidates to 84 candidates (41.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	204	1	205

Merged error: 0.0b

Counts

205 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	21
1	25	21

end0.0ms

sample681.0ms

Algorithm

intervals

Results

305.0ms	8000×	body	80	valid
192.0ms	7878×	body	80	nan