Details

sample47.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	132	86
1	618	75
2	3343	39
3	5001	39

prune24.0ms

Filtered

1 candidates to 1 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: 28.4b

Counts

2 → 2

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) 0.0072644182)
0.2b	(* (* x x) 0.0140005442)
14.8b	(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
24.4b	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

21×	`associate-/r/`
20×	`flip3-+` `flip-+`
16×	`associate-*r/` `frac-add`
12×	`associate-/l/`
7×	`associate-/r*`
4×	`associate-l` `*-commutative`
3×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 40

Calls

4 calls:

4.0ms	(* (* x x) 0.0072644182)
4.0ms	(* (* x x) 0.0140005442)
43.0ms	(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
39.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* x x) 0.0072644182)
24.0ms	(* (* x x) 0.0140005442)
272.0ms	(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
209.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	678	1822
1	3621	1694
2	5001	1690

prune544.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Merged error: 0b

Counts

54 → 3

localize58.0ms

Local error

Found 4 expressions with local error:

20.0b	(- (fma (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971)) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))
20.0b	(- (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))
24.0b	(* (/ (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))) (- (fma (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971)) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))) (- (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
24.4b	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

164×	`flip3-+` `flip-+`
154×	`associate-*r/`
114×	`frac-times`
111×	`associate-/l/`
84×	`frac-sub`
64×	`frac-add`
50×	`associate-/r/`
49×	`associate-/l*`
23×	`flip3--` `flip--`
22×	`associate--l+`
19×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`
15×	`frac-2neg` `clear-num`
13×	`+-commutative`
12×	`associate-+l+`
9×	`div-inv`
8×	`associate--r+`
4×	`sub-neg` `fma-udef`
3×	`associate-+r+` `associate-l`
1×	`*-commutative`

Counts

4 → 204

Calls

4 calls:

3.0ms	(- (fma (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971)) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))
13.0ms	(- (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))
63.0ms	(* (/ (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))) (- (fma (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971)) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))) (- (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
41.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

series826.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (fma (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971)) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))
86.0ms	(- (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))
430.0ms	(* (/ (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))) (- (fma (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971)) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))) (- (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
226.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

simplify261.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2063	24253
1	5003	23544

prune3.5s

Filtered

216 candidates to 192 candidates (88.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	216	3	219

Merged error: 0b

Counts

219 → 3

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* x x) 4)
0.1b	(pow (* x x) 3)
0.2b	(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) x)
27.4b	(/ (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) x) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-down`
3×	`frac-2neg` `clear-num` `div-inv` `associate-/l/`
2×	`pow2` `pow-to-exp` `pow-pow` `*-commutative` `sqr-pow`
1×	`unpow3` `associate-/l*`

Counts

4 → 21

Calls

4 calls:

2.0ms	(pow (* x x) 4)
2.0ms	(pow (* x x) 3)
2.0ms	(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) x)
3.0ms	(/ (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) x) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (* x x) 4)
42.0ms	(pow (* x x) 3)
147.0ms	(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) x)
281.0ms	(/ (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) x) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

simplify116.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	229	247
1	702	242
2	3536	225
3	5001	225

prune327.0ms

Filtered

33 candidates to 20 candidates (60.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	33	3	36

Merged error: 0b

Counts

36 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.10624017004623454 (/ 1 (pow x 3)))
0.1b	(fma 1.00567160026615 (/ 1 x) (* 0.10624017004623454 (/ 1 (pow x 3))))
0.1b	(/ 1 (pow x 3))
0.4b	(/ 1 (fma 2.0 x (- (fma 1.00567160026615 (/ 1 x) (* 0.10624017004623454 (/ 1 (pow x 3)))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

5×	`associate-*r/`
4×	`clear-num` `associate-/r*`
3×	`frac-2neg` `div-inv`
2×	`unpow3` `un-div-inv` `inv-pow` `sqr-pow`
1×	`pow-to-exp` `rec-exp` `pow-flip` `associate-r` `*-commutative` `fma-udef`

Counts

4 → 22

Calls

4 calls:

3.0ms	(* 0.10624017004623454 (/ 1 (pow x 3)))
1.0ms	(fma 1.00567160026615 (/ 1 x) (* 0.10624017004623454 (/ 1 (pow x 3))))
3.0ms	(/ 1 (pow x 3))
2.0ms	(/ 1 (fma 2.0 x (- (fma 1.00567160026615 (/ 1 x) (* 0.10624017004623454 (/ 1 (pow x 3)))))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 0.10624017004623454 (/ 1 (pow x 3)))
80.0ms	(fma 1.00567160026615 (/ 1 x) (* 0.10624017004623454 (/ 1 (pow x 3))))
33.0ms	(/ 1 (pow x 3))
79.0ms	(/ 1 (fma 2.0 x (- (fma 1.00567160026615 (/ 1 x) (* 0.10624017004623454 (/ 1 (pow x 3)))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	116	95
1	324	91
2	1108	89
3	5001	86

prune61.0ms

Filtered

34 candidates to 21 candidates (61.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	34	3	37

Merged error: 0b

Counts

37 → 3

regimes52.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.4b

bsearch455.0ms

Steps

Iters	Range		Point
9	357.20278190505735	4524963932.878733	782.0321228156733
8	-298845738972.0616	-119005586.03332348	-3083517158.917441

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	78
1	99	78

end0.0ms

sample803.0ms

Algorithm

intervals

Results

701.0ms

8000×

body

valid