Details

analyze8.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
81.2%	18.7%	0%	6
100%	0%	0%	7

sample38.0ms

Algorithm

intervals

Results

30.0ms

256×

body

valid

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	132	86
1	557	78
2	2622	41
3	5001	41

prune15.0ms

Filtered

1 candidates to 1 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: 27.3b

Counts

2 → 2

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* x x) 0.0140005442)
0.4b	(* (* x x) 0.0072644182)
11.3b	(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (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)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
120×	`associate-*r/` `frac-add`
102×	`flip3-+` `flip-+`
72×	`add-sqr-sqrt`
71×	`associate-/r/`
70×	`add-cube-cbrt` `*-un-lft-identity`
30×	`associate-/r*`
21×	`add-exp-log` `add-cbrt-cube`
14×	`pow1` `associate-/l/`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative` `unswap-sqr`

Counts

4 → 219

Calls

4 calls:

6.0ms	(* (* x x) 0.0140005442)
6.0ms	(* (* x x) 0.0072644182)
38.0ms	(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
38.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* x x) 0.0140005442)
3.0ms	(* (* x x) 0.0072644182)
31.0ms	(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
23.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

simplify179.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1776	14289
1	5001	13790

prune3.1s

Filtered

196 candidates to 231 candidates (-17.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	229	4	233

Merged error: 0b

Counts

233 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.6665536072 (pow x 2)) (+ (* 0.17858401087518094 (pow x 4)) 1.0))
0.1b	(* 0.17858401087518094 (pow x 4))
0.1b	(* 0.6665536072 (pow x 2))
2.3b	(/ x (+ (* 0.6665536072 (pow x 2)) (+ (* 0.17858401087518094 (pow x 4)) 1.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
9×	`times-frac` `add-log-exp`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `sqr-pow`
3×	`associate-/r` `sum-log` `associate-/l`
2×	`pow-to-exp` `flip3-+` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `unpow2`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 94

Calls

4 calls:

9.0ms	(+ (* 0.6665536072 (pow x 2)) (+ (* 0.17858401087518094 (pow x 4)) 1.0))
6.0ms	(* 0.17858401087518094 (pow x 4))
6.0ms	(* 0.6665536072 (pow x 2))
10.0ms	(/ x (+ (* 0.6665536072 (pow x 2)) (+ (* 0.17858401087518094 (pow x 4)) 1.0)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* 0.6665536072 (pow x 2)) (+ (* 0.17858401087518094 (pow x 4)) 1.0))
7.0ms	(* 0.17858401087518094 (pow x 4))
4.0ms	(* 0.6665536072 (pow x 2))
9.0ms	(/ x (+ (* 0.6665536072 (pow x 2)) (+ (* 0.17858401087518094 (pow x 4)) 1.0)))

simplify62.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	407	737
1	1700	673
2	5002	670

prune200.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	106	4	110

Merged error: 0b

Counts

110 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.15298196345929327 (/ 1 (pow x 5)))
0.3b	(* 0.2514179000665375 (/ 1 (pow x 3)))
0.4b	(/ 1 (pow x 5))
0.4b	(/ 1 (pow x 3))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
118×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
83×	`add-cube-cbrt`
65×	`associate-r`
62×	`add-exp-log`
46×	`unpow-prod-down`
24×	`div-exp`
23×	`cube-prod`
20×	`prod-exp`
19×	`associate-/r*`
18×	`add-cbrt-cube` `sqr-pow`
16×	`unswap-sqr`
12×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
8×	`pow1`
7×	`cube-mult` `unpow3`
6×	`associate-l` `associate-/l*`
4×	`cbrt-undiv` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 259

Calls

4 calls:

12.0ms	(* 0.15298196345929327 (/ 1 (pow x 5)))
16.0ms	(* 0.2514179000665375 (/ 1 (pow x 3)))
6.0ms	(/ 1 (pow x 5))
7.0ms	(/ 1 (pow x 3))

series19.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* 0.15298196345929327 (/ 1 (pow x 5)))
5.0ms	(* 0.2514179000665375 (/ 1 (pow x 3)))
5.0ms	(/ 1 (pow x 5))
4.0ms	(/ 1 (pow x 3))

simplify76.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	631	1184
1	3260	864
2	5001	864

prune349.0ms

Filtered

122 candidates to 271 candidates (-122.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	271	4	275

Merged error: 0b

Counts

275 → 4

localize65.0ms

Local error

Found 4 expressions with local error:

11.2b	(sqrt (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
11.2b	(sqrt (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (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)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (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)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

120×	`associate-*r/` `frac-add`
102×	`flip3-+` `flip-+`
56×	`associate-/r/`
54×	`sqrt-prod`
40×	`add-sqr-sqrt`
38×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
28×	`associate-/l/`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l`
4×	`rem-sqrt-square` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 188

Calls

4 calls:

30.0ms	(sqrt (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
33.0ms	(sqrt (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
40.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
40.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
22.0ms	(sqrt (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
28.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
22.0ms	(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

simplify141.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1278	13070
1	5002	12526

prune5.6s

Filtered

184 candidates to 200 candidates (-8.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	200	4	204

Merged error: 0b

Counts

204 → 4

regimes61.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.0b

bsearch80.0ms

Steps

Iters	Range		Point
7	743.7885655225273	21335.119663673097	753.4875261630243
8	-7.700682112628411e+21	-3.737644638336158e+18	-7.010207109287219e+19

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	51
1	104	51

end0.0ms

analyze8.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
81.2%	18.7%	0%	6
100%	0%	0%	7

sample1.1s

Algorithm

intervals

Results

1.0s

8000×

body

valid

Details

analyze8.0ms

sample38.0ms

simplify107.0ms

prune15.0ms

localize54.0ms

rewrite220.0ms

series61.0ms

simplify179.0ms

prune3.1s

localize12.0ms

rewrite34.0ms

series25.0ms

simplify62.0ms

prune200.0ms

localize16.0ms

rewrite56.0ms

series19.0ms

simplify76.0ms

prune349.0ms

localize65.0ms

rewrite158.0ms

series94.0ms

simplify141.0ms

prune5.6s

regimes61.0ms

bsearch80.0ms

simplify2.0ms

end0.0ms

analyze8.0ms

sample1.1s

Profiling