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

sample84.0ms

Algorithm

intervals

Results

29.0ms

256×

body

valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4938	73
1	4938	73

prune16.0ms

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: 29.0b

Counts

2 → 2

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (* x 0.7715471019))
0.2b	(* 0.0001789971 (* 2.0 (pow x 12)))
14.7b	(* x (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))
28.3b	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

95×	`*-un-lft-identity`
41×	`times-frac`
38×	`distribute-lft-out`
33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `associate-r`
26×	`add-exp-log`
21×	`add-cbrt-cube`
13×	`pow1`
12×	`prod-exp`
9×	`associate-l`
8×	`cbrt-unprod`
5×	`pow-prod-down` `associate-/r*`
4×	`associate-/r/` `associate-/l*` `add-log-exp`
3×	`flip3-+` `*-commutative` `flip-+`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/` `unswap-sqr`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-exp` `clear-num`

Counts

4 → 127

Calls

4 calls:

5.0ms	(* x (* x 0.7715471019))
7.0ms	(* 0.0001789971 (* 2.0 (pow x 12)))
45.0ms	(* x (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))
38.0ms	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* x (* x 0.7715471019))
5.0ms	(* 0.0001789971 (* 2.0 (pow x 12)))
27.0ms	(* x (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))
21.0ms	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))

simplify100.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4955	7607
1	4955	7607

prune810.0ms

Filtered

82 candidates to 139 candidates (-69.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	138	3	141

Merged error: 0b

Counts

141 → 3

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.1049934947 (* x x))
0.2b	(* x (* x 0.7715471019))
0.2b	(* 0.0001789971 (* 2.0 (pow x 12)))
28.3b	(* (* x (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10)))))))) (/ 1 (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
31×	`*-un-lft-identity` `add-cbrt-cube`
25×	`prod-exp`
24×	`associate-r`
21×	`pow1`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `cbrt-unprod`
10×	`associate-l` `pow-prod-down`
9×	`distribute-lft-out`
5×	`associate-*r/`
4×	`div-exp` `*-commutative` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `associate-/r/`
1×	`pow-to-exp` `pow-exp` `un-div-inv` `div-inv` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* 0.1049934947 (* x x))
5.0ms	(* x (* x 0.7715471019))
6.0ms	(* 0.0001789971 (* 2.0 (pow x 12)))
44.0ms	(* (* x (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10)))))))) (/ 1 (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.1049934947 (* x x))
3.0ms	(* x (* x 0.7715471019))
6.0ms	(* 0.0001789971 (* 2.0 (pow x 12)))
24.0ms	(* (* x (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10)))))))) (/ 1 (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))

simplify77.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4979	4000
1	4979	4000

prune504.0ms

Filtered

67 candidates to 118 candidates (-76.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Merged error: 0b

Counts

121 → 3

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.0001789971 (* 2.0 (pow x 12)))
9.3b	(cbrt (pow (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))) 3))
14.7b	(* x (cbrt (pow (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))) 3)))
28.3b	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
106×	`cbrt-prod`
82×	`times-frac`
70×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
54×	`associate-r`
46×	`unpow-prod-down` `cube-prod`
42×	`distribute-lft-out`
18×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`associate-/r/`
8×	`pow1` `prod-exp`
7×	`unswap-sqr`
6×	`flip3-+` `associate-l` `flip-+`
5×	`div-inv`
4×	`associate-/r` `cbrt-unprod` `associate-/l` `add-log-exp`
3×	`sqr-pow`
2×	`cube-div` `cube-mult` `cbrt-div` `unpow3` `pow-prod-down` `*-commutative` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow1/3` `associate-*r/` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube`

Counts

4 → 194

Calls

4 calls:

7.0ms	(* 0.0001789971 (* 2.0 (pow x 12)))
42.0ms	(cbrt (pow (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))) 3))
52.0ms	(* x (cbrt (pow (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))) 3)))
40.0ms	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* 0.0001789971 (* 2.0 (pow x 12)))
21.0ms	(cbrt (pow (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))) 3))
29.0ms	(* x (cbrt (pow (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))) 3)))
21.0ms	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (* x (* x 0.7715471019)) (+ (* (pow x 4) 0.2909738639) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))

simplify139.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5023	14931

prune1.2s

Filtered

101 candidates to 206 candidates (-104.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	206	3	209

Merged error: 0b

Counts

209 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
0.0b	(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
0.1b	(/ 0.15298196345929327 (pow x 5))
0.1b	(/ 0.2514179000665375 (pow x 3))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity` `times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down`
19×	`associate-/r*`
14×	`add-exp-log`
12×	`cube-prod`
11×	`add-log-exp`
8×	`add-cbrt-cube` `sqr-pow`
7×	`distribute-lft-out`
6×	`div-exp` `associate-/l*`
5×	`frac-add`
4×	`pow1` `cube-mult` `unpow3` `sum-log`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`associate-+r+`

Counts

4 → 143

Calls

4 calls:

40.0ms	(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
20.0ms	(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
5.0ms	(/ 0.15298196345929327 (pow x 5))
6.0ms	(/ 0.2514179000665375 (pow x 3))

series24.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
10.0ms	(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
4.0ms	(/ 0.15298196345929327 (pow x 5))
4.0ms	(/ 0.2514179000665375 (pow x 3))

simplify38.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5256	1705

prune213.0ms

Filtered

97 candidates to 155 candidates (-59.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	155	3	158

Merged error: 0b

Counts

158 → 3

regimes52.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.2b

bsearch84.0ms

Steps

Iters	Range		Point
7	185.29969706660688	16554.089206526653	701.6079189610164
8	-5517.510417844453	-15.952734826105884	-2768.633801305457

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	99
1	102	99

end0.0ms

sample2.3s

Algorithm

intervals

Results

930.0ms

8000×

body

valid

Details

analyze8.0ms

sample84.0ms

simplify74.0ms

prune16.0ms

localize45.0ms

rewrite100.0ms

series57.0ms

simplify100.0ms

prune810.0ms

localize45.0ms

rewrite64.0ms

series35.0ms

simplify77.0ms

prune504.0ms

localize48.0ms

rewrite149.0ms

series76.0ms

simplify139.0ms

prune1.2s

localize11.0ms

rewrite76.0ms

series24.0ms

simplify38.0ms

prune213.0ms

regimes52.0ms

bsearch84.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling