Details

analyze249.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample69.0ms

Algorithm

intervals

Results

25.0ms	46×	body	1280	valid
15.0ms	43×	body	640	valid
13.0ms	140×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	6×	body	80	invalid
0.0ms	1×	body	640	invalid
0.0ms	5×	body	80	overflowed

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5720	27

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 27.7b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
2.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out`

Counts

4 → 172

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
13.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
7.0ms	(* (- 1.0 eps) x)
19.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
12.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
5.0ms	(* (- 1.0 eps) x)
48.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4974	6934
1	4974	6934

prune404.0ms

Filtered

99 candidates to 184 candidates (-85.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	2	185

Merged error: 0.1b

Counts

185 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 3) 0.6666666666666667)
6.0b	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-l`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-r` `prod-exp`
2×	`pow1` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 45

Calls

2 calls:

5.0ms	(* (pow x 3) 0.6666666666666667)
7.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* (pow x 3) 0.6666666666666667)
4.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

simplify53.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4959	458
1	4959	458

prune65.0ms

Filtered

33 candidates to 51 candidates (-54.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Merged error: 0.1b

Counts

53 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- (* x 0.6666666666666667) 1.0))
0.8b	(* (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))) (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))
4.5b	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
4.5b	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`sqrt-prod`
23×	`pow1`
16×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
8×	`add-exp-log` `flip3-+` `swap-sqr` `add-cbrt-cube` `flip-+`
5×	`pow-prod-up` `unswap-sqr`
4×	`frac-times` `associate-*r/` `pow-prod-down` `add-log-exp`
3×	`pow-sqr`
2×	`sub-neg` `rem-sqrt-square` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod`
1×	`pow2` `distribute-rgt-in` `flip3--` `distribute-lft-in` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `flip--`

Counts

4 → 109

Calls

4 calls:

7.0ms	(* x (- (* x 0.6666666666666667) 1.0))
10.0ms	(* (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))) (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))
3.0ms	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
3.0ms	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* x (- (* x 0.6666666666666667) 1.0))
4.0ms	(* (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))) (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))
5.0ms	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
6.0ms	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4926	1881
1	4926	1881

prune220.0ms

Filtered

72 candidates to 121 candidates (-68.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	121	3	124

Merged error: 0.1b

Counts

124 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
4.5b	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
5.2b	(sqrt (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))
5.2b	(sqrt (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
3.0ms	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
4.0ms	(sqrt (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))
4.0ms	(sqrt (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
5.0ms	(sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))))
9.0ms	(sqrt (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))
11.0ms	(sqrt (sqrt (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0))))))

simplify37.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5002	1514

prune220.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	84	3	87

Merged error: 0.1b

Counts

87 → 3

regimes105.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.6b

bsearch63.0ms

Steps

Iters	Range		Point
9	0.1193803166968428	1896562.6666856972	481.9795405026713

simplify10.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	522	54
1	522	54

end0.0ms

sample2.2s

Algorithm

intervals

Results

978.0ms	1694×	body	1280	valid
453.0ms	1233×	body	640	valid
352.0ms	4172×	body	80	valid
152.0ms	620×	body	320	valid
49.0ms	281×	body	160	valid
21.0ms	215×	body	80	invalid
16.0ms	205×	body	80	overflowed
6.0ms	14×	body	640	invalid
6.0ms	11×	body	1280	invalid
1.0ms	4×	body	320	invalid
0.0ms	2×	body	160	invalid

Details

analyze249.0ms

sample69.0ms

simplify61.0ms

prune8.0ms

localize17.0ms

rewrite61.0ms

series75.0ms

simplify85.0ms

prune404.0ms

localize9.0ms

rewrite13.0ms

series8.0ms

simplify53.0ms

prune65.0ms

localize12.0ms

rewrite25.0ms

series21.0ms

simplify56.0ms

prune220.0ms

localize14.0ms

rewrite15.0ms

series31.0ms

simplify37.0ms

prune220.0ms

regimes105.0ms

bsearch63.0ms

simplify10.0ms

end0.0ms

sample2.2s

Profiling