Details

analyze269.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample76.0ms

Algorithm

intervals

Results

37.0ms	73×	body	1280	valid
15.0ms	58×	body	640	valid
9.0ms	26×	body	2560	valid
5.0ms	30×	body	320	valid
2.0ms	59×	body	80	valid
1.0ms	10×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

prune2.0ms

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: 54.4b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(+ x (sqrt (+ (* x x) 1.0)))
2.6b	(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b	(sqrt (+ (* x x) 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
5.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
6.0ms	(sqrt (+ (* x x) 1.0))

series17.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
3.0ms	(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5003	592

prune108.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0.0b

Counts

52 → 5

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ x (sqrt 1.0)) (* 1/6 (pow (/ x (sqrt 1.0)) 3)))
0.5b	(* 1/6 (pow (/ x (sqrt 1.0)) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-r`
49×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
25×	`unpow-prod-down` `cube-prod`
20×	`sqrt-prod`
10×	`add-exp-log`
8×	`unswap-sqr`
4×	`prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`associate-l`
2×	`pow1` `cube-div` `associate-*r/` `pow-exp` `div-inv` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `div-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod`

Counts

2 → 87

Calls

2 calls:

8.0ms	(- (/ x (sqrt 1.0)) (* 1/6 (pow (/ x (sqrt 1.0)) 3)))
15.0ms	(* 1/6 (pow (/ x (sqrt 1.0)) 3))

series43.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (/ x (sqrt 1.0)) (* 1/6 (pow (/ x (sqrt 1.0)) 3)))
17.0ms	(* 1/6 (pow (/ x (sqrt 1.0)) 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5245	932

prune132.0ms

Filtered

45 candidates to 93 candidates (-106.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Merged error: 0.0b

Counts

98 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.0625 (pow x 5))
0.6b	(/ 0.125 (pow x 3))
13.9b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
20.4b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
71×	`times-frac`
68×	`*-un-lft-identity`
46×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`associate-/r*`
15×	`add-exp-log`
14×	`cube-prod`
11×	`log-prod`
10×	`difference-of-squares` `sqr-pow`
9×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `frac-sub` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`cube-mult` `unpow3` `distribute-lft-out`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv`
1×	`sub-neg` `rem-log-exp` `sum-log` `log-pow` `associate--r+`

Counts

4 → 159

Calls

4 calls:

4.0ms	(/ 0.0625 (pow x 5))
5.0ms	(/ 0.125 (pow x 3))
34.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
33.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.0625 (pow x 5))
3.0ms	(/ 0.125 (pow x 3))
9.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
5.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify41.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5269	2482

prune286.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0b	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
0.6b	(/ 0.125 (pow x 3))
10.7b	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
51×	`times-frac`
30×	`add-cube-cbrt`
15×	`add-log-exp`
14×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
10×	`add-exp-log` `distribute-lft-out` `difference-of-squares`
6×	`log-prod` `add-cbrt-cube` `sqr-pow`
5×	`pow1` `sum-log`
4×	`cube-mult` `unpow3` `distribute-lft-out--`
3×	`div-exp` `associate-/l*`
2×	`associate-+r-` `log-div` `flip3-+` `diff-log` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `div-inv`

Counts

4 → 124

Calls

4 calls:

26.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
34.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
5.0ms	(/ 0.125 (pow x 3))
33.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series27.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
5.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
3.0ms	(/ 0.125 (pow x 3))
9.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5109	1750

prune163.0ms

Filtered

82 candidates to 136 candidates (-65.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	136	5	141

Merged error: 0.0b

Counts

141 → 5

regimes45.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch43.0ms

Steps

Iters	Range		Point
8	0.00011290081735184878	2.940923890930708	0.89282765018933
10	-2.291280714725737	-1.1351383323604922e-11	-1.0261498276327259

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	55
1	38	55

end0.0ms

analyze262.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample2.2s

Algorithm

intervals

Results

1.1s	2294×	body	1280	valid
449.0ms	1622×	body	640	valid
291.0ms	850×	body	2560	valid
133.0ms	790×	body	320	valid
88.0ms	2065×	body	80	valid
38.0ms	379×	body	160	valid

Details

analyze269.0ms

sample76.0ms

simplify3.0ms

prune2.0ms

localize6.0ms

rewrite17.0ms

series17.0ms

simplify36.0ms

prune108.0ms

localize9.0ms

rewrite28.0ms

series43.0ms

simplify40.0ms

prune132.0ms

localize13.0ms

rewrite82.0ms

series22.0ms

simplify41.0ms

prune286.0ms

localize10.0ms

rewrite102.0ms

series27.0ms

simplify48.0ms

prune163.0ms

regimes45.0ms

bsearch43.0ms

simplify1.0ms

end0.0ms

analyze262.0ms

sample2.2s

Profiling