Details

analyze260.0ms

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

39.0ms	82×	body	1280	valid
14.0ms	48×	body	640	valid
10.0ms	29×	body	2560	valid
3.0ms	70×	body	80	valid
2.0ms	13×	body	320	valid
1.0ms	14×	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: 52.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ x (sqrt (+ (* x x) 1.0)))
2.4b	(log (+ x (sqrt (+ (* x x) 1.0))))
16.8b	(sqrt (+ (* x x) 1.0))

rewrite16.0ms

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:

6.0ms	(+ x (sqrt (+ (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series19.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5075	600

prune105.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	3	52

Merged error: 0b

Counts

52 → 3

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (pow (/ x (sqrt 1.0)) 3) -1/6)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-l`
48×	`add-sqr-sqrt`
40×	`times-frac`
29×	`add-cube-cbrt` `*-un-lft-identity`
25×	`unpow-prod-down` `cube-prod`
20×	`sqrt-prod`
9×	`add-exp-log`
8×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-r` `add-cbrt-cube`
2×	`pow-exp` `div-inv` `sqr-pow`
1×	`pow1` `cube-div` `cube-mult` `pow-to-exp` `unpow3` `div-exp` `associate-l/` `-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 75

Calls

1 calls:

13.0ms

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

series53.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

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

simplify42.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4973	758
1	4973	758

prune122.0ms

Filtered

40 candidates to 78 candidates (-95.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	78	3	81

Merged error: 0b

Counts

81 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.4b	(/ 0.125 (pow x 3))
12.9b	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 106

Calls

3 calls:

29.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
5.0ms	(/ 0.125 (pow x 3))
35.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series20.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(- (/ 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))))))

simplify31.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5723	1429

prune146.0ms

Filtered

70 candidates to 115 candidates (-64.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	115	3	118

Merged error: 0b

Counts

118 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 0.125 (pow x 3))
0.4b	(/ 0.0625 (pow x 5))
15.6b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.4b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite87.0ms

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:

5.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
36.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
36.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series23.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
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))))

simplify257.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5361	2493

prune291.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	171	3	174

Merged error: 0b

Counts

174 → 3

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.5b

bsearch35.0ms

Steps

Iters	Range		Point
10	5.4502705634586025e-06	133904.04974254197	0.8879271987142793
10	-27155451.254620194	-1.0205089123620167e-10	-1.0088560033267078

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	55
1	94	55

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2327×	body	1280	valid
440.0ms	1578×	body	640	valid
270.0ms	816×	body	2560	valid
131.0ms	765×	body	320	valid
92.0ms	2099×	body	80	valid
43.0ms	415×	body	160	valid

Details

analyze260.0ms

sample76.0ms

simplify3.0ms

prune2.0ms

localize6.0ms

rewrite16.0ms

series19.0ms

simplify38.0ms

prune105.0ms

localize9.0ms

rewrite17.0ms

series53.0ms

simplify42.0ms

prune122.0ms

localize10.0ms

rewrite73.0ms

series20.0ms

simplify31.0ms

prune146.0ms

localize12.0ms

rewrite87.0ms

series23.0ms

simplify257.0ms

prune291.0ms

regimes38.0ms

bsearch35.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling