Details

analyze256.0ms

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

sample72.0ms

Algorithm

intervals

Results

29.0ms	60×	body	1280	valid
16.0ms	59×	body	640	valid
10.0ms	29×	body	2560	valid
3.0ms	22×	body	320	valid
3.0ms	72×	body	80	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

prune3.0ms

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:

0.9b	(+ x (sqrt (+ (* x x) 1.0)))
3.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.1b	(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:

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

series17.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(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

prune132.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 0.0b

Counts

52 → 6

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite19.0ms

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:

15.0ms

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

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

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

simplify38.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4973	758
1	4973	758

prune134.0ms

Filtered

40 candidates to 78 candidates (-95.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	78	6	84

Merged error: 0.0b

Counts

84 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.0625 (pow x 5))
0.3b	(/ 0.125 (pow x 3))
13.4b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
17.7b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite88.0ms

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))
37.0ms	(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:

4.0ms	(/ 0.0625 (pow x 5))
3.0ms	(/ 0.125 (pow x 3))
10.0ms	(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))))

simplify57.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5361	2493

prune315.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	171	6	177

Merged error: 0.0b

Counts

177 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.3b	(/ 0.125 (pow x 3))
11.2b	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite106.0ms

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:

35.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
27.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
5.0ms	(/ 0.125 (pow x 3))
34.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series24.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
7.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
4.0ms	(/ 0.125 (pow x 3))
9.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify36.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5226	1749

prune197.0ms

Filtered

82 candidates to 136 candidates (-65.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	136	6	142

Merged error: 0.0b

Counts

142 → 6

regimes202.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.5b

bsearch27.0ms

Steps

Iters	Range		Point
8	0.04819230350268283	611.8774644750025	0.8910125926190827
8	-956.5805619630278	-0.18994506292198085	-1.0037838889050343

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	2339×	body	1280	valid
427.0ms	1517×	body	640	valid
260.0ms	783×	body	2560	valid
130.0ms	766×	body	320	valid
90.0ms	2180×	body	80	valid
42.0ms	415×	body	160	valid

Details

analyze256.0ms

sample72.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite17.0ms

series17.0ms

simplify38.0ms

prune132.0ms

localize9.0ms

rewrite19.0ms

series15.0ms

simplify38.0ms

prune134.0ms

localize11.0ms

rewrite88.0ms

series23.0ms

simplify57.0ms

prune315.0ms

localize10.0ms

rewrite106.0ms

series24.0ms

simplify36.0ms

prune197.0ms

regimes202.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling