Details

analyze283.0ms

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

sample70.0ms

Algorithm

intervals

Results

30.0ms	65×	body	1280	valid
15.0ms	54×	body	640	valid
7.0ms	21×	body	2560	valid
5.0ms	28×	body	320	valid
3.0ms	69×	body	80	valid
2.0ms	19×	body	160	valid

simplify208.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (207.0ms)

Iter	Nodes	Cost
0	2147	9
1	2147	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: 53.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.8b	(+ x (sqrt (+ (* x x) 1.0)))
3.8b	(log (+ x (sqrt (+ (* x x) 1.0))))
13.9b	(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))

series16.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4913	600
1	4913	600

prune129.0ms

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 1 expressions with local error:

0.2b	(* (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)

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

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

simplify41.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5115	758

prune140.0ms

Filtered

40 candidates to 78 candidates (-95.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0.0b

Counts

83 → 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)))))
0.3b	(/ 0.125 (pow x 3))
8.8b	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite100.0ms

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:

27.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
30.0ms	(+ 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))))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify39.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5183	1749

prune201.0ms

Filtered

82 candidates to 136 candidates (-65.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	136	5	141

Merged error: 0.0b

Counts

141 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.0625 (pow x 5))
0.3b	(/ 0.125 (pow x 3))
11.9b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
16.7b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite83.0ms

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))
31.0ms	(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))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.0625 (pow x 5))
3.0ms	(/ 0.125 (pow x 3))
12.0ms	(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))))

simplify67.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5467	2501

prune332.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

regimes144.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.2b

bsearch32.0ms

Steps

Iters	Range		Point
9	0.008061197411102677	832384.7172582594	0.9002269889862665
9	-13.715412002822996	-1.2528568261197825e-07	-0.9954584039899501

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	179	55
1	179	55

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2245×	body	1280	valid
457.0ms	1598×	body	640	valid
288.0ms	830×	body	2560	valid
147.0ms	827×	body	320	valid
96.0ms	2124×	body	80	valid
41.0ms	376×	body	160	valid

Details

analyze283.0ms

sample70.0ms

simplify208.0ms

prune3.0ms

localize7.0ms

rewrite16.0ms

series16.0ms

simplify49.0ms

prune129.0ms

localize9.0ms

rewrite17.0ms

series15.0ms

simplify41.0ms

prune140.0ms

localize10.0ms

rewrite100.0ms

series25.0ms

simplify39.0ms

prune201.0ms

localize12.0ms

rewrite83.0ms

series25.0ms

simplify67.0ms

prune332.0ms

regimes144.0ms

bsearch32.0ms

simplify3.0ms

end0.0ms

sample2.2s

Profiling