Details

analyze266.0ms

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

sample154.0ms

Algorithm

intervals

Results

34.0ms	72×	body	1280	valid
17.0ms	65×	body	640	valid
8.0ms	25×	body	2560	valid
5.0ms	29×	body	320	valid
2.0ms	55×	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: 54.7b

Counts

2 → 1

localize26.0ms

Local error

Found 3 expressions with local error:

12.8b	(sqrt (+ (* x x) 1.0))
17.3b	(+ x (sqrt (+ (* x x) 1.0)))
29.9b	(log (+ x (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:

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

series17.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))

simplify40.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5075	600

prune99.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

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)

simplify39.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4973	758
1	4973	758

prune126.0ms

Filtered

40 candidates to 78 candidates (-95.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Merged error: 0b

Counts

82 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.0625 (pow x 5))
0.1b	(/ 0.125 (pow x 3))
12.6b	(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))))

rewrite89.0ms

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)))))
37.0ms	(- (/ 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)))))
6.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify56.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5361	2493

prune296.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0b

Counts

175 → 4

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.1b	(/ 0.125 (pow x 3))
10.2b	(log (+ (* x 2) (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
51×	`times-frac`
35×	`*-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×	`sqr-pow`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow1` `cube-mult` `unpow3`
3×	`log-prod` `div-exp` `associate-/l*`
2×	`log-div` `distribute-lft-out--`
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 → 103

Calls

3 calls:

28.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
5.0ms	(/ 0.125 (pow x 3))
30.0ms	(log (+ (* x 2) (- (/ 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 2) (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify30.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5451	1389

prune159.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	112	4	116

Merged error: 0b

Counts

116 → 4

regimes101.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch60.0ms

Steps

Iters	Range		Point
9	3.5414994669164844e-06	998.7618487170289	0.8860700991029492
10	-5588807744.785467	-0.09395944944426991	-1.01671876785975

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	55
1	95	55

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.1s	2351×	body	1280	valid
432.0ms	1582×	body	640	valid
256.0ms	779×	body	2560	valid
131.0ms	809×	body	320	valid
82.0ms	2095×	body	80	valid
37.0ms	384×	body	160	valid

Details

analyze266.0ms

sample154.0ms

simplify3.0ms

prune2.0ms

localize26.0ms

rewrite16.0ms

series17.0ms

simplify40.0ms

prune99.0ms

localize10.0ms

rewrite20.0ms

series15.0ms

simplify39.0ms

prune126.0ms

localize19.0ms

rewrite89.0ms

series23.0ms

simplify56.0ms

prune296.0ms

localize15.0ms

rewrite67.0ms

series20.0ms

simplify30.0ms

prune159.0ms

regimes101.0ms

bsearch60.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling