Details

analyze316.0ms

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

sample71.0ms

Algorithm

intervals

Results

32.0ms	66×	body	1280	valid
15.0ms	54×	body	640	valid
9.0ms	26×	body	2560	valid
4.0ms	21×	body	320	valid
3.0ms	73×	body	80	valid
2.0ms	16×	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: 51.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ x (sqrt (+ (* x x) 1.0)))
3.8b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.6b	(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))

series21.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5075	600

prune115.0ms

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:

0.1b	(* (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)

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

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

simplify39.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4973	758
1	4973	758

prune127.0ms

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

localize11.0ms

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)))
0.1b	(/ 0.125 (pow x 3))
9.2b	(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:

32.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
29.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
5.0ms	(/ 0.125 (pow x 3))
32.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify36.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5226	1749

prune174.0ms

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:

0.1b	(/ 0.125 (pow x 3))
0.2b	(/ 0.0625 (pow x 5))
11.2b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
18.7b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite84.0ms

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))
32.0ms	(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))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
10.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
8.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify55.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5361	2493

prune280.0ms

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

regimes137.0ms

Accuracy

99.1% (0.3b remaining)

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

bsearch27.0ms

Steps

Iters	Range		Point
8	8.95276132304425e-05	0.9987375623103671	0.8798157924030638
9	-1029092.613259418	-0.1073922169146093	-1.009741899495162

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	2348×	body	1280	valid
440.0ms	1561×	body	640	valid
287.0ms	842×	body	2560	valid
133.0ms	763×	body	320	valid
91.0ms	2102×	body	80	valid
39.0ms	384×	body	160	valid

Details

analyze316.0ms

sample71.0ms

simplify3.0ms

prune2.0ms

localize6.0ms

rewrite16.0ms

series21.0ms

simplify45.0ms

prune115.0ms

localize9.0ms

rewrite17.0ms

series14.0ms

simplify39.0ms

prune127.0ms

localize11.0ms

rewrite102.0ms

series26.0ms

simplify36.0ms

prune174.0ms

localize12.0ms

rewrite84.0ms

series26.0ms

simplify55.0ms

prune280.0ms

regimes137.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

sample2.2s

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