Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample39.0ms

Algorithm

intervals

Results

9.0ms	64×	body	1280	valid
5.0ms	51×	body	640	valid
3.0ms	110×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	7×	body	160	valid

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	1001	13
1	1001	13

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 34.3b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
34.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 103

Calls

3 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
32.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series13.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
3.0ms	(/ x (+ x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4955	1404
1	4955	1404

prune164.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	4	113

Merged error: 0.2b

Counts

113 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 x) 3.0)
0.2b	(/ 3.0 (pow x 3))
0.3b	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
5.6b	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
42×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
37×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-l`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
11×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1`
5×	`flip3-+` `frac-sub` `flip-+`
4×	`cube-mult` `frac-times` `unpow3` `associate-r/` `div-exp` `associate-r*` `sqr-pow`
3×	`associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `associate-*l/` `prod-exp` `associate--l+` `cbrt-unprod` `div-inv` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `*-commutative` `flip--`

Counts

4 → 134

Calls

4 calls:

6.0ms	(+ (/ 1.0 x) 3.0)
5.0ms	(/ 3.0 (pow x 3))
11.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
17.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (/ 1.0 x) 3.0)
3.0ms	(/ 3.0 (pow x 3))
6.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
6.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

simplify38.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5256	1609

prune191.0ms

Filtered

95 candidates to 146 candidates (-53.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	146	4	150

Merged error: 0.0b

Counts

150 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x))
0.1b	(/ (/ (neg 1.0) x) x)
0.2b	(/ 3.0 (pow x 3))
5.6b	(- (+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x)) (/ 3.0 (pow x 3)))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

281×	`times-frac`
180×	`*-un-lft-identity`
161×	`add-sqr-sqrt`
148×	`add-cube-cbrt`
40×	`distribute-rgt-neg-in`
37×	`associate-/l*`
36×	`distribute-lft-neg-in`
15×	`associate-/r*`
14×	`add-exp-log`
13×	`unpow-prod-down` `cube-prod`
12×	`neg-mul-1`
11×	`add-cbrt-cube` `add-log-exp`
10×	`div-inv` `distribute-lft-out`
8×	`div-sub`
7×	`distribute-frac-neg`
6×	`div-exp`
5×	`neg-sub0` `cube-mult` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
4×	`pow1` `cbrt-undiv` `unpow3`
3×	`associate--l-` `frac-sub`
2×	`associate-+l-` `associate-+r-` `distribute-rgt-out` `frac-2neg` `flip3-+` `diff-log` `unsub-neg` `frac-add` `clear-num` `sum-log` `flip-+`
1×	`+-commutative` `pow-to-exp` `sub-neg` `distribute-neg-out` `flip3--` `pow-exp` `associate--l+` `flip--` `associate-/l/`

Counts

4 → 274

Calls

4 calls:

132.0ms	(+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x))
10.0ms	(/ (/ (neg 1.0) x) x)
5.0ms	(/ 3.0 (pow x 3))
153.0ms	(- (+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x)) (/ 3.0 (pow x 3)))

series16.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x))
3.0ms	(/ (/ (neg 1.0) x) x)
3.0ms	(/ 3.0 (pow x 3))
4.0ms	(- (+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x)) (/ 3.0 (pow x 3)))

simplify79.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4968	3546
1	4968	3546

prune370.0ms

Filtered

183 candidates to 286 candidates (-56.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	286	4	290

Merged error: 0.0b

Counts

290 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.2b	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
34.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
34.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

957×	`*-un-lft-identity`
364×	`times-frac`
261×	`distribute-lft-out--`
202×	`sqrt-prod`
168×	`distribute-lft-out`
110×	`add-sqr-sqrt`
79×	`swap-sqr`
28×	`difference-of-squares`
27×	`sqrt-div`
20×	`pow1`
19×	`associate-r` `associate-l`
13×	`add-cube-cbrt`
11×	`flip3--` `frac-sub` `flip--`
9×	`frac-times` `sqrt-pow1` `pow1/2`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`sub-neg` `diff-log`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 240

Calls

4 calls:

29.0ms	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
72.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
31.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
7.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4937	4815
1	4937	4815

prune258.0ms

Filtered

101 candidates to 252 candidates (-149.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	252	4	256

Merged error: 0.0b

Counts

256 → 4

regimes74.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch37.0ms

Steps

Iters	Range		Point
10	13.25944493701611	9.547425228656423e+18	9798.729158736414
9	-1714524068.3873823	-12.625091796814116	-10334.816621284013

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	190	54
1	190	54

end0.0ms

sample973.0ms

Algorithm

intervals

Results

236.0ms	1723×	body	1280	valid
140.0ms	1291×	body	640	valid
113.0ms	4047×	body	80	valid
51.0ms	631×	body	320	valid
17.0ms	308×	body	160	valid

Details

analyze4.0ms

sample39.0ms

simplify82.0ms

prune4.0ms

localize6.0ms

rewrite49.0ms

series13.0ms

simplify56.0ms

prune164.0ms

localize11.0ms

rewrite45.0ms

series18.0ms

simplify38.0ms

prune191.0ms

localize12.0ms

rewrite317.0ms

series16.0ms

simplify79.0ms

prune370.0ms

localize10.0ms

rewrite192.0ms

series32.0ms

simplify109.0ms

prune258.0ms

regimes74.0ms

bsearch37.0ms

simplify3.0ms

end0.0ms

sample973.0ms

Profiling