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

sample24.0ms

Algorithm

intervals

Results

7.0ms	47×	body	1280	valid
5.0ms	43×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	12×	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: 28.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite46.0ms

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:

5.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4955	1404
1	4955	1404

prune185.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 0.2b

Counts

113 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.1b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(pow (/ x (+ x 1.0)) 3)
2.1b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

354×	`*-un-lft-identity`
216×	`times-frac`
190×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
78×	`add-cube-cbrt`
66×	`distribute-lft-out`
61×	`distribute-lft-out--`
44×	`difference-of-squares`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`associate-/r/`
14×	`sqr-pow`
13×	`pow1`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`cube-div` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 302

Calls

4 calls:

10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
19.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
7.0ms	(pow (/ x (+ x 1.0)) 3)
101.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series23.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.0ms	(pow (/ x (+ x 1.0)) 3)
14.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify85.0ms

Algorithm

egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5059	5149

prune492.0ms

Filtered

132 candidates to 314 candidates (-137.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	312	2	314
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	313	6	319

Merged error: 0.0b

Counts

319 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(pow (/ x (+ x 1.0)) 3)
2.1b	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
2.1b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

485×	`*-un-lft-identity`
264×	`times-frac`
239×	`add-sqr-sqrt`
138×	`unpow-prod-down` `cube-prod`
106×	`distribute-lft-out--`
88×	`distribute-lft-out`
78×	`log-pow`
77×	`exp-prod`
72×	`difference-of-squares`
59×	`add-cube-cbrt`
25×	`sqr-pow`
24×	`swap-sqr`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
13×	`pow1`
12×	`associate-/r/`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`log-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`cube-div` `pow-unpow`
2×	`difference-cubes` `sub-neg` `pow-exp` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `frac-times` `pow-to-exp` `log-div` `flip3--` `pow-pow` `pow-plus` `exp-diff` `diff-log` `unpow3` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub` `flip--`

Counts

4 → 321

Calls

4 calls:

18.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
7.0ms	(pow (/ x (+ x 1.0)) 3)
111.0ms	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
104.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series34.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.0ms	(pow (/ x (+ x 1.0)) 3)
14.0ms	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
14.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4953	5192
1	4953	5192

prune606.0ms

Filtered

137 candidates to 333 candidates (-143.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	332	1	333
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	333	6	339

Merged error: 0.0b

Counts

339 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
2.2b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
80×	`times-frac`
64×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`exp-prod`
30×	`distribute-lft-out`
18×	`add-cube-cbrt`
17×	`log-pow` `difference-of-squares`
9×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`log-prod` `associate-/l*`
3×	`sub-neg`
2×	`flip3--` `exp-diff` `diff-log` `exp-sum` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

4 → 127

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
31.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
34.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4958	1785
1	4958	1785

prune179.0ms

Filtered

86 candidates to 139 candidates (-61.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	139	6	145

Merged error: 0.0b

Counts

145 → 6

regimes93.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.3b

bsearch23.0ms

Steps

Iters	Range		Point
7	3422.165133181475	89249.59109088026	11564.879843644814
9	-24636101295.52703	-67.61204973096547	-13286.958638175067

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	45
1	94	45

end0.0ms

sample703.0ms

Algorithm

intervals

Results

261.0ms	1755×	body	1280	valid
142.0ms	1196×	body	640	valid
128.0ms	4099×	body	80	valid
59.0ms	644×	body	320	valid
22.0ms	306×	body	160	valid

Details

analyze4.0ms

sample24.0ms

simplify82.0ms

prune4.0ms

localize10.0ms

rewrite46.0ms

series12.0ms

simplify58.0ms

prune185.0ms

localize19.0ms

rewrite157.0ms

series23.0ms

simplify85.0ms

prune492.0ms

localize21.0ms

rewrite272.0ms

series34.0ms

simplify93.0ms

prune606.0ms

localize10.0ms

rewrite112.0ms

series24.0ms

simplify58.0ms

prune179.0ms

regimes93.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample703.0ms

Profiling