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

8.0ms	55×	body	1280	valid
4.0ms	125×	body	80	valid
3.0ms	29×	body	640	valid
2.0ms	26×	body	320	valid
1.0ms	21×	body	160	valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

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: 30.2b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
5.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite45.0ms

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))
7.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series13.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
8.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4955	1404
1	4955	1404

prune219.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
5.5b	(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

284×	`*-un-lft-identity`
188×	`cbrt-prod`
171×	`times-frac`
164×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
58×	`associate-r`
51×	`swap-sqr`
49×	`distribute-lft-out`
41×	`distribute-lft-out--`
30×	`pow1` `associate-l`
29×	`difference-of-squares`
28×	`cbrt-div`
15×	`pow1/3`
13×	`add-exp-log`
12×	`associate-/r/` `unswap-sqr`
11×	`frac-times` `associate-*l/` `pow-prod-up`
7×	`flip3--` `pow-plus` `associate-*r/` `pow-prod-down` `frac-sub` `add-cbrt-cube` `flip--`
6×	`div-inv` `add-log-exp`
5×	`associate-/r*` `pow-sqr`
4×	`prod-exp` `cbrt-unprod` `associate-/l*`
3×	`pow2`
2×	`*-commutative` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `pow3` `clear-num` `flip-+`

Counts

4 → 268

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
28.0ms	(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
30.0ms	(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
10.0ms	(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))
14.0ms	(* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))
12.0ms	(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5068	5011

prune542.0ms

Filtered

158 candidates to 280 candidates (-77.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	279	1	280
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	279	6	285

Merged error: 0.0b

Counts

285 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
0.3b	(/ 3.0 (pow x 3))
0.3b	(/ (neg 1.0) (* x x))
5.2b	(- (/ (neg 1.0) (* x x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

61×	`times-frac`
58×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r` `associate-/l`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
9×	`unpow3`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `distribute-lft-out`
5×	`div-exp`
4×	`pow1` `cube-mult` `distribute-rgt-out` `div-inv` `sqr-pow`
3×	`cbrt-undiv` `frac-sub`
2×	`neg-sub0` `neg-mul-1` `frac-2neg` `flip3-+` `diff-log` `div-sub` `frac-add` `clear-num` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `pow-to-exp` `sub-neg` `flip3--` `distribute-frac-neg` `distribute-rgt1-in` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `associate--r+`

Counts

4 → 145

Calls

4 calls:

23.0ms	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
5.0ms	(/ 3.0 (pow x 3))
5.0ms	(/ (neg 1.0) (* x x))
37.0ms	(- (/ (neg 1.0) (* x x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series19.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
4.0ms	(/ 3.0 (pow x 3))
3.0ms	(/ (neg 1.0) (* x x))
4.0ms	(- (/ (neg 1.0) (* x x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify54.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5150	1726

prune201.0ms

Filtered

102 candidates to 157 candidates (-53.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	157	6	163

Merged error: 0.0b

Counts

163 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 3.0 x) (+ 1 (/ 1 (* x x))))
0.3b	(/ (neg 1.0) (* x x))
0.3b	(/ 1 (* x x))
5.2b	(- (/ (neg 1.0) (* x x)) (* (/ 3.0 x) (+ 1 (/ 1 (* x x)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
19×	`add-cbrt-cube`
14×	`pow1`
13×	`associate-l` `associate-/l*`
7×	`div-exp`
6×	`distribute-lft-neg-in` `pow-flip` `distribute-rgt-neg-in` `prod-exp` `add-log-exp`
5×	`cbrt-undiv` `associate-r` `frac-sub`
4×	`frac-times` `flip3-+` `associate-*r/` `cbrt-unprod` `flip-+` `div-inv`
2×	`neg-sub0` `distribute-rgt-in` `neg-mul-1` `rec-exp` `frac-2neg` `distribute-lft-in` `1-exp` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `distribute-lft-out` `associate--r+` `unswap-sqr`
1×	`associate--l-` `pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `distribute-frac-neg` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `inv-pow`

Counts

4 → 128

Calls

4 calls:

10.0ms	(* (/ 3.0 x) (+ 1 (/ 1 (* x x))))
7.0ms	(/ (neg 1.0) (* x x))
5.0ms	(/ 1 (* x x))
9.0ms	(- (/ (neg 1.0) (* x x)) (* (/ 3.0 x) (+ 1 (/ 1 (* x x)))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (/ 3.0 x) (+ 1 (/ 1 (* x x))))
3.0ms	(/ (neg 1.0) (* x x))
2.0ms	(/ 1 (* x x))
4.0ms	(- (/ (neg 1.0) (* x x)) (* (/ 3.0 x) (+ 1 (/ 1 (* x x)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5013	1423

prune156.0ms

Filtered

95 candidates to 140 candidates (-47.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	140	6	146

Merged error: 0.0b

Counts

146 → 6

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch24.0ms

Steps

Iters	Range		Point
9	795.4531078621454	1761006479.4503977	13528.871339198671
8	-2853489.8956074286	-706.3889088011921	-13231.15271243126

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	190	47
1	190	47

end0.0ms

sample725.0ms

Algorithm

intervals

Results

270.0ms	1774×	body	1280	valid
141.0ms	1189×	body	640	valid
133.0ms	4063×	body	80	valid
58.0ms	648×	body	320	valid
20.0ms	326×	body	160	valid

Details

analyze4.0ms

sample24.0ms

simplify80.0ms

prune4.0ms

localize6.0ms

rewrite45.0ms

series13.0ms

simplify54.0ms

prune219.0ms

localize10.0ms

rewrite91.0ms

series34.0ms

simplify74.0ms

prune542.0ms

localize10.0ms

rewrite75.0ms

series19.0ms

simplify54.0ms

prune201.0ms

localize9.0ms

rewrite34.0ms

series17.0ms

simplify47.0ms

prune156.0ms

regimes49.0ms

bsearch24.0ms

simplify3.0ms

end0.0ms

sample725.0ms

Profiling