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

sample27.0ms

Algorithm

intervals

Results

8.0ms	52×	body	1280	valid
5.0ms	42×	body	640	valid
5.0ms	133×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	1001	13
1	1001	13

prune8.0ms

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: 29.2b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite43.0ms

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))
28.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4954	1406
1	4954	1406

prune183.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	3	113

Merged error: 0.0b

Counts

113 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ x 1.0) (/ (+ x 1.0) (* (- x 1.0) (- x 1.0))))
3.5b	(- (* x (/ x (* (+ x 1.0) (+ x 1.0)))) (* (+ x 1.0) (/ (+ x 1.0) (* (- x 1.0) (- x 1.0)))))
14.8b	(/ (+ x 1.0) (* (- x 1.0) (- x 1.0)))
14.8b	(/ x (* (+ x 1.0) (+ x 1.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-/r/`
23×	`add-exp-log` `add-cbrt-cube`
19×	`*-un-lft-identity`
16×	`frac-times` `associate-r`
15×	`add-sqr-sqrt`
13×	`flip3--` `associate-*r/` `flip--`
12×	`times-frac`
11×	`add-cube-cbrt` `flip3-+` `flip-+`
10×	`associate-*l/`
7×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`frac-sub`
4×	`associate-l` `distribute-lft-out`
3×	`div-inv`
2×	`frac-2neg` `clear-num` `associate-/r*` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 120

Calls

4 calls:

17.0ms	(* (+ x 1.0) (/ (+ x 1.0) (* (- x 1.0) (- x 1.0))))
13.0ms	(- (* x (/ x (* (+ x 1.0) (+ x 1.0)))) (* (+ x 1.0) (/ (+ x 1.0) (* (- x 1.0) (- x 1.0)))))
11.0ms	(/ (+ x 1.0) (* (- x 1.0) (- x 1.0)))
8.0ms	(/ x (* (+ x 1.0) (+ x 1.0)))

series21.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ x 1.0) (/ (+ x 1.0) (* (- x 1.0) (- x 1.0))))
11.0ms	(- (* x (/ x (* (+ x 1.0) (+ x 1.0)))) (* (+ x 1.0) (/ (+ x 1.0) (* (- x 1.0) (- x 1.0)))))
3.0ms	(/ (+ x 1.0) (* (- x 1.0) (- x 1.0)))
3.0ms	(/ x (* (+ x 1.0) (+ x 1.0)))

simplify246.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4978	1994
1	4978	1994

prune290.0ms

Filtered

99 candidates to 132 candidates (-33.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	131	4	135

Merged error: 0.0b

Counts

135 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
0.1b	(* x (/ 1 (+ x 1.0)))
8.4b	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
46×	`times-frac`
33×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `distribute-lft-out`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `frac-sub` `flip--` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 136

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ 1 (+ x 1.0))
9.0ms	(* x (/ 1 (+ x 1.0)))
14.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series15.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
2.0ms	(/ 1 (+ x 1.0))
3.0ms	(* x (/ 1 (+ x 1.0)))
7.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4970	1494
1	4970	1494

prune179.0ms

Filtered

93 candidates to 148 candidates (-59.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	148	4	152

Merged error: 0.0b

Counts

152 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.4b	(/ 16.0 (pow x 3))
0.5b	(/ (neg 5.0) (* x x))
6.8b	(- (/ (neg 5.0) (* x x)) (+ (/ 6.0 x) (/ 16.0 (pow x 3))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
63×	`times-frac`
39×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
18×	`distribute-lft-out`
14×	`add-exp-log`
13×	`associate-/r` `associate-/l`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `distribute-lft-out--`
5×	`div-exp`
4×	`pow1` `cube-mult` `unpow3` `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-+` `div-inv` `difference-of-squares`
1×	`+-commutative` `associate--l-` `pow-to-exp` `sub-neg` `flip3--` `distribute-frac-neg` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `associate--r+`

Counts

4 → 144

Calls

4 calls:

30.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
5.0ms	(/ 16.0 (pow x 3))
5.0ms	(/ (neg 5.0) (* x x))
35.0ms	(- (/ (neg 5.0) (* x x)) (+ (/ 6.0 x) (/ 16.0 (pow x 3))))

series16.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
4.0ms	(/ 16.0 (pow x 3))
3.0ms	(/ (neg 5.0) (* x x))
4.0ms	(- (/ (neg 5.0) (* x x)) (+ (/ 6.0 x) (/ 16.0 (pow x 3))))

simplify51.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4967	1832
1	4967	1832

prune248.0ms

Filtered

97 candidates to 156 candidates (-60.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	156	4	160

Merged error: 0.0b

Counts

160 → 4

regimes44.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch27.0ms

Steps

Iters	Range		Point
9	1.4499310323286543	23112182.969475247	15449.082165169788
9	-46059.188652748846	-0.5102213581822865	-13348.764274700028

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	302	69
1	302	69

end0.0ms

sample774.0ms

Algorithm

intervals

Results

283.0ms	1707×	body	1280	valid
159.0ms	1249×	body	640	valid
147.0ms	4122×	body	80	valid
62.0ms	622×	body	320	valid
22.0ms	300×	body	160	valid

Details

analyze4.0ms

sample27.0ms

simplify76.0ms

prune8.0ms

localize7.0ms

rewrite43.0ms

series12.0ms

simplify76.0ms

prune183.0ms

localize19.0ms

rewrite54.0ms

series21.0ms

simplify246.0ms

prune290.0ms

localize8.0ms

rewrite43.0ms

series15.0ms

simplify65.0ms

prune179.0ms

localize18.0ms

rewrite80.0ms

series16.0ms

simplify51.0ms

prune248.0ms

regimes44.0ms

bsearch27.0ms

simplify4.0ms

end0.0ms

sample774.0ms

Profiling