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	52×	body	1280	valid
5.0ms	41×	body	640	valid
4.0ms	125×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	13×	body	160	valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

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: 30.7b

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))
3.6b	(- (/ 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:

8.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
32.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4955	1404
1	4955	1404

prune186.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	7	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	7	113

Merged error: 0.2b

Counts

113 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 3.0 (pow x 3))
0.3b	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
6.4b	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 122

Calls

3 calls:

5.0ms	(/ 3.0 (pow x 3))
11.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
18.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

series15.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify36.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5221	1493

prune179.0ms

Filtered

85 candidates to 131 candidates (-54.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Merged error: 0.0b

Counts

138 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x))
0.1b	(/ 3.0 (pow x 3))
0.1b	(/ (/ (neg 1.0) x) x)
6.4b	(- (+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x)) (/ 3.0 (pow x 3)))

rewrite309.0ms

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:

131.0ms	(+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x))
5.0ms	(/ 3.0 (pow x 3))
10.0ms	(/ (/ (neg 1.0) x) x)
149.0ms	(- (+ (/ (/ (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	(/ 3.0 (pow x 3))
3.0ms	(/ (/ (neg 1.0) x) x)
4.0ms	(- (+ (/ (/ (neg 1.0) x) x) (/ (neg 3.0) x)) (/ 3.0 (pow x 3)))

simplify85.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4968	3546
1	4968	3546

prune374.0ms

Filtered

183 candidates to 286 candidates (-56.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	286	8	294

Merged error: 0.0b

Counts

294 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.1b	(pow (/ x (+ x 1.0)) 3)
3.6b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite154.0ms

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:

19.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
7.0ms	(pow (/ x (+ x 1.0)) 3)
99.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series23.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify86.0ms

Algorithm

egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5059	5149

prune478.0ms

Filtered

132 candidates to 314 candidates (-137.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	313	1	314
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	315	7	322

Merged error: 0.0b

Counts

322 → 7

regimes99.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch24.0ms

Steps

Iters	Range		Point
8	885.3310581862714	9966992.137111468	13483.542986370416
9	-4791157897.469991	-881.013208362474	-9097.76265741964

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	190	54
1	190	54

end0.0ms

sample701.0ms

Algorithm

intervals

Results

253.0ms	1734×	body	1280	valid
148.0ms	1272×	body	640	valid
129.0ms	4066×	body	80	valid
55.0ms	638×	body	320	valid
19.0ms	290×	body	160	valid

Details

analyze4.0ms

sample24.0ms

simplify85.0ms

prune4.0ms

localize6.0ms

rewrite49.0ms

series12.0ms

simplify55.0ms

prune186.0ms

localize10.0ms

rewrite38.0ms

series15.0ms

simplify36.0ms

prune179.0ms

localize12.0ms

rewrite309.0ms

series16.0ms

simplify85.0ms

prune374.0ms

localize18.0ms

rewrite154.0ms

series23.0ms

simplify86.0ms

prune478.0ms

regimes99.0ms

bsearch24.0ms

simplify3.0ms

end0.0ms

sample701.0ms

Profiling