Details

analyze4.0ms (0.1%)

Algorithm

1×

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

sample25.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	66×	body	1280	valid
4.0ms	36×	body	640	valid
4.0ms	125×	body	80	valid
1.0ms	17×	body	160	valid
1.0ms	12×	body	320	valid

simplify97.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	1001	13
1	1001	13

prune4.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 30.6b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
3.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite41.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

2 → 70

Calls

2 calls:

31.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
7.0ms	(/ (+ x 1.0) (- x 1.0))

series10.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

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

simplify32.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5024	1087

prune154.0ms (5.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Merged error: 0.2b

Counts

77 → 3

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 x) 3.0)
0.2b	(/ 3.0 (pow x 3))
0.2b	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
8.8b	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

rewrite46.0ms (1.7%)

Algorithm

1×	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:

17.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))
11.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
7.0ms	(/ 3.0 (pow x 3))
6.0ms	(+ (/ 1.0 x) 3.0)

series16.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
4.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))
3.0ms	(/ 3.0 (pow x 3))
3.0ms	(+ (/ 1.0 x) 3.0)

simplify35.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5256	1609

prune288.0ms (10.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	144	5	149

Merged error: 0.1b

Counts

149 → 5

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 x) 3.0)
0.1b	(/ (neg (+ (/ 1.0 x) 3.0)) x)
0.2b	(/ 3.0 (pow x 3))
8.8b	(- (/ (neg (+ (/ 1.0 x) 3.0)) x) (/ 3.0 (pow x 3)))

rewrite97.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`times-frac`
87×	`*-un-lft-identity`
85×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
18×	`distribute-rgt-neg-in`
16×	`distribute-lft-neg-in`
15×	`associate-/r` `associate-/l`
14×	`unpow-prod-down` `cube-prod`
11×	`add-exp-log`
10×	`distribute-lft-out` `difference-of-squares`
8×	`add-cbrt-cube` `add-log-exp`
6×	`sqr-pow`
4×	`pow1` `cube-mult` `neg-mul-1` `unpow3` `div-exp` `distribute-lft-out--`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+` `div-inv` `associate-/l/` `distribute-neg-frac`
1×	`+-commutative` `associate--l-` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `distribute-frac-neg` `pow-exp` `sum-log` `frac-sub` `flip--`

Counts

4 → 171

Calls

4 calls:

67.0ms	(- (/ (neg (+ (/ 1.0 x) 3.0)) x) (/ 3.0 (pow x 3)))
11.0ms	(/ (neg (+ (/ 1.0 x) 3.0)) x)
7.0ms	(+ (/ 1.0 x) 3.0)
5.0ms	(/ 3.0 (pow x 3))

series17.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

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

simplify67.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4990	2284
1	4990	2284

prune357.0ms (13.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	183	5	188

Merged error: 0.1b

Counts

188 → 5

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
3.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite123.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

189×	`*-un-lft-identity`
80×	`times-frac`
53×	`add-sqr-sqrt`
52×	`distribute-lft-out--`
32×	`distribute-lft-out`
16×	`cbrt-prod` `difference-of-squares`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `frac-sub` `add-cbrt-cube` `flip--`
3×	`sub-neg` `cbrt-div` `diff-log`
1×	`pow1/3`

Counts

4 → 102

Calls

4 calls:

31.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
28.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
28.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series37.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt (- (/ 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)))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify40.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4989	2272
1	4989	2272

prune388.0ms (14.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	114	5	119

Merged error: 0.0b

Counts

119 → 5

regimes86.0ms (3.2%)

Accuracy

Total 0.0b remaining (27.9%)

Threshold costs 0.0b (27.9%)

bsearch25.0ms (0.9%)

Steps

Iters	Range		Point
7	12302.25956354686	381651.6294982458	15314.37957646558
9	-30114.87532477197	-0.16605346141893446	-11903.191960040664

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	116	69
1	116	69

end0.0ms (0%)

sample703.0ms (25.8%)

Algorithm

1×

intervals

Results

260.0ms	1698×	body	1280	valid
139.0ms	1201×	body	640	valid
130.0ms	4139×	body	80	valid
60.0ms	628×	body	320	valid
20.0ms	334×	body	160	valid

Details

analyze4.0ms (0.1%)

sample25.0ms (0.9%)

simplify97.0ms (3.6%)

prune4.0ms (0.2%)

localize6.0ms (0.2%)

rewrite41.0ms (1.5%)

series10.0ms (0.4%)

simplify32.0ms (1.2%)

prune154.0ms (5.6%)

localize9.0ms (0.3%)

rewrite46.0ms (1.7%)

series16.0ms (0.6%)

simplify35.0ms (1.3%)

prune288.0ms (10.5%)

localize9.0ms (0.3%)

rewrite97.0ms (3.5%)

series17.0ms (0.6%)

simplify67.0ms (2.5%)

prune357.0ms (13.1%)

localize10.0ms (0.4%)

rewrite123.0ms (4.5%)

series37.0ms (1.3%)

simplify40.0ms (1.5%)

prune388.0ms (14.2%)

regimes86.0ms (3.2%)

bsearch25.0ms (0.9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample703.0ms (25.8%)

Profiling