Details

analyze6.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample27.0ms (1.3%)

Algorithm

1×

intervals

Results

8.0ms	57×	body	640	valid
5.0ms	136×	body	80	valid
4.0ms	24×	body	1280	valid
2.0ms	22×	body	320	valid
1.0ms	17×	body	160	valid

simplify55.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	880	15
1	880	15

prune4.0ms (0.2%)

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: 8.7b

Counts

2 → 1

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.6b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite62.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+l+`

Counts

4 → 112

Calls

4 calls:

32.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
16.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))

series18.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
3.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.0ms	(/ 1.0 (- x 1.0))
2.0ms	(/ 1.0 (+ x 1.0))

simplify47.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4954	1594
1	4954	1594

prune238.0ms (11.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	3	125

Merged error: 0.3b

Counts

125 → 3

localize17.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.0b	(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
0.0b	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
0.0b	(* x (- (* x x) (* 1.0 1.0)))
16.3b	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

rewrite33.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`associate-*r/`
20×	`flip3--` `flip--`
16×	`frac-add`
14×	`add-sqr-sqrt`
12×	`frac-times`
10×	`*-un-lft-identity`
9×	`flip3-+` `flip-+`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube` `add-log-exp`
7×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r`
6×	`associate-*l/`
4×	`associate-+r+`
2×	`associate-+l+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `diff-log` `sum-log` `distribute-lft-out--`

Counts

4 → 97

Calls

4 calls:

12.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))
8.0ms	(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
6.0ms	(* x (- (* x x) (* 1.0 1.0)))
3.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))

series14.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(* x (- (* x x) (* 1.0 1.0)))
3.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
3.0ms	(* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0)))
1.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

simplify44.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5300	2792

prune286.0ms (13.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Merged error: 0.3b

Counts

112 → 4

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(* x (- (* x x) (* 1.0 1.0)))
0.3b	(/ 2.0 (* x (- (* x x) (* 1.0 1.0))))

rewrite14.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `associate-r/` `associate-r*`
3×	`times-frac` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

2 → 46

Calls

2 calls:

6.0ms	(/ 2.0 (* x (- (* x x) (* 1.0 1.0))))
6.0ms	(* x (- (* x x) (* 1.0 1.0)))

series11.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(* x (- (* x x) (* 1.0 1.0)))
5.0ms	(/ 2.0 (* x (- (* x x) (* 1.0 1.0))))

simplify48.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5673	585

prune99.0ms (4.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	2	0	2
Picked	0	1	1
Done	1	0	1
Total	51	5	56

Merged error: 0b

Counts

56 → 5

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.1b	(/ (/ 2.0 x) (- (* x x) (* 1.0 1.0)))

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac`
50×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`difference-of-squares`
13×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube` `div-inv`
4×	`associate-/r*`
3×	`cbrt-undiv` `div-exp`
2×	`associate-/r/`
1×	`pow1` `flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/` `add-log-exp`

Counts

1 → 86

Calls

1 calls:

8.0ms

(/ (/ 2.0 x) (- (* x x) (* 1.0 1.0)))

series5.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

4.0ms

(/ (/ 2.0 x) (- (* x x) (* 1.0 1.0)))

simplify43.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5015	1723

prune154.0ms (7.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	89	5	94

Merged error: 0b

Counts

94 → 5

regimes33.0ms (1.6%)

Accuracy

Total 0.1b remaining (89.4%)

Threshold costs 0.1b (89.4%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	11
1	26	11

end0.0ms (0%)

sample761.0ms (37.1%)

Algorithm

1×

intervals

Results

264.0ms	1882×	body	640	valid
165.0ms	4217×	body	80	valid
98.0ms	914×	body	320	valid
94.0ms	524×	body	1280	valid
33.0ms	463×	body	160	valid

Details

analyze6.0ms (0.3%)

sample27.0ms (1.3%)

simplify55.0ms (2.7%)

prune4.0ms (0.2%)

localize9.0ms (0.5%)

rewrite62.0ms (3%)

series18.0ms (0.9%)

simplify47.0ms (2.3%)

prune238.0ms (11.6%)

localize17.0ms (0.8%)

rewrite33.0ms (1.6%)

series14.0ms (0.7%)

simplify44.0ms (2.2%)

prune286.0ms (13.9%)

localize7.0ms (0.3%)

rewrite14.0ms (0.7%)

series11.0ms (0.5%)

simplify48.0ms (2.3%)

prune99.0ms (4.8%)

localize6.0ms (0.3%)

rewrite12.0ms (0.6%)

series5.0ms (0.2%)

simplify43.0ms (2.1%)

prune154.0ms (7.5%)

regimes33.0ms (1.6%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample761.0ms (37.1%)

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