Details

analyze10.0ms (0.4%)

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

sample36.0ms (1.5%)

Algorithm

1×

intervals

Results

11.0ms	69×	body	640	valid
9.0ms	116×	body	80	valid
4.0ms	21×	body	1280	valid
4.0ms	33×	body	320	valid
1.0ms	17×	body	160	valid

simplify65.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

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: 11.7b

Counts

2 → 1

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
3.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite63.0ms (2.6%)

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:

30.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
19.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))

series17.0ms (0.7%)

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))

simplify44.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4954	1594
1	4954	1594

prune237.0ms (9.8%)

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

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(* x (+ 1.0 x))
0.0b	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (* (- x 1.0) (* x (+ 1.0 x))))
0.1b	(* (- x 1.0) (* x (+ 1.0 x)))
18.0b	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

rewrite59.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`associate-*r/`
32×	`frac-add`
30×	`flip3--` `flip--`
25×	`flip3-+` `flip-+`
24×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/l/`
13×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`associate-*l/`
11×	`pow1`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-cube-cbrt`
8×	`associate-l` `associate-/r/`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`associate-r`
4×	`associate-+r+` `pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`sub-neg` `associate-+l+` `*-commutative`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 137

Calls

4 calls:

23.0ms	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (* (- x 1.0) (* x (+ 1.0 x))))
12.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))
9.0ms	(* (- x 1.0) (* x (+ 1.0 x)))
6.0ms	(* x (+ 1.0 x))

series19.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (- x 1.0) (* x (+ 1.0 x)))
6.0ms	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (* (- x 1.0) (* x (+ 1.0 x))))
4.0ms	(* x (+ 1.0 x))
1.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

simplify35.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5144	4177

prune467.0ms (19.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	149	3	152

Merged error: 0.3b

Counts

152 → 3

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(* x (+ 1.0 x))
0.1b	(* (- x 1.0) (* x (+ 1.0 x)))
0.4b	(/ 2.0 (* (- x 1.0) (* x (+ 1.0 x))))

rewrite31.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 86

Calls

3 calls:

13.0ms	(/ 2.0 (* (- x 1.0) (* x (+ 1.0 x))))
10.0ms	(* (- x 1.0) (* x (+ 1.0 x)))
6.0ms	(* x (+ 1.0 x))

series17.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(* (- x 1.0) (* x (+ 1.0 x)))
5.0ms	(/ 2.0 (* (- x 1.0) (* x (+ 1.0 x))))
4.0ms	(* x (+ 1.0 x))

simplify49.0ms (2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4957	1079
1	4957	1079

prune155.0ms (6.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	88	7	95
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	91	7	98

Merged error: 0b

Counts

98 → 7

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (- x 1.0))
0.0b	(* x (+ 1.0 x))
0.1b	(/ (/ 2.0 (- x 1.0)) (* x (+ 1.0 x)))

rewrite29.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`add-cube-cbrt`
24×	`associate-/l*`
19×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
5×	`pow1`
4×	`associate-r/` `associate-r*` `div-inv`
3×	`flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

3 → 124

Calls

3 calls:

12.0ms	(/ (/ 2.0 (- x 1.0)) (* x (+ 1.0 x)))
6.0ms	(* x (+ 1.0 x))
5.0ms	(/ 2.0 (- x 1.0))

series12.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (/ 2.0 (- x 1.0)) (* x (+ 1.0 x)))
4.0ms	(* x (+ 1.0 x))
2.0ms	(/ 2.0 (- x 1.0))

simplify56.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4976	1502
1	4976	1502

prune203.0ms (8.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	134	6	140

Merged error: 0b

Counts

140 → 6

regimes34.0ms (1.4%)

Accuracy

Total 0.1b remaining (87%)

Threshold costs 0.1b (87%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms (0%)

sample746.0ms (30.7%)

Algorithm

1×

intervals

Results

276.0ms	1925×	body	640	valid
152.0ms	4160×	body	80	valid
100.0ms	573×	body	1280	valid
93.0ms	902×	body	320	valid
30.0ms	440×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze10.0ms (0.4%)

sample36.0ms (1.5%)

simplify65.0ms (2.7%)

prune4.0ms (0.2%)

localize8.0ms (0.3%)

rewrite63.0ms (2.6%)

series17.0ms (0.7%)

simplify44.0ms (1.8%)

prune237.0ms (9.8%)

localize13.0ms (0.5%)

rewrite59.0ms (2.4%)

series19.0ms (0.8%)

simplify35.0ms (1.4%)

prune467.0ms (19.3%)

localize6.0ms (0.3%)

rewrite31.0ms (1.3%)

series17.0ms (0.7%)

simplify49.0ms (2%)

prune155.0ms (6.4%)

localize6.0ms (0.3%)

rewrite29.0ms (1.2%)

series12.0ms (0.5%)

simplify56.0ms (2.3%)

prune203.0ms (8.4%)

regimes34.0ms (1.4%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample746.0ms (30.7%)

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