Details

analyze10.0ms

Algorithm

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

sample28.0ms

Algorithm

intervals

Results

11.0ms	72×	body	640	valid
5.0ms	128×	body	80	valid
3.0ms	18×	body	1280	valid
3.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	880	15
1	880	15

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: 10.2b

Counts

2 → 1

localize9.0ms

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))
2.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite68.0ms

Algorithm

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:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
18.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
36.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4954	1594
1	4954	1594

prune192.0ms

Filtered

95 candidates to 124 candidates (-30.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	4	125

Merged error: 0.3b

Counts

125 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.3b	(cbrt (+ 1.0 x))
0.3b	(cbrt (+ 1.0 x))
18.8b	(+ (- (* (/ 1 (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (/ 1.0 (cbrt (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
5×	`frac-add`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
3×	`pow1/3` `frac-sub`
2×	`sum-log`
1×	`+-commutative` `frac-times` `associate-+l-` `sub-neg` `associate-+l+` `flip3--` `diff-log` `associate-r/` `associate-l/` `flip--`

Counts

4 → 62

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 x))
3.0ms	(cbrt (+ 1.0 x))
3.0ms	(cbrt (+ 1.0 x))
36.0ms	(+ (- (* (/ 1 (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (/ 1.0 (cbrt (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 x))
6.0ms	(cbrt (+ 1.0 x))
6.0ms	(cbrt (+ 1.0 x))
11.0ms	(+ (- (* (/ 1 (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (/ 1.0 (cbrt (+ 1.0 x)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5015	1051

prune158.0ms

Filtered

61 candidates to 74 candidates (-21.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	74	4	78

Merged error: 0.3b

Counts

78 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
0.0b	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (* x (- (* x x) (* 1.0 1.0))))
0.0b	(* x (- (* x x) (* 1.0 1.0)))
17.5b	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

4.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
19.0ms	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (* x (- (* x x) (* 1.0 1.0))))
6.0ms	(* x (- (* x x) (* 1.0 1.0)))
14.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (* 1.0 x) (* (+ 1.0 x) 2.0))
5.0ms	(/ (+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x)))) (* x (- (* x x) (* 1.0 1.0))))
7.0ms	(* x (- (* x x) (* 1.0 1.0)))
1.0ms	(+ (* (- x 1.0) (- (* 1.0 x) (* (+ 1.0 x) 2.0))) (* 1.0 (* x (+ 1.0 x))))

simplify50.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5445	3703

prune345.0ms

Filtered

97 candidates to 120 candidates (-23.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	120	4	124

Merged error: 0.3b

Counts

124 → 4

localize6.0ms

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))))

rewrite15.0ms

Algorithm

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:

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

series11.0ms

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))))

simplify49.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5673	585

prune66.0ms

Filtered

39 candidates to 52 candidates (-33.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	53	3	56

Merged error: 0.0b

Counts

56 → 3

regimes26.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	13
1	29	13

end0.0ms

sample743.0ms

Algorithm

intervals

Results

256.0ms	1860×	body	640	valid
156.0ms	4149×	body	80	valid
106.0ms	971×	body	320	valid
99.0ms	547×	body	1280	valid
33.0ms	473×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze10.0ms

sample28.0ms

simplify55.0ms

prune4.0ms

localize9.0ms

rewrite68.0ms

series18.0ms

simplify48.0ms

prune192.0ms

localize14.0ms

rewrite47.0ms

series30.0ms

simplify44.0ms

prune158.0ms

localize16.0ms

rewrite49.0ms

series17.0ms

simplify50.0ms

prune345.0ms

localize6.0ms

rewrite15.0ms

series11.0ms

simplify49.0ms

prune66.0ms

regimes26.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample743.0ms

Profiling