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	47×	body	1280	valid
5.0ms	45×	body	640	valid
4.0ms	130×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

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: 29.0b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.4b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite51.0ms

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:

5.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
34.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series13.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
8.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4955	1404
1	4955	1404

prune184.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	3	113

Merged error: 0.2b

Counts

113 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- x 1.0))
0.0b	(* (+ x 1.0) (+ x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
16.7b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
35×	`*-un-lft-identity`
32×	`frac-sub`
30×	`flip3-+` `flip-+`
25×	`add-sqr-sqrt`
20×	`frac-times` `flip3--` `flip--`
19×	`add-cube-cbrt`
18×	`associate-/l/`
13×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
9×	`associate-r`
7×	`associate-l`
6×	`swap-sqr` `distribute-lft-out` `add-log-exp`
5×	`sub-neg` `difference-of-squares`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate--l+` `associate-/r/` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--`

Counts

4 → 147

Calls

4 calls:

6.0ms	(* x (- x 1.0))
9.0ms	(* (+ x 1.0) (+ x 1.0))
14.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
9.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify53.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5309	3115

prune305.0ms

Filtered

114 candidates to 159 candidates (-39.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	158	4	162

Merged error: 0b

Counts

162 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (+ x 1.0))
0.0b	(- (* x (- x (+ 1.0 (+ x 1.0)))) (* (+ x 1.0) 1.0))
1.5b	(- x (+ 1.0 (+ x 1.0)))
13.7b	(/ (- (* x (- x (+ 1.0 (+ x 1.0)))) (* (+ x 1.0) 1.0)) (- (* x x) (* 1.0 1.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
20×	`add-log-exp`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
8×	`flip3--` `associate-r/` `associate-l/` `frac-sub` `flip--`
6×	`add-exp-log` `sum-log` `add-cbrt-cube` `associate-/l/` `distribute-lft-out`
5×	`flip3-+` `flip-+` `difference-of-squares`
4×	`pow1` `sub-neg` `diff-log` `associate-/r*`
3×	`associate-/l*` `distribute-lft-out--`
2×	`associate--l+` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `associate-+r+` `frac-2neg` `distribute-lft-in` `div-sub` `div-exp` `clear-num` `div-inv` `associate--r+`

Counts

4 → 90

Calls

4 calls:

8.0ms	(+ 1.0 (+ x 1.0))
12.0ms	(- (* x (- x (+ 1.0 (+ x 1.0)))) (* (+ x 1.0) 1.0))
8.0ms	(- x (+ 1.0 (+ x 1.0)))
17.0ms	(/ (- (* x (- x (+ 1.0 (+ x 1.0)))) (* (+ x 1.0) 1.0)) (- (* x x) (* 1.0 1.0)))

series11.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify71.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4941	2117
1	4941	2117

prune171.0ms

Filtered

79 candidates to 102 candidates (-29.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	102	4	106

Merged error: 0b

Counts

106 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (* x (+ (* x 1.0) 3.0)))
0.0b	(* x (+ (* x 1.0) 3.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 35

Calls

2 calls:

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

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify50.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4999	411
1	4999	411

prune42.0ms

Filtered

28 candidates to 41 candidates (-46.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Merged error: 0b

Counts

45 → 4

regimes41.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 26.2b

bsearch36.0ms

Steps

Iters	Range		Point
10	2.0152362568064248e-08	104912728.60688464	268163.1256190682
11	-6.948150448154976e+41	-204373392765662.97	-10771490727067154.0

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	140	48
1	140	48

end0.0ms

sample698.0ms

Algorithm

intervals

Results

250.0ms	1660×	body	1280	valid
144.0ms	1227×	body	640	valid
132.0ms	4172×	body	80	valid
55.0ms	623×	body	320	valid
21.0ms	318×	body	160	valid

Details

analyze4.0ms

sample24.0ms

simplify89.0ms

prune4.0ms

localize6.0ms

rewrite51.0ms

series13.0ms

simplify63.0ms

prune184.0ms

localize11.0ms

rewrite45.0ms

series18.0ms

simplify53.0ms

prune305.0ms

localize13.0ms

rewrite48.0ms

series11.0ms

simplify71.0ms

prune171.0ms

localize5.0ms

rewrite11.0ms

series9.0ms

simplify50.0ms

prune42.0ms

regimes41.0ms

bsearch36.0ms

simplify3.0ms

end0.0ms

sample698.0ms

Profiling