Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	55×	body	640	valid
5.0ms	130×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	33×	body	320	valid
1.0ms	13×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

prune2.0ms

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: 9.7b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.3b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

5.0ms	(/ 1.0 (- x 1.0))
15.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
32.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series15.0ms

Counts

3 → 9

Calls

3 calls:

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)))

simplify39.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	421	692
1	1417	662
2	5001	653

prune136.0ms

Filtered

66 candidates to 90 candidates (-36.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	3	91

Merged error: 0.5b

Counts

91 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
16.3b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

21.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
9.0ms	(* (* (+ x 1.0) x) (- x 1.0))
3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
12.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series19.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129

prune364.0ms

Filtered

108 candidates to 136 candidates (-25.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Merged error: 0.5b

Counts

139 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (+ x 1.0) (* x (- x 1.0))))
0.0b	(* (+ x 1.0) (* x (- x 1.0)))
0.2b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
16.3b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

76×	`associate-*l/`
32×	`frac-add`
31×	`flip3--` `flip--`
24×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
18×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1` `*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `sub-neg`
6×	`prod-exp` `cbrt-unprod`
4×	`associate-+l+` `associate-l`
3×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
1×	`+-commutative` `frac-2neg` `diff-log` `associate-r` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 127

Calls

4 calls:

21.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (+ x 1.0) (* x (- x 1.0))))
9.0ms	(* (+ x 1.0) (* x (- x 1.0)))
3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
10.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series21.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (+ x 1.0) (* x (- x 1.0))))
10.0ms	(* (+ x 1.0) (* x (- x 1.0)))
4.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
1.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	990	2286
1	5001	2101

prune342.0ms

Filtered

104 candidates to 139 candidates (-33.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	139	4	143

Merged error: 0.5b

Counts

143 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ 1.0 (- x 1.0)))
0.4b	(cbrt (/ 1.0 (- x 1.0)))
0.4b	(cbrt (/ 1.0 (- x 1.0)))
20.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
39×	`cbrt-div`
31×	`add-cube-cbrt`
21×	`frac-add`
15×	`frac-times` `associate-*l/`
10×	`flip3--` `flip--`
9×	`associate-*r/` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`frac-sub`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `div-inv`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

4 → 126

Calls

4 calls:

5.0ms	(cbrt (/ 1.0 (- x 1.0)))
5.0ms	(cbrt (/ 1.0 (- x 1.0)))
5.0ms	(cbrt (/ 1.0 (- x 1.0)))
22.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt (/ 1.0 (- x 1.0)))
9.0ms	(cbrt (/ 1.0 (- x 1.0)))
9.0ms	(cbrt (/ 1.0 (- x 1.0)))
18.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	651	2130
1	1912	1998
2	5002	1878

prune377.0ms

Filtered

106 candidates to 138 candidates (-30.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	138	4	142

Merged error: 0.5b

Counts

142 → 4

regimes43.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 25.2b

bsearch32.0ms

Steps

Iters	Range		Point
10	0.0364262917160445	547825979.610153	95.30458877857272
8	-442.47528987694835	-0.030191044061917315	-92.03427948234645

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	25
1	43	25

end0.0ms

sample826.0ms

Algorithm

intervals

Results

285.0ms	1864×	body	640	valid
164.0ms	4225×	body	80	valid
107.0ms	935×	body	320	valid
97.0ms	497×	body	1280	valid
38.0ms	482×	body	160	valid

Details

sample28.0ms

simplify15.0ms

prune2.0ms

localize8.0ms

rewrite55.0ms

series15.0ms

simplify39.0ms

prune136.0ms

localize12.0ms

rewrite52.0ms

series19.0ms

simplify49.0ms

prune364.0ms

localize14.0ms

rewrite50.0ms

series21.0ms

simplify45.0ms

prune342.0ms

localize12.0ms

rewrite41.0ms

series45.0ms

simplify96.0ms

prune377.0ms

regimes43.0ms

bsearch32.0ms

simplify2.0ms

end0.0ms

sample826.0ms

Profiling