Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	63×	body	640	valid
8.0ms	141×	body	80	valid
3.0ms	27×	body	320	valid
3.0ms	16×	body	1280	valid
1.0ms	9×	body	160	valid

simplify19.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 9.4b

Counts

2 → 1

localize8.0ms

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))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite62.0ms

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` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
7.0ms	(/ 1.0 (+ x 1.0))
16.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1.0 (- x 1.0))
24.0ms	(/ 1.0 (+ x 1.0))
47.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
214.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5002	816

prune208.0ms

Filtered

126 candidates to 92 candidates (73.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	3	127

Merged error: 0.2b

Counts

127 → 3

localize13.0ms

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	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
16.0b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite59.0ms

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:

22.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
15.0ms	(* (* (+ x 1.0) x) (- x 1.0))
11.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series233.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
44.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
97.0ms	(* (* (+ x 1.0) x) (- x 1.0))
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 (27.0ms)

Iter	Nodes	Cost
0	997	2264
1	5001	2129

prune372.0ms

Filtered

136 candidates to 108 candidates (79.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Merged error: 0.2b

Counts

139 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
0.2b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

6.0ms	(* (+ x 1.0) x)
9.0ms	(* (* (+ x 1.0) x) (- x 1.0))
11.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (+ x 1.0) x)
93.0ms	(* (* (+ x 1.0) x) (- x 1.0))
87.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	430	600
1	2219	516
2	5002	515

prune127.0ms

Filtered

93 candidates to 62 candidates (66.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	93	4	97

Merged error: 0b

Counts

97 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
0.6b	(/ 2.0 (* (+ x 1.0) x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 122

Calls

3 calls:

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

series169.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (+ x 1.0) x)
87.0ms	(/ (/ 2.0 (* (+ x 1.0) x)) (- x 1.0))
35.0ms	(/ 2.0 (* (+ x 1.0) x))

simplify69.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	560	1012
1	2547	928
2	5001	928

prune178.0ms

Filtered

131 candidates to 96 candidates (73.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	131	4	135

Merged error: 0b

Counts

135 → 4

regimes13.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

end0.0ms

sample718.0ms

Algorithm

intervals

Results

258.0ms	1884×	body	640	valid
153.0ms	4183×	body	80	valid
95.0ms	561×	body	1280	valid
93.0ms	924×	body	320	valid
30.0ms	450×	body	160	valid