Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	65×	body	640	valid
8.0ms	130×	body	80	valid
3.0ms	19×	body	1280	valid
2.0ms	24×	body	320	valid
1.0ms	18×	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

Filtered

1 candidates to 0 candidates (100.0%)

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: 12.3b

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)) (/ 2.0 x))
0.0b	(/ 1.0 (+ x 1.0))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite61.0ms

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))
18.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
29.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5001	816

prune190.0ms

Filtered

126 candidates to 92 candidates (27.0%)

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: 0.4b

Counts

127 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
11.0b	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite298.0ms

Algorithm

rewrite-expression-head

Rules

413×	`times-frac`
324×	`*-un-lft-identity`
243×	`add-sqr-sqrt`
234×	`sqrt-prod`
188×	`add-cube-cbrt`
60×	`distribute-lft-out`
30×	`associate-/l*`
20×	`sqrt-div` `associate-/r/`
14×	`associate-/r*` `difference-of-squares`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
10×	`div-inv`
6×	`distribute-lft-out--`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`frac-add`
2×	`sub-neg` `associate-+l+` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+l-` `associate-/l/`

Counts

4 → 336

Calls

4 calls:

118.0ms	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
137.0ms	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
10.0ms	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

348 → 348

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	1025	4541
1	3846	3998
2	5001	3964

prune477.0ms

Filtered

348 candidates to 157 candidates (54.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	348	0	348
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	348	3	351

Merged error: 0.4b

Counts

351 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.1b	(* (* (+ x 1.0) x) (- x 1.0))
15.3b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

48×	`associate-*l/`
21×	`flip3--` `flip--`
17×	`add-sqr-sqrt`
16×	`frac-times` `frac-add`
15×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `flip3-+` `associate-r` `add-cbrt-cube` `flip-+`
9×	`add-cube-cbrt`
8×	`associate-r/` `associate-l*`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`associate-+l+`
3×	`*-commutative`
2×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 116

Calls

4 calls:

5.0ms	(* (+ x 1.0) x)
8.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
9.0ms	(* (* (+ x 1.0) x) (- x 1.0))
10.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series20.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ x 1.0) x)
3.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
11.0ms	(* (* (+ 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))

simplify130.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	805	1580
1	4760	1496
2	5001	1496

prune261.0ms

Filtered

128 candidates to 91 candidates (28.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	127	4	131

Merged error: 0.4b

Counts

131 → 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))
0.4b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite27.0ms

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:

5.0ms	(* (+ x 1.0) x)
9.0ms	(* (* (+ x 1.0) x) (- x 1.0))
10.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series17.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify57.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (49.0ms)

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

prune97.0ms

Filtered

93 candidates to 62 candidates (33.3%)

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: 0.0b

Counts

97 → 4

regimes29.0ms

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

sample753.0ms

Algorithm

intervals

Results

247.0ms	1844×	body	640	valid
149.0ms	4161×	body	80	valid
98.0ms	573×	body	1280	valid
94.0ms	917×	body	320	valid
34.0ms	507×	body	160	valid

Details

sample30.0ms

simplify15.0ms

prune2.0ms

localize8.0ms

rewrite61.0ms

series17.0ms

simplify47.0ms

prune190.0ms

localize10.0ms

rewrite298.0ms

series26.0ms

simplify102.0ms

prune477.0ms

localize12.0ms

rewrite37.0ms

series20.0ms

simplify130.0ms

prune261.0ms

localize6.0ms

rewrite27.0ms

series17.0ms

simplify57.0ms

prune97.0ms

regimes29.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample753.0ms

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