Details

sample14.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	79×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

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: 0.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3-+` `associate-/r/` `flip-+`
1×	`+-commutative` `frac-2neg` `clear-num` `div-inv`

Counts

2 → 8

Calls

2 calls:

2.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series180.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
139.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify96.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	193	127
1	699	110
2	4000	98
3	5001	96

prune41.0ms

Filtered

14 candidates to 12 candidates (85.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Merged error: 0.0b

Counts

15 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
2.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.0b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
31×	`flip3-+` `flip-+`
28×	`associate-*r/`
16×	`frac-sub`
12×	`frac-times`
10×	`*-commutative`
8×	`associate-*l/`
7×	`pow1/2`
4×	`prod-diff` `sub-div`
2×	`distribute-rgt-out--` `fma-neg` `associate-/r/` `distribute-lft-out--`
1×	`pow2` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `sqrt-unprod` `unpow3` `pow-prod-down` `clear-num` `associate-/r*` `rem-square-sqrt` `pow-sqr` `sum-cubes` `pow-prod-up` `sqrt-pow2` `flip--` `div-inv` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
2.0ms	(pow (sqrt (+ x 1.0)) 3)
11.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
66.0ms	(pow (sqrt (+ x 1.0)) 3)
62.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
190.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify57.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	558	946
1	1896	772
2	5001	758

prune217.0ms

Filtered

72 candidates to 44 candidates (61.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	70	5	75

Merged error: 0b

Counts

75 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
2.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.0b	(/ x (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
36×	`flip3-+` `flip-+`
30×	`associate-*r/`
19×	`*-commutative`
18×	`frac-times`
16×	`frac-sub`
12×	`associate-+r+` `prod-diff`
11×	`associate-*l/`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`pow1/2`
4×	`frac-2neg` `clear-num` `associate-/r/` `sub-div`
3×	`sub-neg` `associate-l`
2×	`+-commutative` `distribute-rgt-out--` `fma-neg` `div-inv` `distribute-lft-out--`
1×	`pow2` `flip3--` `sqrt-unprod` `pow-prod-down` `rem-square-sqrt` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 85

Calls

4 calls:

20.0ms	(* (/ x (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
5.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
11.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.0ms	(/ x (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0)))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

378.0ms	(* (/ x (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
63.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
186.0ms	(/ x (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0)))))

simplify104.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	943	1846
1	3820	1517
2	5001	1502

prune265.0ms

Filtered

97 candidates to 57 candidates (58.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	97	5	102

Merged error: 0b

Counts

102 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (* 1.0 1.0) (+ x 1.0))
2.5b	(- (* 1.0 1.0) (+ x 1.0))
2.6b	(- (sqrt (+ x 1.0)) 1.0)
13.1b	(/ (* (fma (sqrt (+ x 1.0)) (- (sqrt (+ x 1.0)) 1.0) (* 1.0 1.0)) (* (+ (- (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) x)) (* (+ (- (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*r/`
20×	`associate-/r/`
19×	`flip3-+` `flip-+`
16×	`sqrt-div` `frac-add`
13×	`*-commutative`
12×	`frac-times` `associate-*l/`
11×	`flip3--` `flip--`
8×	`times-frac`
6×	`associate-r` `associate-/l/`
4×	`fma-neg` `associate-/l*` `associate--r+`
3×	`sub-neg`
2×	`+-commutative` `associate-/r*`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 63

Calls

4 calls:

5.0ms	(- (* 1.0 1.0) (+ x 1.0))
5.0ms	(- (* 1.0 1.0) (+ x 1.0))
3.0ms	(- (sqrt (+ x 1.0)) 1.0)
24.0ms	(/ (* (fma (sqrt (+ x 1.0)) (- (sqrt (+ x 1.0)) 1.0) (* 1.0 1.0)) (* (+ (- (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) x)) (* (+ (- (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0))))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (* 1.0 1.0) (+ x 1.0))
12.0ms	(- (* 1.0 1.0) (+ x 1.0))
49.0ms	(- (sqrt (+ x 1.0)) 1.0)
554.0ms	(/ (* (fma (sqrt (+ x 1.0)) (- (sqrt (+ x 1.0)) 1.0) (* 1.0 1.0)) (* (+ (- (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) x)) (* (+ (- (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) (+ (pow 1.0 3) (* (+ x 1.0) (sqrt (+ x 1.0))))))

simplify104.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	890	1756
1	4524	1463
2	5001	1458

prune392.0ms

Filtered

75 candidates to 64 candidates (85.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	75	5	80

Merged error: 0b

Counts

80 → 5

regimes48.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample354.0ms

Algorithm

intervals

Results

182.0ms	7997×	body	80	valid
51.0ms	2660×	body	80	nan
0.0ms	3×	body	1280	valid