Details

sample44.0ms

Algorithm

intervals

Results

19.0ms	82×	body	1280	valid
6.0ms	132×	body	80	valid
5.0ms	9×	body	160	valid
3.0ms	17×	body	640	valid
2.0ms	16×	body	320	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	12
1	32	12

prune5.0ms

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: 16.7b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
17.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
16.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5021	879

prune154.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Merged error: 16.1b

Counts

79 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7b	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
19.0ms	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
10.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
41.0ms	(/ (* 1.0 (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify23.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	5047	1522

prune223.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 16.1b

Counts

93 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))
0.0b	(/ (* 1.0 (/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.2b	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
1.6b	(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
64×	`times-frac`
57×	`add-sqr-sqrt`
48×	`frac-sub`
45×	`add-cube-cbrt`
41×	`frac-times`
39×	`flip3--` `flip--`
30×	`associate-*r/`
29×	`associate-*l/`
27×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`distribute-lft-out`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `associate-/r*`
7×	`difference-of-squares`
6×	`prod-exp` `associate-/r/` `cbrt-unprod` `div-inv` `add-log-exp`
5×	`associate-/l*` `distribute-lft-out--`
4×	`associate--l+` `unswap-sqr`
3×	`sub-neg`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `frac-add` `clear-num` `flip-+`
1×	`pow2` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 208

Calls

4 calls:

25.0ms	(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))
23.0ms	(/ (* 1.0 (/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
12.0ms	(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))
71.0ms	(/ (* 1.0 (/ (- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
14.0ms	(- (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))))

simplify64.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5051	6002

prune949.0ms

Filtered

151 candidates to 220 candidates (-45.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	213	7	220
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	217	9	226

Merged error: 15.7b

Counts

226 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
0.2b	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
0.8b	(pow (sqrt (/ 0.5 (hypot 1.0 x))) 4)
1.6b	(- (* (* (- 1.0 0.5) (- 1.0 0.5)) (* (- 1.0 0.5) (- 1.0 0.5))) (* (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

3402×	`frac-times`
1621×	`flip3--` `flip--`
1542×	`associate-r/` `associate-l/`
1200×	`frac-sub`
93×	`add-sqr-sqrt`
89×	`times-frac`
69×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-exp-log`
28×	`add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
16×	`unpow-prod-down`
13×	`sqrt-prod`
9×	`div-inv`
8×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `prod-exp` `associate--l+` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp`
5×	`sub-neg`
3×	`pow-unpow` `pow-pow`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `diff-log` `pow-exp` `sqrt-pow2` `difference-of-squares` `sqr-pow`

Counts

4 → 1388

Calls

4 calls:

11.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
11.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
6.0ms	(pow (sqrt (/ 0.5 (hypot 1.0 x))) 4)
84.0ms	(- (* (* (- 1.0 0.5) (- 1.0 0.5)) (* (- 1.0 0.5) (- 1.0 0.5))) (* (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
12.0ms	(* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))
26.0ms	(pow (sqrt (/ 0.5 (hypot 1.0 x))) 4)
18.0ms	(- (* (* (- 1.0 0.5) (- 1.0 0.5)) (* (- 1.0 0.5) (- 1.0 0.5))) (* (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x))) (* (/ 0.5 (hypot 1.0 x)) (/ 0.5 (hypot 1.0 x)))))

simplify592.0ms

Algorithm

egg-herbie

Counts

1400 → 1400

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5401	98992

prune38.4s

Filtered

1099 candidates to 1400 candidates (-27.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1395	5	1400
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	1400	9	1409

Merged error: 15.7b

Counts

1409 → 9

regimes601.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	50
1	29	50

end0.0ms

sample1.2s

Algorithm

intervals

Results

656.0ms	2911×	body	1280	valid
173.0ms	3981×	body	80	valid
118.0ms	631×	body	640	valid
39.0ms	304×	body	320	valid
14.0ms	173×	body	160	valid

Details

sample44.0ms

simplify3.0ms

prune5.0ms

localize8.0ms

rewrite22.0ms

series45.0ms

simplify51.0ms

prune154.0ms

localize14.0ms

rewrite45.0ms

series71.0ms

simplify23.0ms

prune223.0ms

localize21.0ms

rewrite84.0ms

series126.0ms

simplify64.0ms

prune949.0ms

localize27.0ms

rewrite338.0ms

series66.0ms

simplify592.0ms

prune38.4s

regimes601.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

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