Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	22×	body	1280	valid
7.0ms	192×	body	80	valid
5.0ms	21×	body	2560	valid
4.0ms	256×	pre	80	true
2.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	9

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: 14.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 63

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
272.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify103.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	260	581
1	922	542
2	3335	537
3	5001	533

prune250.0ms

Filtered

75 candidates to 64 candidates (85.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	65	10	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	10	76

Merged error: 13.7b

Counts

76 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (pow x 2) (fma (* 4.0 p) p (* x x)))
1.6b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
87×	`add-cube-cbrt`
80×	`times-frac`
72×	`prod-diff`
34×	`sqrt-prod`
12×	`unpow-prod-down`
10×	`sqrt-div`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `associate-/r/` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `unpow2` `sqr-pow`
3×	`fma-neg` `div-exp` `associate-/r*` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

4 → 178

Calls

4 calls:

5.0ms	(/ (pow x 2) (fma (* 4.0 p) p (* x x)))
16.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (pow x 2) (fma (* 4.0 p) p (* x x)))
79.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify102.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	760	4872
1	2876	3417
2	5001	3216

prune708.0ms

Filtered

190 candidates to 105 candidates (55.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	191	9	200

Merged error: 13.7b

Counts

200 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.6b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
9×	`pow1` `add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`sqrt-prod` `log-pow`
4×	`add-exp-log` `expm1-log1p-u` `exp-prod` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod` `fma-def` `sqrt-pow1` `flip3-+` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `rem-log-exp` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

4 → 67

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
16.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series686.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
282.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
78.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify130.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	251	704
1	672	655
2	1841	654
3	4942	653
4	5001	653

prune314.0ms

Filtered

79 candidates to 71 candidates (89.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 13.7b

Counts

88 → 11

localize42.0ms

Local error

Found 4 expressions with local error:

13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 4 (81.0ms)

Iter	Nodes	Cost
0	106	548
1	323	528
2	963	528
3	2523	528
4	5002	524

prune713.0ms

Filtered

80 candidates to 72 candidates (90.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	80	11	91

Merged error: 13.7b

Counts

91 → 11

regimes445.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	65
1	52	65

end0.0ms

sample828.0ms

Algorithm

intervals

Results

217.0ms	6044×	body	80	valid
173.0ms	791×	body	2560	valid
113.0ms	613×	body	1280	valid
105.0ms	8000×	pre	80	true
41.0ms	303×	body	640	valid
18.0ms	171×	body	320	valid
5.0ms	78×	body	160	valid