Details

sample32.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
4.0ms	18×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	19×	body	1280	valid
2.0ms	11×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

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

prune3.0ms

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: 11.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

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

series224.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
77.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify149.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	296	867
1	1081	815
2	4584	798
3	5001	795

prune322.0ms

Filtered

103 candidates to 79 candidates (76.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	89	14	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	14	104

Merged error: 11.1b

Counts

104 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

1.1b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.8b	(/ x (fma (* 4.0 p) p (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
78×	`add-cube-cbrt`
72×	`prod-diff`
65×	`times-frac`
34×	`sqrt-prod`
10×	`sqrt-div`
6×	`pow1` `add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-/r` `associate-/l` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

4 → 156

Calls

4 calls:

16.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(/ x (fma (* 4.0 p) p (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(/ x (fma (* 4.0 p) p (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify81.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	682	4617
1	2256	3256
2	5001	2931

prune627.0ms

Filtered

168 candidates to 94 candidates (56.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	168	14	182

Merged error: 11.1b

Counts

182 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.3b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `prod-exp` `flip-+` `log1p-expm1-u`
3×	`associate-l`
2×	`+-commutative` `div-exp` `sum-log` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
14.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	867
1	1999	779
2	5001	742

prune314.0ms

Filtered

110 candidates to 81 candidates (73.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	12	1	13
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Merged error: 11.1b

Counts

124 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

17.0ms	(+ 1.0 (/ x (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)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ 1.0 (/ x (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)))

simplify112.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 4 (100.0ms)

Iter	Nodes	Cost
0	180	566
1	522	535
2	1457	534
3	3954	533
4	5001	525

prune320.0ms

Filtered

80 candidates to 72 candidates (90.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	80	5	85

Merged error: 11.1b

Counts

85 → 5

regimes83.0ms

Accuracy

0% (1.2b remaining)

Error of 14.4b against oracle of 13.2b and baseline of 14.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	19
1	27	19

end0.0ms

sample843.0ms

Algorithm

intervals

Results

215.0ms	6001×	body	80	valid
187.0ms	852×	body	2560	valid
112.0ms	8000×	pre	80	true
106.0ms	608×	body	1280	valid
43.0ms	315×	body	640	valid
15.0ms	145×	body	320	valid
5.0ms	79×	body	160	valid