Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	27×	body	2560	valid
8.0ms	205×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (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: 10.7b

Counts

2 → 1

localize12.0ms

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))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
85×	`add-sqr-sqrt`
69×	`associate-l`
45×	`sqrt-prod`
37×	`distribute-lft-out`
36×	`times-frac`
32×	`add-cube-cbrt`
25×	`fma-def`
22×	`unswap-sqr`
15×	`hypot-def`
12×	`associate-/r*`
8×	`add-log-exp`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
5×	`pow1` `*-commutative`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
3×	`swap-sqr` `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`

Counts

4 → 163

Calls

4 calls:

26.0ms	(+ (* (* 4.0 p) p) (* x x))
26.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
36.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* (* 4.0 p) p) (* x x))
59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
82.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify172.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 3 (157.0ms)

Iter	Nodes	Cost
0	286	1113
1	1026	1063
2	4293	992
3	5001	987

prune324.0ms

Filtered

175 candidates to 107 candidates (38.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	166	9	175
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	9	176

Merged error: 10.5b

Counts

176 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
0.0b	(fma (* 4.0 p) p (* x x))
0.4b	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
15.7b	(sqrt (fma (* 4.0 p) p (* x x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

4.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
1.0ms	(fma (* 4.0 p) p (* x x))
7.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
2.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ x (sqrt (fma (* 4.0 p) p (* x x))))
42.0ms	(fma (* 4.0 p) p (* x x))
85.0ms	(+ 1.0 (/ x (sqrt (fma (* 4.0 p) p (* x x)))))
72.0ms	(sqrt (fma (* 4.0 p) p (* x x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	212	673
1	604	632
2	2322	621
3	5001	620

prune236.0ms

Filtered

95 candidates to 73 candidates (23.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 10.5b

Counts

104 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

300×	`sqrt-prod`
249×	`*-un-lft-identity`
177×	`associate-l`
141×	`add-sqr-sqrt`
109×	`distribute-lft-out`
69×	`swap-sqr`
45×	`unswap-sqr`
34×	`sqrt-pow1`
30×	`hypot-def`
29×	`pow1`
28×	`sqrt-div`
19×	`add-cube-cbrt`
18×	`pow1/2`
15×	`associate-r`
9×	`flip3-+` `pow-prod-up` `flip-+`
7×	`*-commutative`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`fma-def`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `cbrt-unprod`

Counts

4 → 238

Calls

4 calls:

60.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
123.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
83.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
67.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	295	1868
1	1092	1670
2	5001	1640

prune416.0ms

Filtered

250 candidates to 107 candidates (57.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	246	4	250
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	249	10	259

Merged error: 10.5b

Counts

259 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

127×	`add-sqr-sqrt`
112×	`*-un-lft-identity`
102×	`sqrt-prod`
56×	`associate-l`
45×	`times-frac`
39×	`distribute-lft-out`
36×	`unswap-sqr`
35×	`add-cube-cbrt`
30×	`hypot-def`
15×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `swap-sqr` `*-commutative` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `div-inv`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log`

Counts

4 → 174

Calls

4 calls:

31.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
112.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
102.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
68.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify181.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 3 (157.0ms)

Iter	Nodes	Cost
0	348	1704
1	1178	1611
2	4690	1491
3	5001	1458

prune407.0ms

Filtered

186 candidates to 107 candidates (42.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	180	6	186
Fresh	4	4	8
Picked	1	0	1
Done	1	0	1
Total	186	10	196

Merged error: 10.5b

Counts

196 → 10

regimes154.0ms

Accuracy

0% (1.6b remaining)

Error of 14.4b against oracle of 12.9b and baseline of 14.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	32
1	34	32

end0.0ms

sample877.0ms

Algorithm

intervals

Results

227.0ms	6074×	body	80	valid
185.0ms	768×	body	2560	valid
114.0ms	8000×	pre	80	true
114.0ms	604×	body	1280	valid
48.0ms	298×	body	640	valid
19.0ms	170×	body	320	valid
6.0ms	86×	body	160	valid