Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	197×	body	80	valid
10.0ms	25×	body	2560	valid
5.0ms	256×	pre	80	true
3.0ms	10×	body	1280	valid
3.0ms	10×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	7×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

27.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
27.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series402.0ms

Counts

3 → 9

Calls

3 calls:

270.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
74.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify127.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	221	478
1	628	449
2	1782	448
3	4860	447
4	5001	447

prune199.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.6b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.4b	(/ (* x x) (fma (* 4.0 p) p (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

36.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(/ (* x x) (fma (* 4.0 p) p (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(/ (* x x) (fma (* 4.0 p) p (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	702	4569
1	2493	3205
2	5001	2930

prune552.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.4b	(/ (* x x) (fma (* 4.0 p) p (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

37.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(/ (* x x) (fma (* 4.0 p) p (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
52.0ms	(/ (* x x) (fma (* 4.0 p) p (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	702	4569
1	2493	3205
2	5001	2930

prune609.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize17.0ms

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)))))
7.0b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
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` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 136

Calls

4 calls:

57.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
51.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	305	1424
1	1151	1313
2	5001	1274

prune351.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.6b

regimes203.0ms

Accuracy

0% (0.2b remaining)

Error of 12.7b against oracle of 12.5b and baseline of 12.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	27
1	29	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

461.0ms	6123×	body	80	valid
287.0ms	717×	body	2560	valid
193.0ms	594×	body	1280	valid
146.0ms	8000×	pre	80	true
81.0ms	322×	body	640	valid
28.0ms	58×	body	5120	valid
24.0ms	125×	body	320	valid
8.0ms	61×	body	160	valid