Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	99×	body	1280	valid
4.0ms	130×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	9×	body	640	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	26	6
2	33	6
3	35	6
4	41	6
5	44	6
6	44	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`prod-diff`
8×	`add-log-exp`
7×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `fma-neg`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`+-commutative` `sub-neg` `hypot-udef` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `sum-log` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 73

Calls

4 calls:

0.0ms	(hypot 1.0 x)
10.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series743.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot 1.0 x)
97.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
250.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
345.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	496	1013
1	1734	765
2	5001	762

prune238.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.2b	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `div-inv`
1×	`flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `flip-+` `fma-udef`

Counts

4 → 83

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1.0 (hypot 1.0 x))
96.0ms	(/ 1.0 (hypot 1.0 x))
255.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
141.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	416	637
1	1550	603
2	5002	596

prune358.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.1b	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

168×	`prod-diff`
112×	`add-sqr-sqrt`
109×	`unpow-prod-down` `cube-prod`
98×	`*-un-lft-identity`
88×	`add-cube-cbrt`
36×	`sqr-pow`
28×	`cube-mult` `unpow3`
27×	`sqrt-prod`
16×	`difference-of-squares`
12×	`fma-neg`
11×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
4×	`expm1-log1p-u` `pow-pow` `sqrt-pow1` `sqrt-div` `associate-*r/` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cube-div` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
1×	`difference-cubes` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `sqrt-pow2` `flip--` `fma-udef` `rem-cube-cbrt`

Counts

4 → 274

Calls

4 calls:

11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
17.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
31.0ms	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

series2.7s

Counts

4 → 12

Calls

4 calls:

244.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
694.0ms	(fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
649.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.2s	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

simplify204.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1168	6509
1	4825	4547
2	5001	4547

prune473.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)
1.1b	(- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
45×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
33×	`unpow-prod-down`
25×	`sqr-pow`
20×	`cube-prod`
12×	`fma-neg`
10×	`pow1`
8×	`difference-of-squares`
7×	`add-exp-log`
6×	`cube-mult` `unpow3` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow`
2×	`pow-pow` `sqrt-pow1` `sqrt-div` `associate-*r/` `pow-prod-down` `pow-exp`
1×	`pow-to-exp` `sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `prod-exp` `sqrt-prod` `flip--` `flip-+` `fma-udef` `distribute-lft-out--`

Counts

4 → 139

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
14.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)
22.0ms	(- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2))

series1.7s

Counts

4 → 12

Calls

4 calls:

258.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
494.0ms	(fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
426.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2)
517.0ms	(- (pow 1.0 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3/2))

simplify115.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	775	2922
1	3052	1962
2	5003	1951

prune415.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

regimes396.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.9b

bsearch127.0ms

Steps

Iters	Range		Point
9	1.3330246063773173e-09	3.618674152218468	0.00037624397799526725
5	-0.002309702793432406	-0.000702289593969892	-0.001253099710940862

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	91
1	79	91

end0.0ms

sample902.0ms

Algorithm

intervals

Results

505.0ms	2927×	body	1280	valid
128.0ms	4026×	body	80	valid
81.0ms	580×	body	640	valid
28.0ms	307×	body	320	valid
9.0ms	160×	body	160	valid