Details

sample32.0ms

Algorithm

intervals

Results

15.0ms	98×	body	1280	valid
4.0ms	122×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	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: 18.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
99.0ms	(/ 1.0 (hypot 1.0 x))
100.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
335.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	533	1129
1	2036	878
2	5001	876

prune272.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.4b

localize16.0ms

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	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(+ 1.0 (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 1.0))

series663.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1.0 (hypot 1.0 x))
102.0ms	(/ 1.0 (hypot 1.0 x))
308.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
152.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	430	681
1	1662	625
2	5001	623

prune355.0ms

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	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.1b	(/ 1.0 (sqrt (hypot 1.0 x)))
0.2b	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
1.3b	(fma (- 0.5) (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))) (* 1.0 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
159×	`*-un-lft-identity`
157×	`add-sqr-sqrt` `add-cube-cbrt`
144×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef` `associate-/l/` `distribute-lft-out`

Counts

4 → 245

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
19.0ms	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
0.0ms	(fma (- 0.5) (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))) (* 1.0 1.0))

series718.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
136.0ms	(/ 1.0 (sqrt (hypot 1.0 x)))
103.0ms	(/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))
157.0ms	(fma (- 0.5) (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))) (* 1.0 1.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	946	3168
1	3691	2780
2	5002	2771

prune627.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.5b	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3b	(fma (- 0.5) (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))) (* 1.0 1.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

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

series3.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
154.0ms	(fma (- 0.5) (+ 1.0 (/ (/ 1.0 (sqrt (hypot 1.0 x))) (sqrt (hypot 1.0 x)))) (* 1.0 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	428	1421
1	1673	1315
2	5002	1296

prune431.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

regimes318.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.4b

bsearch146.0ms

Steps

Iters	Range		Point
8	1.317141247235427e-05	0.43775957865898985	0.0013551915349228707
9	-3096.4512561506854	-0.0006592480666379122	-0.0007332210515937477

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	99
1	62	99

end0.0ms

sample833.0ms

Algorithm

intervals

Results

451.0ms	2825×	body	1280	valid
120.0ms	4043×	body	80	valid
81.0ms	653×	body	640	valid
28.0ms	327×	body	320	valid
11.0ms	152×	body	160	valid