Details

sample32.0ms

Algorithm

intervals

Results

17.0ms	100×	body	1280	valid
4.0ms	133×	body	80	valid
2.0ms	14×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 12.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
1.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r` `sqrt-prod` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 60

Calls

2 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series473.0ms

Counts

2 → 6

Calls

2 calls:

106.0ms	(/ 1.0 (hypot 1.0 x))
367.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	422	844
1	1629	601
2	5001	599

prune186.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.7b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`associate-/r/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 103

Calls

4 calls:

6.0ms	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
104.0ms	(/ 1.0 (hypot 1.0 x))
102.0ms	(/ 1.0 (hypot 1.0 x))
159.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	764	1571
1	3539	1461
2	5001	1448

prune431.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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	(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.2b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`times-frac`
29×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
13×	`add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-l` `div-inv` `distribute-lft-out` `unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r/` `cbrt-unprod`
1×	`rec-exp` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip-+` `fma-udef`

Counts

4 → 111

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1.0 (hypot 1.0 x))
104.0ms	(/ 1.0 (hypot 1.0 x))
1.2s	(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
157.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	860	1600
1	4158	1445
2	5001	1434

prune453.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(* (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt 1) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.5b	(/ (sqrt 1) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.2b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

151×	`add-sqr-sqrt`
146×	`times-frac`
137×	`sqrt-prod`
121×	`*-un-lft-identity`
83×	`add-cube-cbrt`
48×	`associate-r`
27×	`associate-l`
21×	`unswap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
16×	`distribute-lft-out`
10×	`associate-/r*`
9×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `sqrt-div` `div-exp` `associate-/r/`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sqrt-undiv` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 229

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
35.0ms	(* (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt 1) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
12.0ms	(/ (sqrt 1) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ 1.0 (hypot 1.0 x))
1.3s	(* (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt 1) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.1s	(/ (sqrt 1) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
161.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1333	5759
1	5001	5474

prune851.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes144.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 15.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	47
1	48	47

end0.0ms

sample836.0ms

Algorithm

intervals

Results

482.0ms	2846×	body	1280	valid
120.0ms	4041×	body	80	valid
81.0ms	622×	body	640	valid
30.0ms	341×	body	320	valid
9.0ms	150×	body	160	valid