Details

sample36.0ms

Algorithm

intervals

Results

19.0ms	94×	body	1280	valid
4.0ms	126×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

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: 14.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

1.0ms	(hypot 1.0 x)
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

62.0ms	(hypot 1.0 x)
475.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
119.0ms	(/ 1.0 (hypot 1.0 x))
390.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	533	1074
1	2023	830
2	5002	827

prune270.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.3b

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	(/ (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)))))))
1.4b	(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:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ (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)))))))
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:

109.0ms	(/ 1.0 (hypot 1.0 x))
109.0ms	(/ 1.0 (hypot 1.0 x))
1.3s	(/ (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)))))))
162.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify92.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (76.0ms)

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

prune440.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (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)))))))))
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))))))))
0.5b	(/ 1 (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.4b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
106×	`times-frac`
98×	`*-un-lft-identity`
67×	`sqrt-prod`
64×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
14×	`associate-/r*` `distribute-lft-out`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 205

Calls

4 calls:

31.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (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)))))))))
7.0ms	(/ (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))))))))
7.0ms	(/ 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))

series4.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (/ 1 (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (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)))))))))
1.9s	(/ (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))))))))
1.1s	(/ 1 (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
167.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1412	5724
1	5002	5334

prune711.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

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)))))))
1.4b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite12.0ms

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:

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

series4.3s

Counts

4 → 12

Calls

4 calls:

1.3s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.5s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3s	(cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
167.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	419	1369
1	1647	1263
2	5002	1251

prune514.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes220.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	68
1	55	68

end0.0ms

sample851.0ms

Algorithm

intervals

Results

500.0ms	2965×	body	1280	valid
123.0ms	3992×	body	80	valid
81.0ms	606×	body	640	valid
27.0ms	299×	body	320	valid
8.0ms	138×	body	160	valid