Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	188×	body	80	valid
6.0ms	26×	body	2560	valid
3.0ms	18×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	10×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`pow1` `add-sqr-sqrt` `sqrt-prod`
6×	`add-cube-cbrt` `fma-def`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `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` `hypot-def` `distribute-lft-out`

Counts

3 → 53

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

174.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320

prune193.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.3b	(+ re (hypot re im))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

15.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
3.0ms	(+ re (hypot re im))

series244.0ms

Counts

2 → 6

Calls

2 calls:

189.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
54.0ms	(+ re (hypot re im))

simplify88.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	194	185
1	791	167
2	3233	161
3	5001	161

prune119.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
0.3b	(+ re (hypot re im))
0.3b	(+ re (hypot re im))
0.4b	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

148×	`sqrt-pow1`
146×	`pow1`
76×	`pow-prod-down`
31×	`sqrt-prod`
30×	`associate-*r/`
28×	`add-sqr-sqrt` `sqrt-div`
22×	`pow1/2`
21×	`pow-prod-up`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`pow-sqr`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`+-commutative` `associate-*l/` `sum-log` `distribute-lft-out`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 154

Calls

4 calls:

10.0ms	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
2.0ms	(+ re (hypot re im))
3.0ms	(+ re (hypot re im))
80.0ms	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im))))))
60.0ms	(+ re (hypot re im))
60.0ms	(+ re (hypot re im))
190.0ms	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	408	1059
1	1918	954
2	5001	921

prune402.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ re (hypot re im))
0.4b	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (cbrt (pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3)))
0.4b	(cbrt (pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3))
0.5b	(pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod`
49×	`add-sqr-sqrt`
46×	`sqrt-prod`
34×	`associate-*r/`
32×	`sqrt-div`
25×	`unpow-prod-down` `*-un-lft-identity` `cube-prod`
23×	`add-cube-cbrt` `associate-r`
14×	`pow1` `unswap-sqr`
10×	`cube-div`
9×	`flip3-+` `flip-+`
8×	`cbrt-div` `sqrt-pow1`
7×	`add-exp-log` `pow-pow` `associate-l`
6×	`add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `log1p-expm1-u`
3×	`cube-mult` `pow-unpow` `fma-def` `unpow3`
2×	`pow1/2` `associate-*l/`
1×	`+-commutative` `pow-to-exp` `pow1/3` `pow-exp` `prod-exp` `sum-log` `*-commutative` `sqrt-pow2` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

3.0ms	(+ re (hypot re im))
66.0ms	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (cbrt (pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3)))
4.0ms	(cbrt (pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3))
12.0ms	(pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3)

series822.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ re (hypot re im))
187.0ms	(* (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) (cbrt (pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3)))
226.0ms	(cbrt (pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3))
350.0ms	(pow (sqrt (sqrt (* 2.0 (* 1 (+ re (hypot re im)))))) 3)

simplify79.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	628	2003
1	2645	1608
2	5001	1516

prune466.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.4b

regimes95.0ms

Accuracy

-8.3% (6.3b remaining)

Error of 13.9b against oracle of 7.6b and baseline of 13.4b

bsearch167.0ms

Steps

Iters	Range		Point
9	5.81386847535435e+28	3.7661988674960076e+36	9.065835919646247e+35
8	9.54075249316399e-134	6.345363242268133e-131	2.4301831339222963e-131
9	-1.2579556351517705e+22	-5516994550455459.0	-2.4549770529786184e+20
4	-1.1860998636736231e+119	-5.962254730089143e+118	-8.108176740370824e+118

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	40	32
1	45	32
2	51	13
3	54	13
4	60	13
5	71	13
6	78	13
7	79	13
8	79	13

end0.0ms

sample742.0ms

Algorithm

intervals

Results

218.0ms	6010×	body	80	valid
168.0ms	747×	body	2560	valid
90.0ms	476×	body	1280	valid
74.0ms	283×	body	5120	valid
41.0ms	275×	body	640	valid
14.0ms	137×	body	320	valid
5.0ms	72×	body	160	valid