Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	203×	body	80	valid
3.0ms	19×	body	2560	valid
2.0ms	9×	body	5120	valid
1.0ms	10×	body	1280	valid
1.0ms	6×	body	640	valid
0.0ms	6×	body	160	valid
0.0ms	3×	body	320	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 39.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
1.4b	(+ (sqrt (+ (* re re) (* im im))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (* re re) (* im im))
35.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
32.0ms	(+ (* re re) (* im im))
45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune224.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.0b	(hypot re im)
1.4b	(+ re (hypot re im))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

22.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.0ms	(hypot re im)
9.0ms	(+ re (hypot re im))

series292.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
45.0ms	(hypot re im)
61.0ms	(+ re (hypot re im))

simplify84.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	208	209
1	808	191
2	3269	185
3	5001	185

prune155.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
12.4b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt re)
1.0ms	(cbrt re)
1.0ms	(cbrt re)
0.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

series739.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt re)
187.0ms	(cbrt re)
182.0ms	(cbrt re)
188.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify72.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	60	220
1	121	195
2	359	187
3	1734	185
4	5001	185

prune232.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
12.4b	(fma (* (cbrt re) (cbrt re)) (* (cbrt (* (cbrt re) (cbrt re))) (cbrt (cbrt re))) (hypot re im))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt re)
1.0ms	(cbrt re)
1.0ms	(cbrt re)
0.0ms	(fma (* (cbrt re) (cbrt re)) (* (cbrt (* (cbrt re) (cbrt re))) (cbrt (cbrt re))) (hypot re im))

series735.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt re)
192.0ms	(cbrt re)
178.0ms	(cbrt re)
187.0ms	(fma (* (cbrt re) (cbrt re)) (* (cbrt (* (cbrt re) (cbrt re))) (cbrt (cbrt re))) (hypot re im))

simplify122.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (19.0ms)

Iter	Nodes	Cost
0	68	298
1	150	262
2	479	256
3	2651	254
4	5003	254

prune258.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

regimes104.0ms

Accuracy

0% (6.1b remaining)

Error of 13.5b against oracle of 7.5b and baseline of 13.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	6
1	19	6
2	19	6

end0.0ms

sample704.0ms

Algorithm

intervals

Results

196.0ms	6015×	body	80	valid
132.0ms	682×	body	2560	valid
75.0ms	497×	body	1280	valid
62.0ms	264×	body	5120	valid
34.0ms	288×	body	640	valid
15.0ms	167×	body	320	valid
8.0ms	87×	body	160	valid