Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	196×	body	80	valid
5.0ms	27×	body	2560	valid
2.0ms	16×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

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: 37.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

8.0ms	(+ (* re re) (* im im))
36.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series118.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* re re) (* im im))
52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	194	279
1	769	246
2	2332	233
3	5002	230

prune187.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.3b	(+ re (hypot re im))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `hypot-udef` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 27

Calls

2 calls:

0.0ms	(hypot re im)
6.0ms	(+ re (hypot re im))

series116.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(hypot re im)
63.0ms	(+ re (hypot re im))

simplify73.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	88	84
1	176	78
2	370	78
3	1004	78
4	3138	78
5	5001	78

prune101.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.1b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
13.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot re im)
53.0ms	(hypot re im)
48.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
64.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify174.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	171	341
1	603	286
2	3648	275
3	5001	275

prune259.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.1b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `hypot-udef` `flip3-+` `sum-log` `flip-+`

Counts

2 → 26

Calls

2 calls:

0.0ms	(hypot re im)
6.0ms	(+ re (* (sqrt 1) (hypot re im)))

series111.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(hypot re im)
58.0ms	(+ re (* (sqrt 1) (hypot re im)))

simplify104.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	110	123
1	299	107
2	873	106
3	3652	103
4	5001	103

prune109.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.1b

regimes108.0ms

Accuracy

22.2% (4.3b remaining)

Error of 12.0b against oracle of 7.6b and baseline of 13.2b

bsearch141.0ms

Steps

Iters	Range	Point
9	-1.257508563021492e-70	-2.656711351641578e-76	-1.941232155667052e-71
7	-1.989428328455626e-07	-1.1960025753651706e-08	-1.0136200979503546e-07
9	-1.621829926510464e+42	-8.804681707553006e+35	-1.7761354360071877e+40

Iters

Range

Point

-1.257508563021492e-70

-2.656711351641578e-76

-1.941232155667052e-71

-1.989428328455626e-07

-1.1960025753651706e-08

-1.0136200979503546e-07

-1.621829926510464e+42

-8.804681707553006e+35

-1.7761354360071877e+40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	41	30
1	46	15
2	49	15
3	49	15

end0.0ms

sample704.0ms

Algorithm

intervals

Results

199.0ms	6034×	body	80	valid
133.0ms	716×	body	2560	valid
67.0ms	463×	body	1280	valid
62.0ms	279×	body	5120	valid
30.0ms	262×	body	640	valid
16.0ms	158×	body	320	valid
5.0ms	88×	body	160	valid