Details

sample34.0ms

Algorithm

intervals

Results

12.0ms	200×	body	80	valid
4.0ms	18×	body	2560	valid
3.0ms	16×	body	1280	valid
2.0ms	14×	body	640	valid
2.0ms	6×	body	5120	valid
0.0ms	2×	body	320	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: 39.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
30.7b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:

3.0ms	(+ (* re re) (* im im))
18.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series113.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (61.0ms)

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

prune184.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

3.0ms

(+ (* 1 (hypot re im)) re)

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(+ (* 1 (hypot re im)) re)

simplify57.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	96	77
1	240	67
2	714	66
3	2180	63
4	5001	62

prune67.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.8b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`pow1`
17×	`*-un-lft-identity`
12×	`sqrt-div`
11×	`add-cube-cbrt`
9×	`swap-sqr`
8×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
7×	`associate-r` `associate-l` `add-log-exp`
6×	`distribute-lft-out`
5×	`add-exp-log` `pow-prod-up` `add-cbrt-cube`
4×	`frac-times` `unswap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `log1p-expm1-u`
2×	`+-commutative` `fma-def` `associate-r/` `associate-l/` `sum-log`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

3 → 92

Calls

3 calls:

6.0ms	(+ (* 1 (hypot re im)) re)
3.0ms	(+ (* 1 (hypot re im)) re)
24.0ms	(* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))

series176.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ (* 1 (hypot re im)) re)
60.0ms	(+ (* 1 (hypot re im)) re)
56.0ms	(* (sqrt (+ (* 1 (hypot re im)) re)) (sqrt (+ (* 1 (hypot re im)) re)))

simplify38.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	195	576
1	728	494
2	5001	465

prune260.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (* 1 (hypot re im)) re)
3.9b	(expm1 (log1p (+ (* 1 (hypot re im)) re)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

3.0ms	(+ (* 1 (hypot re im)) re)
0.0ms	(expm1 (log1p (+ (* 1 (hypot re im)) re)))

series195.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(+ (* 1 (hypot re im)) re)
135.0ms	(expm1 (log1p (+ (* 1 (hypot re im)) re)))

simplify42.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	136	144
1	334	125
2	1008	119
3	5001	110

prune93.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.8b

regimes136.0ms

Accuracy

-7.1% (6.2b remaining)

Error of 13.4b against oracle of 7.2b and baseline of 13.0b

bsearch211.0ms

Steps

Iters	Range		Point
10	2.5709113650304338e+95	1.5039667669020633e+106	6.702754729213891e+102
10	4.122383429310145e-42	2.7948480569723964e-28	1.090864784373749e-38
8	-4.795657389400237e-125	-1.8415330889540858e-127	-1.1781651487664911e-125
6	-3.9131830259355673e-87	-4.6068756624254715e-88	-1.47033881827273e-87

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	41	32
1	46	32
2	52	13
3	55	13
4	61	13
5	72	13
6	79	13
7	80	13
8	80	13

end0.0ms

sample950.0ms

Algorithm

intervals

Results

383.0ms	6066×	body	80	valid
163.0ms	648×	body	2560	valid
103.0ms	482×	body	1280	valid
81.0ms	276×	body	5120	valid
50.0ms	287×	body	640	valid
20.0ms	142×	body	320	valid
10.0ms	99×	body	160	valid