Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	187×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	15×	body	2560	valid
2.0ms	10×	body	5120	valid
1.0ms	10×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
16×	`sqrt-prod`
7×	`add-log-exp`
6×	`fma-neg`
4×	`pow1`
3×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `fma-def` `sqrt-pow1` `pow1/2` `diff-log` `sum-log` `flip--` `hypot-def` `distribute-lft-out--`

Counts

3 → 73

Calls

3 calls:

8.0ms	(+ (* re re) (* im im))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series113.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify36.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	250	664
1	1037	430
2	5002	381

prune184.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
1.0b	(- (hypot re im) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `hypot-udef` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

0.0ms	(hypot re im)
7.0ms	(- (hypot re im) re)

series105.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(hypot re im)
56.0ms	(- (hypot re im) re)

simplify50.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	130	223
1	366	140
2	1695	131
3	5001	109

prune105.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.7b

localize11.0ms

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)))
7.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`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×	`prod-diff` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
13.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
13.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series202.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot re im)
45.0ms	(hypot re im)
48.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
60.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify38.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	198	388
1	788	297
2	5002	285

prune235.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
9.2b	(- (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
83.0ms	(- (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

series398.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
60.0ms	(- (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

simplify85.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	171	538
1	580	440
2	2985	425
3	5002	371

prune249.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.7b

regimes105.0ms

Accuracy

31.9% (4.2b remaining)

Error of 11.2b against oracle of 7.1b and baseline of 13.1b

bsearch48.0ms

Steps

Iters	Range		Point
9	1.661404138935296e-22	3.2716599026957865e-16	3.226330986754208e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	35	14
2	35	14

end0.0ms

sample708.0ms

Algorithm

intervals

Results

195.0ms	6046×	body	80	valid
128.0ms	661×	body	2560	valid
78.0ms	510×	body	1280	valid
76.0ms	300×	body	5120	valid
32.0ms	273×	body	640	valid
12.0ms	134×	body	320	valid
5.0ms	76×	body	160	valid