Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
4.0ms	24×	body	2560	valid
3.0ms	19×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	6×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	1×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

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))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`fma-neg`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `fma-def` `diff-log` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

53.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (* re re) (* im im))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
23.0ms	(+ (* re re) (* im im))
43.0ms	(- (sqrt (+ (* re re) (* im im))) re)
32.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	342	834
1	1366	586
2	5001	533

prune222.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
1.0b	(- (hypot re im) re)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

22.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
6.0ms	(- (hypot re im) re)

series211.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
49.0ms	(- (hypot re im) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	273	321
1	1082	232
2	5001	228

prune117.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
16.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `-un-lft-identity` `sqrt-pow1` `sqrt-div` `associate-r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `flip-+` `fma-udef`

Counts

2 → 25

Calls

2 calls:

7.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series331.0ms

Counts

2 → 6

Calls

2 calls:

209.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
122.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify36.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	192	304
1	720	267
2	5001	251

prune104.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

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))
10.5b	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite33.0ms

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))
30.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series348.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (hypot re im))
98.0ms	(cbrt (hypot re im))
100.0ms	(cbrt (hypot re im))
53.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify95.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	167	446
1	570	322
2	2968	294
3	5001	292

prune226.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

regimes107.0ms

Accuracy

33.1% (4.0b remaining)

Error of 11.1b against oracle of 7.2b and baseline of 13.1b

bsearch49.0ms

Steps

Iters	Range		Point
9	3039113653047454.0	3.846186531777652e+24	2.044923130240911e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	33	14
2	33	14

end0.0ms

sample685.0ms

Algorithm

intervals

Results

200.0ms	6039×	body	80	valid
132.0ms	715×	body	2560	valid
71.0ms	472×	body	1280	valid
64.0ms	290×	body	5120	valid
31.0ms	266×	body	640	valid
12.0ms	141×	body	320	valid
5.0ms	77×	body	160	valid