Details

analyze3.4s (7.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	98.2%	1.8%	8
0%	94.3%	5.7%	9
0.4%	93%	6.6%	10
7.4%	83.3%	9.3%	11
12.4%	75.2%	12.4%	12
14.4%	68.9%	16.7%	13
16.8%	65.4%	17.8%	14

Compiler

Compiled 45 to 33 computations (26.7% saved)

sample178.0ms (0.4%)

Algorithm

1×

intervals

Results

33.0ms	175×	body	128	valid
21.0ms	29×	body	1024	valid
19.0ms	19×	body	2048	nan
18.0ms	25×	body	1024	nan
18.0ms	17×	body	2048	valid
15.0ms	28×	body	512	nan
13.0ms	21×	body	512	valid
12.0ms	72×	body	128	nan
5.0ms	14×	body	256	valid
3.0ms	9×	body	256	nan

Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify86.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

560×	`associate-l_binary64`
528×	`associate-r_binary64`
455×	`distribute-rgt-in_binary64`
450×	`fma-def_binary64`
449×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	66	49
2	202	49
3	721	49
4	2973	49
5	4968	49
6	4966	49
7	4969	49
8	4939	49

prune6.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

48.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	49.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	51.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))

Status

Error

Program

▶

49.4b

(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

51.7b

(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	5.2b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	14.1b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
✓	21.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

rewrite40.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
31×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`

Counts

4 → 140

Calls

4 calls:

9.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
8.0ms	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
6.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
5.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series15.7s (35.3%)

Counts

4 → 124

Calls

4 calls:

8.5s	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
6.9s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
235.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
53.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify570.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
274×	`associate-/l*_binary64`
213×	`associate-*l/_binary64`
183×	`associate-/r*_binary64`
149×	`times-frac_binary64`

Counts

264 → 417

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2448	45159
1	5052	45159

prune1.1s (2.4%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	389	28	417
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	390	29	419

Error

24.8b

Counts

419 → 29

Alt Table

Status	Error	Program
	49.0b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	57.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (/.f64 (.f64 B B) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.1b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.6b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (cbrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))) (/.f64 (neg.f64 (cbrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	59.8b	(/.f64 (neg.f64 (-.f64 (fma.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (.f64 (sqrt.f64 2) B) (.f64 1/2 (.f64 (.f64 A (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B))))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 C C) (.f64 B B)) F) (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B))))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 C C) (.f64 B B)) (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(-.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) (+.f64 (.f64 B B) (.f64 C C))))) (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B))) (fma.f64 2 (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 C C) (.f64 B B)) F) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3))) (fma.f64 2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (sqrt.f64 2)) B)) (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (*.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B))))))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	51.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	49.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))))) (.f64 A C))))))
	59.8b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	55.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	57.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
▶	48.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.9b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))

Compiler

Compiled 62608 to 34194 computations (45.4% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))
	1.9b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	10.5b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	20.0b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

9.0ms

(/.f64 (sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))

7.0ms

(sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

1.0ms

(sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))

series4.0s (8.9%)

Counts

3 → 60

Calls

3 calls:

3.0s

(/.f64 (sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))

932.0ms

(sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

40.0ms

(sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))

simplify274.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

657×	`*-commutative_binary64`
324×	`fma-def_binary64`
297×	`associate-r_binary64`
284×	`associate-+r+_binary64`
170×	`associate-/l*_binary64`

Counts

142 → 222

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1519	26044
1	5201	26044

prune708.0ms (1.6%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	303	8	311
Fresh	3	25	28
Picked	1	0	1
Done	0	0	0
Total	307	33	340

Error

16.3b

Counts

340 → 33

Alt Table

Status	Error	Program
▶	48.5b	(.f64 -1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))))
	59.8b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	53.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	57.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (/.f64 (.f64 B B) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.0b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	56.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	49.2b	(.f64 -1 (sqrt.f64 (/.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	58.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 2 C))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	49.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	57.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.1b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(/.f64 (neg.f64 (-.f64 (fma.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (.f64 (sqrt.f64 2) B) (.f64 1/2 (.f64 (.f64 A (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B))))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 C C) (.f64 B B)) F) (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B))))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 C C) (.f64 B B)) (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(-.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) (+.f64 (.f64 B B) (.f64 C C))))) (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B))) (fma.f64 2 (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 C C) (.f64 B B)) F) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3))) (fma.f64 2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (sqrt.f64 2)) B)) (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (*.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B))))))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	57.6b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.2b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))))) (.f64 A C))))))
	53.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	55.9b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	51.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))

Compiler

Compiled 41241 to 23201 computations (43.7% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.9b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	10.5b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
	22.9b	(cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
✓	22.9b	(cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))

series53.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

53.0ms

(cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))

simplify98.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
374×	`fma-neg_binary64`
373×	`cancel-sign-sub-inv_binary64`
245×	`distribute-rgt-neg-in_binary64`
239×	`distribute-lft-neg-in_binary64`

Counts

49 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2243
1	564	2203
2	2065	2145
3	4785	2145
4	5041	2145

prune441.0ms (1%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	427	1	428
Fresh	0	32	32
Picked	0	1	1
Done	0	0	0
Total	427	34	461

Error

16.3b

Counts

461 → 34

Alt Table

Status	Error	Program
✓	48.5b	(.f64 -1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))))
	59.8b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.2b	(.f64 -1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 2 C)))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))))
	53.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	57.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (/.f64 (.f64 B B) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
▶	49.0b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	56.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	49.2b	(.f64 -1 (sqrt.f64 (/.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	58.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 2 C))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	49.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	57.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.1b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(/.f64 (neg.f64 (-.f64 (fma.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (.f64 (sqrt.f64 2) B) (.f64 1/2 (.f64 (.f64 A (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B))))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 C C) (.f64 B B)) F) (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B))))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 C C) (.f64 B B)) (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(-.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) (+.f64 (.f64 B B) (.f64 C C))))) (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B))) (fma.f64 2 (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 C C) (.f64 B B)) F) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3))) (fma.f64 2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (sqrt.f64 2)) B)) (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (*.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B))))))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	57.6b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.2b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))))) (.f64 A C))))))
	53.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	55.9b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	55.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	51.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))

Compiler

Compiled 25061 to 14450 computations (42.3% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	10.5b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	10.5b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	20.0b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

rewrite35.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`
40×	`associate-r_binary64`

Counts

2 → 136

Calls

2 calls:

13.0ms

(*.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))

6.0ms

(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

series5.2s (11.7%)

Counts

2 → 40

Calls

2 calls:

3.5s

(*.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))

1.7s

(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

simplify345.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

384×	`fma-def_binary64`
342×	`associate-+r+_binary64`
341×	`associate-r_binary64`
222×	`associate-/l*_binary64`
190×	`associate-*l/_binary64`

Counts

176 → 259

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1803	33367
1	5433	33367

prune866.0ms (1.9%)

Pruning

34 alts after pruning (32 fresh and 2 done)

	Pruned	Kept	Total
New	431	0	431
Fresh	0	32	32
Picked	0	1	1
Done	0	1	1
Total	431	34	465

Error

16.3b

Counts

465 → 34

Alt Table

Status	Error	Program
✓	48.5b	(.f64 -1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))))
	59.8b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.2b	(.f64 -1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 2 C)))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))))
	53.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	57.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (/.f64 (.f64 B B) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	49.0b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	56.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	49.2b	(.f64 -1 (sqrt.f64 (/.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	58.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 2 C))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	49.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	57.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.1b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(/.f64 (neg.f64 (-.f64 (fma.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))) (.f64 (sqrt.f64 2) B) (.f64 1/2 (.f64 (.f64 A (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B))))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 C C) (.f64 B B)) F) (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B))))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 C C) (.f64 B B)) (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (+.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(-.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) (+.f64 (.f64 B B) (.f64 C C))))) (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B))) (fma.f64 2 (.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 (.f64 C C) (.f64 B B)) F) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3))) (fma.f64 2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (/.f64 (.f64 A (sqrt.f64 2)) B)) (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (*.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B))))))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (cbrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	57.6b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.2b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))))) (.f64 A C))))))
	53.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	55.9b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	55.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	51.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))

Compiler

Compiled 53408 to 29101 computations (45.5% saved)

regimes4.7s (10.5%)

Accuracy

Total 22.9b remaining (57.5%)

Threshold costs 0b (0%)

Compiler

Compiled 50502 to 30397 computations (39.8% saved)

bsearch382.0ms (0.9%)

Steps

Iters	Range		Point
8	0.0001855694547458208	0.14795290643157671	0.00018787339796933887
6	4.2216439191601243e-246	4.422670979632252e-245	1.9737339501045438e-245
4	-1.1228602956022147e-92	-6.228117315192861e-93	-8.208527862976466e-93
7	-1.6629266261350396e+125	-3.2213189260050886e+123	-5.66563505439078e+123

Compiler

Compiled 5 to 4 computations (20% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
20×	`+-commutative_binary64`
16×	`sub-neg_binary64`
14×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	208
1	106	208
2	133	208
3	155	208
4	170	208
5	175	208
6	176	208
7	175	208

end2.0ms (0%)

Compiler: Compiled 142 to 81 computations (43% saved)

sample6.4s (14.3%)

Algorithm

1×

intervals

Results

1.0s	5518×	body	128	valid
760.0ms	913×	body	1024	valid
609.0ms	632×	body	2048	valid
602.0ms	839×	body	1024	nan
595.0ms	2791×	body	128	nan
554.0ms	574×	body	2048	nan
406.0ms	595×	body	512	nan
339.0ms	597×	body	512	valid
120.0ms	319×	body	256	nan
119.0ms	339×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 1613 to 948 computations (41.2% saved)

Details

analyze3.4s (7.5%)

sample178.0ms (0.4%)

simplify86.0ms (0.2%)

prune6.0ms (0%)

localize17.0ms (0%)

rewrite40.0ms (0.1%)

series15.7s (35.3%)

simplify570.0ms (1.3%)

prune1.1s (2.4%)

localize17.0ms (0%)

rewrite24.0ms (0.1%)

series4.0s (8.9%)

simplify274.0ms (0.6%)

prune708.0ms (1.6%)

localize23.0ms (0.1%)

rewrite1.0ms (0%)

series53.0ms (0.1%)

simplify98.0ms (0.2%)

prune441.0ms (1%)

localize19.0ms (0%)

rewrite35.0ms (0.1%)

series5.2s (11.7%)

simplify345.0ms (0.8%)

prune866.0ms (1.9%)

regimes4.7s (10.5%)

bsearch382.0ms (0.9%)

simplify11.0ms (0%)

end2.0ms (0%)

sample6.4s (14.3%)

Profiling