Details

analyze3.3s (7.9%)

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)

sample6.8s (16.1%)

Results

1.5s	5751×	body	128	valid
839.0ms	896×	body	1024	valid
811.0ms	650×	body	2048	invalid
783.0ms	839×	body	1024	invalid
767.0ms	2966×	body	128	invalid
762.0ms	657×	body	2048	valid
510.0ms	616×	body	512	valid
403.0ms	596×	body	512	invalid
169.0ms	380×	body	256	invalid
160.0ms	334×	body	256	valid
3.0ms	2×	body	4096	valid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify76.0ms (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

46.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	50.5b	(/.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)))
▶	47.1b	(/.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)))

Status

Error

Program

50.5b

(/.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)))

▶

47.1b

(/.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)))

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	3.7b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	14.5b	(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)))))))
✓	20.7b	(/.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)))

series16.9s (40%)

Counts

4 → 124

Calls

4 calls:

8.7s	(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)))))))
7.9s	(/.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)))
205.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
52.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite43.0ms (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:

10.0ms	(.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)))))))
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)))
4.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify477.0ms (1.1%)

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 → 361

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2448	45159
1	5052	45159

prune1.2s (2.8%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	333	28	361
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	334	29	363

Error

22.1b

Counts

363 → 29

Alt Table

Status	Error	Program
	58.8b	(/.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)))
	52.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	47.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	59.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.7b	(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))))))
	56.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	56.8b	(/.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)))
	50.5b	(/.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)))
	59.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	52.3b	(/.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)))
	57.8b	(/.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)))
	57.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	51.1b	(/.f64 (/.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)))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	54.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.1b	(/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
	55.6b	(/.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)))
	47.2b	(/.f64 (sqrt.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.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)))))))))))
	59.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	57.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.5b	(/.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)))
▶	45.5b	(.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)))))
	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)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	47.2b	(.f64 (sqrt.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 (sqrt.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))))
	54.1b	(/.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)))
	59.3b	(-.f64 (.f64 1/16 (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (.f64 (pow.f64 A 2) (.f64 C (sqrt.f64 (.f64 -1/2 (/.f64 F A))))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	56.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (-.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))

Compiler

Compiled 61958 to 33984 computations (45.1% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 A (.f64 C -4) (.f64 B B))
	0.8b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	11.4b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	17.8b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series1.2s (2.7%)

Counts

3 → 76

Calls

3 calls:

1.1s	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
41.0ms	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
10.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-*r/_binary64`
4×	`*-un-lft-identity_binary64`
4×	`sqrt-prod_binary64`

Counts

3 → 41

Calls

3 calls:

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)))
0.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

simplify118.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
457×	`associate-l_binary64`
213×	`associate-/r*_binary64`
195×	`*-commutative_binary64`
163×	`associate-*r/_binary64`

Counts

117 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	525	6271
1	1642	5185
2	4962	5170
3	4981	5170

prune1.0s (2.4%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	192	8	200
Fresh	5	23	28
Picked	1	0	1
Done	0	0	0
Total	198	31	229

Error

16.1b

Counts

229 → 31

Alt Table

Status	Error	Program
	58.8b	(/.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)))
	52.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	47.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	59.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.7b	(.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)))))
	54.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	61.7b	(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))))))
	56.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	56.8b	(/.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)))
	50.5b	(/.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)))
	52.3b	(/.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)))
	57.8b	(/.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)))
	51.1b	(/.f64 (/.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)))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	54.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	52.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	47.2b	(/.f64 (sqrt.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.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)))))))))))
	59.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (-.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))
▶	45.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	57.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	57.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.5b	(/.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)))
	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)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	47.2b	(.f64 (sqrt.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 (sqrt.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))))
	47.1b	(/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
	58.7b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 A F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	58.7b	(.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)))))
	55.0b	(.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)))))

Compiler

Compiled 14827 to 8580 computations (42.1% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))
	0.8b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	11.4b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	13.0b	(sqrt.f64 (.f64 A (.f64 C -4)))

series264.0ms (0.6%)

Counts

2 → 14

Calls

2 calls:

244.0ms	(cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))
20.0ms	(sqrt.f64 (.f64 A (.f64 C -4)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64`
3×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-pow1_binary64`
3×	`pow-prod-down_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(sqrt.f64 (.f64 A (.f64 C -4)))
2.0ms	(cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

787×	`associate-l_binary64`
529×	`fma-neg_binary64`
484×	`distribute-lft-neg-in_binary64`
481×	`distribute-rgt-neg-in_binary64`
425×	`unswap-sqr_binary64`

Counts

41 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	928
1	279	888
2	822	868
3	2820	856
4	5193	856

prune512.0ms (1.2%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	333	6	339
Fresh	0	30	30
Picked	1	0	1
Done	0	0	0
Total	334	36	370

Error

16.1b

Counts

370 → 36

Alt Table

Status	Error	Program
	58.8b	(/.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)))
	52.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	47.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	59.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.7b	(.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)))))
	54.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	61.7b	(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))))))
	56.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	56.8b	(/.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)))
▶	45.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	50.5b	(/.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)))
	52.3b	(/.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)))
	47.2b	(.f64 (sqrt.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 (sqrt.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))))
	47.0b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	57.8b	(/.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)))
	51.1b	(/.f64 (/.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)))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	54.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.3b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	52.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	47.2b	(/.f64 (sqrt.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.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)))))))))))
	59.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.5b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	56.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (-.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))
	60.1b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))))))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	57.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	57.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.5b	(/.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)))
	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)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	45.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	47.1b	(/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
	58.7b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 A F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	58.7b	(.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)))))
	55.0b	(.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)))))

Compiler

Compiled 27628 to 17052 computations (38.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))
	0.8b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	11.4b	(sqrt.f64 (.f64 2 (.f64 F (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))
	13.0b	(sqrt.f64 (.f64 A (.f64 C -4)))

series1.3s (3%)

Counts

2 → 56

Calls

2 calls:

1.0s

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

248.0ms

(cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))

rewrite48.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`associate-*r/_binary64`
56×	`cbrt-div_binary64`
28×	`flip-+_binary64`
28×	`frac-times_binary64`
28×	`flip3-+_binary64`

Counts

2 → 59

Calls

2 calls:

22.0ms

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

4.0ms

(cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))

simplify354.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

455×	`*-commutative_binary64`
235×	`associate-r_binary64`
188×	`times-frac_binary64`
183×	`+-commutative_binary64`
159×	`fma-def_binary64`

Counts

115 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1078	13486
1	3166	11981
2	4994	11979
3	4956	11979

prune1.5s (3.6%)

Pruning

39 alts after pruning (38 fresh and 1 done)

	Pruned	Kept	Total
New	694	4	698
Fresh	1	34	35
Picked	0	1	1
Done	0	0	0
Total	695	39	734

Error

16.0b

Counts

734 → 39

Alt Table

Status	Error	Program
	58.8b	(/.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)))
	60.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (cbrt.f64 (.f64 2 A)))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	52.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	47.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	60.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (pow.f64 (.f64 2 A) 1/3)) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	55.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	59.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.7b	(.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)))))
	54.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	61.7b	(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))))))
	56.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	56.8b	(/.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)))
✓	45.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	50.5b	(/.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)))
	52.3b	(/.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)))
	47.2b	(.f64 (sqrt.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 (sqrt.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))))
	47.0b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	57.8b	(/.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)))
	51.1b	(/.f64 (/.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)))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	54.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.3b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	52.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	47.2b	(/.f64 (sqrt.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.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)))))))))))
	59.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.5b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	56.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (-.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))
	60.1b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))))))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	57.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	57.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (cbrt.f64 (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	47.5b	(/.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)))
	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)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	45.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	59.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (cbrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (pow.f64 (.f64 2 C) 1/3))))) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	47.1b	(/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
	58.7b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 A F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	58.7b	(.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)))))

Compiler

Compiled 80486 to 42463 computations (47.2% saved)

regimes4.6s (11%)

Accuracy

Total 26.9b remaining (62.9%)

Threshold costs 0b (0%)

Counts

184 → 12

Compiler

Compiled 58093 to 35863 computations (38.3% saved)

bsearch1.4s (3.4%)

Steps

Iters	Range		Point
10	4.980840315721753e+172	4.8089051275019884e+188	9.070489695444037e+172
10	1.1585210531147694e+159	2.7960833938947674e+169	5.48701879697187e+159
9	1.2236568351887733e+152	2.6082655323060756e+158	1.8247188167373362e+153
8	4.501335300082188e+114	2.301610243396325e+117	7.020914566277488e+115
9	4.277146904588747e+21	7.184725522327955e+28	1.525172088274872e+28
3	1.4359632913725204e-196	1.8377347828038433e-196	1.461074009586978e-196
11	-1.5003871474398763e-58	-1.742933409196347e-79	-7.898288287255473e-59
8	-14059214864599069000.0	-33092260147620876.0	-13902718134128933000.0
10	-1.035474797313275e+82	-5.133417069522795e+71	-1.0277110279859103e+73
7	-4.999675215128283e+94	-4.7895807335777225e+92	-6.715914155896905e+93
8	-3.11997341852303e+163	-5.464803961195357e+158	-1.547843111002865e+160

Compiler

Compiled 5 to 4 computations (20% saved)

simplify25.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

63×	`*-commutative_binary64`
41×	`+-commutative_binary64`
33×	`sub-neg_binary64`
29×	`neg-sub0_binary64`
26×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	138	670
1	229	670
2	286	670
3	344	670
4	376	670
5	389	670
6	393	670
7	391	670

end882.0ms (2.1%)

Compiler: Compiled 2478 to 1505 computations (39.3% saved)

Details

analyze3.3s (7.9%)

sample6.8s (16.1%)

simplify76.0ms (0.2%)

prune6.0ms (0%)

localize16.0ms (0%)

series16.9s (40%)

rewrite43.0ms (0.1%)

simplify477.0ms (1.1%)

prune1.2s (2.8%)

localize18.0ms (0%)

series1.2s (2.7%)

rewrite10.0ms (0%)

simplify118.0ms (0.3%)

prune1.0s (2.4%)

localize19.0ms (0%)

series264.0ms (0.6%)

rewrite5.0ms (0%)

simplify50.0ms (0.1%)

prune512.0ms (1.2%)

localize22.0ms (0.1%)

series1.3s (3%)

rewrite48.0ms (0.1%)

simplify354.0ms (0.8%)

prune1.5s (3.6%)

regimes4.6s (11%)

bsearch1.4s (3.4%)

simplify25.0ms (0.1%)

end882.0ms (2.1%)

Profiling