Details

analyze4.3s (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%	98.2%	1.8%	7
0%	92%	8%	8
0%	91.2%	8.8%	9
0%	89.7%	10.3%	10
1.3%	85.5%	13.3%	11
2.4%	80%	17.5%	12
3.4%	78.3%	18.3%	13
5.3%	75%	19.7%	14

Compiler

Compiled 45 to 33 computations (26.7% saved)

sample6.7s (7.9%)

Results

1.6s	5781×	body	128	valid
802.0ms	867×	body	1024	valid
802.0ms	628×	body	2048	valid
787.0ms	842×	body	1024	invalid
753.0ms	617×	body	2048	invalid
641.0ms	2615×	body	128	invalid
462.0ms	649×	body	512	valid
417.0ms	620×	body	512	invalid
186.0ms	326×	body	256	valid
164.0ms	361×	body	256	invalid
7.0ms	5×	body	4096	valid

Compiler

Compiled 90 to 66 computations (26.7% saved)

preprocess32.0ms (0%)

Algorithm

2×	egg-herbie

Rules

580×	`associate-l_binary64`
566×	`associate-r_binary64`
435×	`distribute-rgt-in_binary64`
411×	`distribute-lft-in_binary64`
232×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	427
1	323	343
2	1158	343
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Rules

470×	`associate-l_binary64`
454×	`associate-r_binary64`
420×	`distribute-rgt-in_binary64`
410×	`distribute-lft-in_binary64`
306×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	61	49
2	195	49
3	836	49
4	4456	49

Stop Event

1×	node limit

Counts

1 → 2

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

48.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	53.9b	(/.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)))
▶	48.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))

Status

Error

Program

53.9b

(/.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)))

▶

48.6b

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

Compiler

Compiled 239 to 160 computations (33.1% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))
✓	7.6b	(.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)
✓	19.9b	(sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))
✓	23.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))

series8.1s (9.6%)

Counts

4 → 136

Calls

48 calls:

1.8s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	F	-inf
1.4s	(sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))	F	0
1.4s	(sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))	F	-inf
1.2s	(sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))	F	inf
411.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	A	0

rewrite45.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

232×	`add-sqr-sqrt_binary64`
220×	`log1p-expm1-u_binary64`
220×	`expm1-log1p-u_binary64`
219×	`add-cbrt-cube_binary64`
215×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	129
1	455	127

Stop Event

1×	node limit

Counts

4 → 97

simplify263.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
492×	`associate-r_binary64`
252×	`associate-*l/_binary64`
251×	`associate-/l*_binary64`
166×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2081	36919

Stop Event

1×	node limit

Counts

233 → 256

prune915.0ms (1.1%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	230	26	256
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	231	27	258

Error

26.7b

Counts

258 → 27

Alt Table

Status	Error	Program
	56.8b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 (.f64 C F) (.f64 B B)) (neg.f64 (.f64 (.f64 16 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	55.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 -4 (.f64 A (.f64 C F))) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	56.2b	(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	60.5b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	55.2b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) 2))) (sqrt.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 F (.f64 B B)) (-.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	61.2b	(sqrt.f64 (/.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (pow.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) 2)))
	62.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (.f64 C F) (.f64 B B)) (fma.f64 2 (.f64 (.f64 A F) (.f64 B B)) (.f64 10 (.f64 (.f64 A C) (.f64 F B))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F))) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.8b	(.f64 (/.f64 -1 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4))))) (/.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4))))))
	59.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 8 (.f64 (.f64 A F) (.f64 B B)))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 F (/.f64 C (pow.f64 B 4))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	55.0b	(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	49.2b	(/.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (+.f64 (pow.f64 B 2) (pow.f64 C 2))) (.f64 2 (.f64 A C)))))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 A 2) (.f64 F (pow.f64 B 2))) C)) (.f64 8 (.f64 A (.f64 F (pow.f64 B 2))))) (+.f64 (.f64 16 (.f64 (pow.f64 A 2) (.f64 C F))) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 F (-.f64 (fma.f64 2 (.f64 C (.f64 B B)) (fma.f64 2 (.f64 A (.f64 B B)) (.f64 (.f64 8 (.f64 A C)) (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (+.f64 (.f64 C C) (.f64 B B))) (.f64 -2 (.f64 A C))))))) (fma.f64 2 (.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (+.f64 (.f64 C C) (.f64 B B))) (.f64 -2 (.f64 A C)))) (.f64 B B)) (.f64 8 (+.f64 (.f64 A (.f64 C C)) (.f64 (.f64 A A) C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 C C) (/.f64 A (.f64 F (.f64 B B)))) (.f64 8 (.f64 (.f64 C F) (.f64 B B)))) (+.f64 (/.f64 F (/.f64 A (pow.f64 B 4))) (.f64 (.f64 16 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	61.7b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (fma.f64 2 (.f64 (.f64 C F) (.f64 B B)) (fma.f64 2 (.f64 (.f64 A F) (.f64 B B)) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C)))))) (.f64 -10 (.f64 (.f64 A C) (.f64 F B)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
▶	48.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	50.7b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
✓	48.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	55.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))

Compiler

Compiled 54552 to 30808 computations (43.5% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.6b	(.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)
✓	19.9b	(sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))
✓	23.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
✓	24.0b	(cbrt.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F))

series6.2s (7.3%)

Counts

3 → 52

Calls

36 calls:

1.3s	(sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))	F	0
1.2s	(sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))	F	-inf
1.2s	(sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))	F	inf
390.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	A	0
301.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	B	0

rewrite45.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

247×	`add-sqr-sqrt_binary64`
238×	`log1p-expm1-u_binary64`
238×	`expm1-log1p-u_binary64`
235×	`add-cbrt-cube_binary64`
230×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	99
1	514	99

Stop Event

1×	node limit

Counts

3 → 64

simplify227.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

452×	`fma-def_binary64`
420×	`associate-r_binary64`
414×	`associate-+r+_binary64`
250×	`associate-*l/_binary64`
241×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1858	32609

Stop Event

1×	node limit

Counts

116 → 160

prune788.0ms (0.9%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	176	6	182
Fresh	4	21	25
Picked	0	1	1
Done	1	0	1
Total	181	28	209

Error

26.7b

Counts

209 → 28

Alt Table

Status	Error	Program
	56.8b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
▶	49.1b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) -1)
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 (.f64 C F) (.f64 B B)) (neg.f64 (.f64 (.f64 16 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	56.2b	(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	60.5b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 F (.f64 B B)) (-.f64 C (sqrt.f64 (+.f64 (.f64 C C) (.f64 B B)))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	60.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (.f64 A A) (-.f64 (.f64 C C) (.f64 2 (*.f64 A C))))))) C)))) (sqrt.f64 2)))
	61.2b	(sqrt.f64 (/.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (pow.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) 2)))
	60.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	63.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F))) 2) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	56.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 A (.f64 C F)) 1/3) (cbrt.f64 -4)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	62.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (.f64 C F) (.f64 B B)) (fma.f64 2 (.f64 (.f64 A F) (.f64 B B)) (.f64 10 (.f64 (.f64 A C) (.f64 F B))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.8b	(.f64 (/.f64 -1 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4))))) (/.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4))))))
	59.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 8 (.f64 (.f64 A F) (.f64 B B)))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 F (/.f64 C (pow.f64 B 4))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	55.0b	(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (+.f64 (pow.f64 B 2) (pow.f64 C 2))) (.f64 2 (.f64 A C)))))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 A 2) (.f64 F (pow.f64 B 2))) C)) (.f64 8 (.f64 A (.f64 F (pow.f64 B 2))))) (+.f64 (.f64 16 (.f64 (pow.f64 A 2) (.f64 C F))) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 F (-.f64 (fma.f64 2 (.f64 C (.f64 B B)) (fma.f64 2 (.f64 A (.f64 B B)) (.f64 (.f64 8 (.f64 A C)) (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (+.f64 (.f64 C C) (.f64 B B))) (.f64 -2 (.f64 A C))))))) (fma.f64 2 (.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (+.f64 (.f64 C C) (.f64 B B))) (.f64 -2 (.f64 A C)))) (.f64 B B)) (.f64 8 (+.f64 (.f64 A (.f64 C C)) (.f64 (.f64 A A) C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 C C) (/.f64 A (.f64 F (.f64 B B)))) (.f64 8 (.f64 (.f64 C F) (.f64 B B)))) (+.f64 (/.f64 F (/.f64 A (pow.f64 B 4))) (.f64 (.f64 16 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	61.7b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (fma.f64 2 (.f64 (.f64 C F) (.f64 B B)) (fma.f64 2 (.f64 (.f64 A F) (.f64 B B)) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C)))))) (.f64 -10 (.f64 (.f64 A C) (.f64 F B)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)))) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
✓	48.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	50.7b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.2b	(cbrt.f64 (pow.f64 (neg.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))) 3))
	55.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))

Compiler

Compiled 49183 to 28572 computations (41.9% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.0b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	7.6b	(.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)
✓	16.8b	(sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	22.3b	(/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))

series49.1s (57.8%)

Counts

3 → 76

Calls

33 calls:

43.8s	(/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))	F	-inf
1.2s	(sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))	F	0
1.2s	(sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))	F	-inf
1.1s	(sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))	F	inf
441.0ms	(/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))	A	0

rewrite40.0ms (0%)

Algorithm

1×	batch-egg-rewrite

Rules

224×	`add-sqr-sqrt_binary64`
212×	`log1p-expm1-u_binary64`
212×	`expm1-log1p-u_binary64`
211×	`add-cbrt-cube_binary64`
207×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	96
1	444	94

Stop Event

1×	node limit

Counts

3 → 96

simplify196.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

441×	`associate-r_binary64`
411×	`fma-def_binary64`
229×	`associate-/l*_binary64`
223×	`associate-/r*_binary64`
218×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1957	29971

Stop Event

1×	node limit

Counts

172 → 239

prune771.0ms (0.9%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	250	11	261
Fresh	9	17	26
Picked	1	0	1
Done	0	1	1
Total	260	29	289

Error

25.6b

Counts

289 → 29

Alt Table

Status	Error	Program
	56.8b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	58.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 C C) (/.f64 A (.f64 F (.f64 B B)))) (.f64 8 (.f64 (.f64 C F) (.f64 B B)))) (+.f64 (/.f64 F (/.f64 A (pow.f64 B 4))) (.f64 (.f64 16 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	57.2b	(pow.f64 (neg.f64 (+.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 -2 A) F)) (sqrt.f64 2)) (.f64 1/4 (/.f64 (/.f64 (.f64 B B) C) (.f64 (.f64 F (sqrt.f64 (/.f64 (.f64 -2 A) F))) (sqrt.f64 2)))))) -1)
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 (.f64 C F) (.f64 B B)) (neg.f64 (.f64 (.f64 16 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.8b	(pow.f64 (neg.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 -2 A) F)) (sqrt.f64 2))) -1)
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	56.2b	(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	60.5b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	55.9b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (.f64 2 C)))))) -1)
	60.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (+.f64 A (-.f64 C (sqrt.f64 (+.f64 (.f64 A A) (-.f64 (.f64 C C) (.f64 2 (*.f64 A C))))))) C)))) (sqrt.f64 2)))
	62.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (.f64 C F) (.f64 B B)) (fma.f64 2 (.f64 (.f64 A F) (.f64 B B)) (.f64 10 (.f64 (.f64 A C) (.f64 F B))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.8b	(.f64 (/.f64 -1 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4))))) (/.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4))))))
	55.0b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))))) -1)
✓	48.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 8 (.f64 (.f64 A F) (.f64 B B)))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 F (/.f64 C (pow.f64 B 4))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	55.0b	(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (+.f64 (pow.f64 B 2) (pow.f64 C 2))) (.f64 2 (.f64 A C)))))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	56.7b	(pow.f64 (neg.f64 (fma.f64 1/4 (/.f64 (/.f64 (.f64 B B) A) (.f64 (.f64 F (sqrt.f64 (.f64 -2 (/.f64 C F)))) (sqrt.f64 2))) (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2)))) -1)
	58.3b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (fma.f64 (sqrt.f64 A) (sqrt.f64 A) (-.f64 C (hypot.f64 B (-.f64 A C))))))))) -1)
	61.2b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 B))))) -1)
	55.2b	(pow.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2))) -1)
	54.2b	(cbrt.f64 (pow.f64 (neg.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))) 3))
	54.4b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (.f64 2 A) (*.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) -1)
	60.7b	(pow.f64 (neg.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 1 F) (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B)))))) (/.f64 B (sqrt.f64 2)))) -1)
	56.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 A (.f64 C F)) 1/3) (cbrt.f64 -4)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
▶	50.7b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	63.2b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (.f64 (sqrt.f64 (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F))))) -1)
	55.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))

Compiler

Compiled 49050 to 27967 computations (43% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.0b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	9.9b	(sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	10.1b	(sqrt.f64 (.f64 C (.f64 A -4)))
✓	11.8b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))

series2.0s (2.4%)

Counts

3 → 28

Calls

30 calls:

269.0ms	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	F	-inf
236.0ms	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	F	inf
220.0ms	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	F	0
135.0ms	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	C	-inf
123.0ms	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))	A	0

rewrite34.0ms (0%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`add-sqr-sqrt_binary64`
228×	`log1p-expm1-u_binary64`
228×	`expm1-log1p-u_binary64`
227×	`add-cbrt-cube_binary64`
223×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	80
1	490	77

Stop Event

1×	node limit

Counts

3 → 70

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
512×	`times-frac_binary64`
392×	`associate-/l*_binary64`
271×	`*-commutative_binary64`
121×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	604	8056
1	2175	6399

Stop Event

1×	node limit

Counts

98 → 126

prune347.0ms (0.4%)

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	217	8	225
Fresh	5	22	27
Picked	0	1	1
Done	0	1	1
Total	222	32	254

Error

21.2b

Counts

254 → 32

Alt Table

Status	Error	Program
	56.8b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	58.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 C C) (/.f64 A (.f64 F (.f64 B B)))) (.f64 8 (.f64 (.f64 C F) (.f64 B B)))) (+.f64 (/.f64 F (/.f64 A (pow.f64 B 4))) (.f64 (.f64 16 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	57.2b	(pow.f64 (neg.f64 (+.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 -2 A) F)) (sqrt.f64 2)) (.f64 1/4 (/.f64 (/.f64 (.f64 B B) C) (.f64 (.f64 F (sqrt.f64 (/.f64 (.f64 -2 A) F))) (sqrt.f64 2)))))) -1)
	58.1b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (.f64 2 A) (/.f64 (.f64 1/2 (.f64 B B)) C))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.8b	(pow.f64 (neg.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 -2 A) F)) (sqrt.f64 2))) -1)
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	56.2b	(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	60.5b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.5b	(.f64 (/.f64 (sqrt.f64 2) B) (neg.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 C B))))))
	55.9b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (.f64 2 C)))))) -1)
	55.3b	(.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (neg.f64 (/.f64 (sqrt.f64 2) B)))
	60.7b	(pow.f64 (neg.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 1 F) (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B)))))) (/.f64 B (sqrt.f64 2)))) -1)
	53.7b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (cbrt.f64 (pow.f64 (.f64 (.f64 F 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))) 3/2)))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	62.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (.f64 C F) (.f64 B B)) (fma.f64 2 (.f64 (.f64 A F) (.f64 B B)) (.f64 10 (.f64 (.f64 A C) (.f64 F B))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.8b	(.f64 (/.f64 -1 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4))))) (/.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4))))))
	55.0b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))))) -1)
✓	48.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 8 (.f64 (.f64 A F) (.f64 B B)))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 F (/.f64 C (pow.f64 B 4))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	55.0b	(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	48.8b	(neg.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 F 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))) (fma.f64 B B (.f64 C (.f64 A -4))))) (fma.f64 B B (.f64 C (*.f64 A -4)))))
	56.7b	(pow.f64 (neg.f64 (fma.f64 1/4 (/.f64 (/.f64 (.f64 B B) A) (.f64 (.f64 F (sqrt.f64 (.f64 -2 (/.f64 C F)))) (sqrt.f64 2))) (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2)))) -1)
	58.6b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (+.f64 (.f64 2 C) (.f64 -1/2 (/.f64 (.f64 B B) A)))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.2b	(cbrt.f64 (pow.f64 (neg.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 C (*.f64 A -4))))) 3))
	57.6b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	61.2b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 B))))) -1)
	55.2b	(pow.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2))) -1)
	54.4b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (sqrt.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (.f64 2 (-.f64 (.f64 2 A) (*.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) -1)
	60.4b	(.f64 1/4 (.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -4 (.f64 A C)))) (.f64 A C)) (sqrt.f64 (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (*.f64 A C)))))))))
✓	50.7b	(/.f64 (neg.f64 (.f64 (hypot.f64 B (sqrt.f64 (.f64 C (.f64 A -4)))) (sqrt.f64 (.f64 F (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	63.2b	(pow.f64 (/.f64 (fma.f64 B B (.f64 C (.f64 A -4))) (neg.f64 (.f64 (sqrt.f64 (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F))))) -1)
	55.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))

Compiler

Compiled 19621 to 11698 computations (40.4% saved)

regimes4.0s (4.7%)

Accuracy

Total 20.1b remaining (49.7%)

Threshold costs 0b (0%)

Counts

198 → 5

Compiler

Compiled 60347 to 38738 computations (35.8% saved)

bsearch14.0ms (0%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(/.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)))
0.0ms	(/.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)))
0.0ms	(/.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)))
0.0ms	(/.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)))

Steps

Iters	Point		Range
#hash((type . real) (value . +inf))	∈ [	#hash((type . real) (value . +inf))	,	#hash((type . real) (value . NaN))	]
0.0	∈ [	0.0	,	3.0175306534206063e-123	]
-1.4924876823199194e-182	∈ [	-1.4924876823199194e-182	,	0.0	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-2.087812653506548e+267	]

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Rules

44×	`*-commutative_binary64`
34×	`+-commutative_binary64`
31×	`sub-neg_binary64`
24×	`neg-sub0_binary64`
24×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	462
1	151	462
2	218	462
3	265	462
4	287	462
5	292	462
6	293	462

Stop Event

1×

saturated

end606.0ms (0.7%)

Stop Event

1×

fuel

Compiler

Compiled 1690 to 1134 computations (32.9% saved)

Details

analyze4.3s (5%)

sample6.7s (7.9%)

preprocess32.0ms (0%)

simplify24.0ms (0%)

prune6.0ms (0%)

localize22.0ms (0%)

series8.1s (9.6%)

rewrite45.0ms (0.1%)

simplify263.0ms (0.3%)

prune915.0ms (1.1%)

localize21.0ms (0%)

series6.2s (7.3%)

rewrite45.0ms (0.1%)

simplify227.0ms (0.3%)

prune788.0ms (0.9%)

localize18.0ms (0%)

series49.1s (57.8%)

rewrite40.0ms (0%)

simplify196.0ms (0.2%)

prune771.0ms (0.9%)

localize17.0ms (0%)

series2.0s (2.4%)

rewrite34.0ms (0%)

simplify88.0ms (0.1%)

prune347.0ms (0.4%)

regimes4.0s (4.7%)

bsearch14.0ms (0%)

simplify13.0ms (0%)

end606.0ms (0.7%)

Profiling