Details

analyze3.3s (11.2%)

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)

sample6.5s (22%)

Results

1.5s	5734×	body	128	valid
808.0ms	891×	body	1024	valid
805.0ms	686×	body	2048	valid
781.0ms	881×	body	1024	invalid
761.0ms	631×	body	2048	invalid
732.0ms	3003×	body	128	invalid
424.0ms	601×	body	512	valid
384.0ms	569×	body	512	invalid
167.0ms	342×	body	256	valid
149.0ms	334×	body	256	invalid
3.0ms	2×	body	4096	valid

Compiler

Compiled 90 to 66 computations (26.7% saved)

preprocess34.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

663×	`associate-l_binary64`
649×	`associate-r_binary64`
560×	`distribute-rgt-in_binary64`
528×	`distribute-lft-in_binary64`
364×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	427
1	360	343
2	1374	343
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

552×	`associate-l_binary64`
520×	`associate-r_binary64`
455×	`distribute-rgt-in_binary64`
450×	`fma-def_binary64`
449×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	66	49
2	225	49
3	1003	49

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (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
	52.9b	(/.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 2 (.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))

Status

Error

Program

52.9b

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

Compiler

Compiled 239 to 160 computations (33.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.1b	(.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))
✓	5.5b	(.f64 (fma.f64 B B (.f64 A (*.f64 C -4))) F)
✓	15.7b	(sqrt.f64 (.f64 2 (.f64 (.f64 (fma.f64 B B (.f64 A (*.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))
✓	22.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))

series8.4s (28.3%)

Counts

4 → 136

Calls

48 calls:

2.0s	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	F	-inf
1.4s	(sqrt.f64 (.f64 2 (.f64 (.f64 (fma.f64 B B (.f64 A (*.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))	F	0
1.3s	(sqrt.f64 (.f64 2 (.f64 (.f64 (fma.f64 B B (.f64 A (*.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))	F	inf
1.2s	(sqrt.f64 (.f64 2 (.f64 (.f64 (fma.f64 B B (.f64 A (*.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))	F	-inf
387.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	A	0

rewrite43.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`add-sqr-sqrt_binary64`
228×	`pow1_binary64`
227×	`*-un-lft-identity_binary64`
219×	`add-exp-log_binary64`
219×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	126
1	454	124

Stop Event

1×	node limit

Counts

4 → 82

simplify270.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

542×	`fma-def_binary64`
490×	`associate-r_binary64`
257×	`associate-/l*_binary64`
210×	`associate-*l/_binary64`
171×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2074	36539

Stop Event

1×	node limit

Counts

218 → 242

prune919.0ms (3.1%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	218	24	242
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	219	25	244

Error

27.7b

Counts

244 → 25

Alt Table

Status	Error	Program
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (+.f64 (.f64 4 (.f64 (.f64 A F) (.f64 B B))) (.f64 -8 (.f64 (.f64 A A) (.f64 C F))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	61.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (+.f64 (.f64 C (.f64 F (pow.f64 B 2))) (+.f64 (.f64 A (.f64 F (pow.f64 B 2))) (.f64 5 (.f64 A (.f64 C (.f64 F B)))))) (+.f64 (.f64 F (pow.f64 B 3)) (+.f64 (.f64 1/2 (.f64 (pow.f64 A 2) (.f64 F B))) (.f64 1/2 (.f64 (pow.f64 C 2) (.f64 F B))))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	55.8b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 F (/.f64 (sqrt.f64 (.f64 -8 (.f64 C F))) (.f64 (sqrt.f64 2) (.f64 B B)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	60.5b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 -2 (*.f64 A C)))))) C))))))
	57.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))) (pow.f64 B 2)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	60.4b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))) (*.f64 A C))))))
	63.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (log.f64 (pow.f64 (exp.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))) (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	60.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (+.f64 (.f64 C (.f64 F (pow.f64 B 2))) (+.f64 (.f64 A (.f64 F (pow.f64 B 2))) (+.f64 (.f64 F (pow.f64 B 3)) (+.f64 (.f64 1/2 (.f64 (pow.f64 A 2) (.f64 F B))) (.f64 1/2 (.f64 (pow.f64 C 2) (.f64 F B))))))) (.f64 5 (.f64 A (.f64 C (.f64 F B)))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	58.3b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	56.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (cbrt.f64 (pow.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F) 3)) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	59.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (+.f64 (.f64 4 (.f64 (.f64 C F) (.f64 B B))) (.f64 (.f64 -8 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	48.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) 3) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 -8 (.f64 A (.f64 (pow.f64 C 2) F)))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	58.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)))) (+.f64 (.f64 C (.f64 F (pow.f64 B 2))) (+.f64 (.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))) 3))))) (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C)))) (.f64 F (pow.f64 B 2))) (.f64 A (.f64 F (pow.f64 B 2))))))) (+.f64 (.f64 4 (.f64 A (.f64 (pow.f64 C 2) F))) (+.f64 (.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 2)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))) (+.f64 (.f64 4 (.f64 (pow.f64 A 2) (.f64 C F))) (.f64 4 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	56.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
✓	48.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	48.7b	(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 F (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4)))))
	58.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 -8 (.f64 (pow.f64 A 2) (.f64 C F)))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	54.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (fma.f64 2 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 4 (.f64 (.f64 A F) (.f64 B B)))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 1/2 (/.f64 F (/.f64 C (pow.f64 B 4))))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	56.2b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 B B (.f64 A (.f64 C -4))))
▶	45.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	63.4b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 F (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) 1/4) (hypot.f64 B (sqrt.f64 (.f64 A (*.f64 C -4))))) 2)
	56.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 (.f64 -8 A) F)) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 (.f64 F (sqrt.f64 2)) (.f64 B B)) (sqrt.f64 (.f64 (.f64 -8 A) F))))) (fma.f64 B B (.f64 A (.f64 C -4))))

Compiler

Compiled 53465 to 30608 computations (42.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 B B (.f64 A (.f64 C -4)))
	5.5b	(.f64 (fma.f64 B B (.f64 A (*.f64 C -4))) F)
✓	20.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
✓	20.1b	(sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)))

series1.8s (6.1%)

Counts

3 → 76

Calls

33 calls:

381.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	A	0
318.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	B	0
312.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	F	inf
289.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	F	0
202.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	C	0

rewrite39.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

241×	`add-sqr-sqrt_binary64`
233×	`pow1_binary64`
231×	`*-un-lft-identity_binary64`
223×	`add-exp-log_binary64`
223×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	79
1	471	79

Stop Event

1×	node limit

Counts

3 → 57

simplify215.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

523×	`*-commutative_binary64`
262×	`+-commutative_binary64`
254×	`fma-def_binary64`
242×	`associate-r_binary64`
234×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1144	18983
1	4709	17143

Stop Event

1×	node limit

Counts

133 → 125

prune601.0ms (2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	159	9	168
Fresh	8	15	23
Picked	1	0	1
Done	1	0	1
Total	169	24	193

Error

22.5b

Counts

193 → 24

Alt Table

Status	Error	Program
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (fma.f64 2 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 4 (.f64 (.f64 A F) (.f64 B B)))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 1/2 (/.f64 F (/.f64 C (pow.f64 B 4))))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	53.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 A B))))) (/.f64 (sqrt.f64 2) B))
	55.8b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 F (/.f64 (sqrt.f64 (.f64 -8 (.f64 C F))) (.f64 (sqrt.f64 2) (.f64 B B)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	60.5b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 -2 (*.f64 A C)))))) C))))))
	61.0b	(pow.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4)))) 3) 1/3)
	60.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (+.f64 (.f64 C (.f64 F (pow.f64 B 2))) (+.f64 (.f64 A (.f64 F (pow.f64 B 2))) (+.f64 (.f64 F (pow.f64 B 3)) (+.f64 (.f64 1/2 (.f64 (pow.f64 A 2) (.f64 F B))) (.f64 1/2 (.f64 (pow.f64 C 2) (.f64 F B))))))) (.f64 5 (.f64 A (.f64 C (.f64 F B)))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	58.3b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	58.2b	(/.f64 (neg.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 F)) (.f64 (sqrt.f64 2) B)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	53.3b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 -4 (.f64 A C)) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	59.7b	(exp.f64 (log.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))))
	48.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) 3) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
▶	46.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))
	56.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	58.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)))) (+.f64 (.f64 C (.f64 F (pow.f64 B 2))) (+.f64 (.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))) 3))))) (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C)))) (.f64 F (pow.f64 B 2))) (.f64 A (.f64 F (pow.f64 B 2))))))) (+.f64 (.f64 4 (.f64 A (.f64 (pow.f64 C 2) F))) (+.f64 (.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 2)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))) (+.f64 (.f64 4 (.f64 (pow.f64 A 2) (.f64 C F))) (.f64 4 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	48.7b	(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 F (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4)))))
	58.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	47.4b	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	63.4b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 F (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) 1/4) (hypot.f64 B (sqrt.f64 (.f64 A (*.f64 C -4))))) 2)
	60.4b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))) (*.f64 A C))))))
	53.9b	(.f64 (neg.f64 (sqrt.f64 (.f64 F (+.f64 C (hypot.f64 C B))))) (/.f64 (sqrt.f64 2) B))
	59.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (+.f64 (.f64 4 (.f64 (.f64 C F) (.f64 B B))) (.f64 (.f64 -8 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	54.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (pow.f64 B 2) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	54.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	56.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 (.f64 -8 A) F)) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 (.f64 F (sqrt.f64 2)) (.f64 B B)) (sqrt.f64 (.f64 (.f64 -8 A) F))))) (fma.f64 B B (.f64 A (.f64 C -4))))

Compiler

Compiled 29312 to 17573 computations (40% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.5b	(.f64 (fma.f64 B B (.f64 A (*.f64 C -4))) F)
✓	20.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))
	20.1b	(sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)))
✓	23.5b	(cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))

series1.8s (5.9%)

Counts

2 → 32

Calls

21 calls:

378.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))	A	0
325.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))	B	0
319.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))	F	inf
280.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))	F	0
214.0ms	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))	C	0

rewrite32.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

260×	`add-sqr-sqrt_binary64`
252×	`pow1_binary64`
249×	`*-un-lft-identity_binary64`
241×	`add-log-exp_binary64`
241×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	62
1	541	62

Stop Event

1×	node limit

Counts

2 → 30

simplify201.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

522×	`*-commutative_binary64`
262×	`+-commutative_binary64`
254×	`fma-def_binary64`
239×	`associate-r_binary64`
234×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1165	18217
1	4734	16377

Stop Event

1×	node limit

Counts

62 → 86

prune547.0ms (1.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	181	25	206

Error

22.5b

Counts

206 → 25

Alt Table

Status	Error	Program
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (fma.f64 2 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 4 (.f64 (.f64 A F) (.f64 B B)))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 1/2 (/.f64 F (/.f64 C (pow.f64 B 4))))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	53.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 A B))))) (/.f64 (sqrt.f64 2) B))
	55.8b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 F (/.f64 (sqrt.f64 (.f64 -8 (.f64 C F))) (.f64 (sqrt.f64 2) (.f64 B B)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	60.5b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 -2 (*.f64 A C)))))) C))))))
	61.0b	(pow.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4)))) 3) 1/3)
	60.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (+.f64 (.f64 C (.f64 F (pow.f64 B 2))) (+.f64 (.f64 A (.f64 F (pow.f64 B 2))) (+.f64 (.f64 F (pow.f64 B 3)) (+.f64 (.f64 1/2 (.f64 (pow.f64 A 2) (.f64 F B))) (.f64 1/2 (.f64 (pow.f64 C 2) (.f64 F B))))))) (.f64 5 (.f64 A (.f64 C (.f64 F B)))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	58.3b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	58.2b	(/.f64 (neg.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 F)) (.f64 (sqrt.f64 2) B)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	53.3b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 -4 (.f64 A C)) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	59.7b	(exp.f64 (log.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))))
	48.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) 3) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	56.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	47.6b	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))
	58.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)))) (+.f64 (.f64 C (.f64 F (pow.f64 B 2))) (+.f64 (.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))) 3))))) (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C)))) (.f64 F (pow.f64 B 2))) (.f64 A (.f64 F (pow.f64 B 2))))))) (+.f64 (.f64 4 (.f64 A (.f64 (pow.f64 C 2) F))) (+.f64 (.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 2)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))) (+.f64 (.f64 4 (.f64 (pow.f64 A 2) (.f64 C F))) (.f64 4 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	48.7b	(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 F (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4)))))
	58.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
▶	47.4b	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	63.4b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 F (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) 1/4) (hypot.f64 B (sqrt.f64 (.f64 A (*.f64 C -4))))) 2)
	53.9b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 -4 (.f64 A (.f64 C F))))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))
	60.4b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))) (*.f64 A C))))))
	53.9b	(.f64 (neg.f64 (sqrt.f64 (.f64 F (+.f64 C (hypot.f64 C B))))) (/.f64 (sqrt.f64 2) B))
	59.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (+.f64 (.f64 4 (.f64 (.f64 C F) (.f64 B B))) (.f64 (.f64 -8 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	54.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (pow.f64 B 2) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	54.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	56.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 (.f64 -8 A) F)) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 (.f64 F (sqrt.f64 2)) (.f64 B B)) (sqrt.f64 (.f64 (.f64 -8 A) F))))) (fma.f64 B B (.f64 A (.f64 C -4))))

Compiler

Compiled 32408 to 19675 computations (39.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))
	1.2b	(fma.f64 B B (.f64 A (.f64 C -4)))
✓	18.1b	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
✓	22.3b	(pow.f64 (.f64 2 (fma.f64 B B (.f64 A (*.f64 C -4)))) 1/2)

series1.7s (5.7%)

Counts

3 → 76

Calls

30 calls:

386.0ms	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	A	0
317.0ms	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	B	0
308.0ms	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	F	inf
280.0ms	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	F	0
209.0ms	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))	C	0

rewrite38.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`add-sqr-sqrt_binary64`
251×	`pow1_binary64`
249×	`*-un-lft-identity_binary64`
241×	`add-log-exp_binary64`
241×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	82
1	516	82

Stop Event

1×	node limit

Counts

3 → 57

simplify162.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

565×	`*-commutative_binary64`
332×	`+-commutative_binary64`
297×	`fma-def_binary64`
279×	`associate-+r+_binary64`
246×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1312	20056

Stop Event

1×	node limit

Counts

133 → 186

prune555.0ms (1.9%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	221	7	228
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	225	28	253

Error

21.9b

Counts

253 → 28

Alt Table

Status	Error	Program
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (fma.f64 2 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 4 (.f64 (.f64 A F) (.f64 B B)))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 1/2 (/.f64 F (/.f64 C (pow.f64 B 4))))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	53.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 A B))))) (/.f64 (sqrt.f64 2) B))
	57.3b	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	55.8b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 F (/.f64 (sqrt.f64 (.f64 -8 (.f64 C F))) (.f64 (sqrt.f64 2) (.f64 B B)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	60.5b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 -2 (*.f64 A C)))))) C))))))
	61.0b	(pow.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4)))) 3) 1/3)
	54.9b	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	53.9b	(.f64 (neg.f64 (sqrt.f64 (.f64 F (+.f64 C (hypot.f64 C B))))) (/.f64 (sqrt.f64 2) B))
	58.1b	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (.f64 2 C)))) (fma.f64 B B (.f64 A (.f64 C -4))))
	58.2b	(/.f64 (neg.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 F)) (.f64 (sqrt.f64 2) B)) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	53.3b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 -4 (.f64 A C)) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	47.1b	(neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4))))) (.f64 (sqrt.f64 F) (sqrt.f64 (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4)))))
	59.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (+.f64 (.f64 4 (.f64 (.f64 C F) (.f64 B B))) (.f64 (.f64 -8 A) (.f64 (.f64 C C) F)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	59.7b	(exp.f64 (log.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))))
	48.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) F)) 3) (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	47.1b	(pow.f64 (/.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 (.f64 (sqrt.f64 (.f64 2 (fma.f64 B B (.f64 A (*.f64 C -4))))) (sqrt.f64 F)) (neg.f64 (sqrt.f64 (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C)))))))) -1)
	56.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	47.3b	(pow.f64 (cbrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4))))) (sqrt.f64 F)) (neg.f64 (sqrt.f64 (+.f64 C (+.f64 A (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))) 3)
	54.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (pow.f64 B 2) F))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	48.7b	(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 F (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 A (*.f64 C -4)))))
	58.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	63.4b	(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (fma.f64 B B (.f64 A (.f64 C -4))) (.f64 F (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) 1/4) (hypot.f64 B (sqrt.f64 (.f64 A (*.f64 C -4))))) 2)
	53.9b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 -4 (.f64 A (.f64 C F))))) (sqrt.f64 (+.f64 (+.f64 C A) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4)))) 2) (cbrt.f64 (fma.f64 B B (.f64 A (.f64 C -4))))))
	60.4b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (.f64 A C))))))) (*.f64 A C))))))
	52.5b	(/.f64 (neg.f64 (.f64 (.f64 (pow.f64 (.f64 2 (fma.f64 B B (.f64 A (.f64 C -4)))) 1/2) (sqrt.f64 F)) (sqrt.f64 (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))))) (fma.f64 B B (.f64 A (*.f64 C -4))))
	60.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (-.f64 (+.f64 (.f64 C (.f64 F (pow.f64 B 2))) (+.f64 (.f64 A (.f64 F (pow.f64 B 2))) (+.f64 (.f64 F (pow.f64 B 3)) (+.f64 (.f64 1/2 (.f64 (pow.f64 A 2) (.f64 F B))) (.f64 1/2 (.f64 (pow.f64 C 2) (.f64 F B))))))) (.f64 5 (.f64 A (.f64 C (.f64 F B)))))))) (fma.f64 B B (.f64 A (.f64 C -4))))
	54.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	56.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 (.f64 -8 A) F)) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 (.f64 F (sqrt.f64 2)) (.f64 B B)) (sqrt.f64 (.f64 (.f64 -8 A) F))))) (fma.f64 B B (.f64 A (.f64 C -4))))

Compiler

Compiled 33547 to 19224 computations (42.7% saved)

regimes1.8s (6.1%)

Accuracy

Total 15.9b remaining (44.7%)

Threshold costs 0b (0%)

Counts

115 → 4

Compiler

Compiled 30178 to 20016 computations (33.7% saved)

bsearch8.0ms (0%)

Algorithm

3×	left-value

Calls

3 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)))

Steps

Iters	Point		Range
#hash((type . real) (value . +inf))	∈ [	#hash((type . real) (value . +inf))	,	#hash((type . real) (value . NaN))	]
-0.0	∈ [	-0.0	,	2.3275153388053987e-173	]
-4.325573197083108e-208	∈ [	-4.325573197083108e-208	,	-0.0	]

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Rules

54×	`*-commutative_binary64`
39×	`+-commutative_binary64`
32×	`sub-neg_binary64`
30×	`neg-sub0_binary64`
30×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	380
1	153	380
2	231	380
3	293	378
4	330	378
5	345	378
6	349	378

Stop Event

1×

saturated

end609.0ms (2%)

Stop Event

1×

fuel

Compiler

Compiled 1530 to 1021 computations (33.3% saved)

Details

analyze3.3s (11.2%)

sample6.5s (22%)

preprocess34.0ms (0.1%)

simplify15.0ms (0.1%)

prune7.0ms (0%)

localize17.0ms (0.1%)

series8.4s (28.3%)

rewrite43.0ms (0.1%)

simplify270.0ms (0.9%)

prune919.0ms (3.1%)

localize19.0ms (0.1%)

series1.8s (6.1%)

rewrite39.0ms (0.1%)

simplify215.0ms (0.7%)

prune601.0ms (2%)

localize34.0ms (0.1%)

series1.8s (5.9%)

rewrite32.0ms (0.1%)

simplify201.0ms (0.7%)

prune547.0ms (1.8%)

localize22.0ms (0.1%)

series1.7s (5.7%)

rewrite38.0ms (0.1%)

simplify162.0ms (0.5%)

prune555.0ms (1.9%)

regimes1.8s (6.1%)

bsearch8.0ms (0%)

simplify13.0ms (0%)

end609.0ms (2%)

Profiling