Details

analyze3.2s (7.2%)

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%	98.2%	1.8%	7
0%	92%	8%	8
0%	91.2%	8.8%	9
0.4%	89.3%	10.3%	10
7.1%	79.2%	13.6%	11
11.9%	70.2%	17.9%	12
13.8%	67.4%	18.7%	13
16.6%	63.3%	20.1%	14

Compiler

Compiled 45 to 33 computations (26.7% saved)

sample6.3s (14.2%)

Results

1.5s	5693×	body	128	valid
850.0ms	888×	body	1024	valid
785.0ms	698×	body	2048	valid
743.0ms	855×	body	1024	invalid
642.0ms	2576×	body	128	invalid
585.0ms	542×	body	2048	invalid
437.0ms	615×	body	512	valid
397.0ms	597×	body	512	invalid
168.0ms	364×	body	256	invalid
165.0ms	360×	body	256	valid
3.0ms	2×	body	4096	valid

Compiler

Compiled 90 to 66 computations (26.7% saved)

preprocess34.0ms (0.1%)

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)

simplify25.0ms (0.1%)

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

45.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	49.5b	(/.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)))
▶	45.3b	(/.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

49.5b

(/.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)))

▶

45.3b

(/.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)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))
✓	5.5b	(.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)
✓	15.5b	(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)))))))
✓	22.5b	(/.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))))

series7.8s (17.5%)

Counts

4 → 136

Calls

48 calls:

1.7s	(/.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
1.3s	(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
1.3s	(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
362.0ms	(/.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

rewrite46.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`add-sqr-sqrt_binary64`
229×	`pow1_binary64`
228×	`*-un-lft-identity_binary64`
220×	`add-exp-log_binary64`
220×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	129
1	455	127

Stop Event

1×	node limit

Counts

4 → 82

simplify271.0ms (0.6%)

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

218 → 241

prune979.0ms (2.2%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	212	29	241
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	213	30	243

Error

25.6b

Counts

243 → 30

Alt Table

Status	Error	Program
	58.2b	(/.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))))
	54.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	51.0b	(/.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))))
	55.7b	(/.f64 (neg.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 C (*.f64 A -4))))
	56.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	55.5b	(/.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))))
	60.0b	(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)))
	59.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	55.3b	(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 F (/.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 (sqrt.f64 2) (.f64 B B))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
✓	45.3b	(/.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))))
	46.0b	(/.f64 (neg.f64 (sqrt.f64 (pow.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)))))) 3))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	60.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 -2 (*.f64 A C))))) C)))) (sqrt.f64 2)))
	63.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (exp.f64 (log.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))))
	55.3b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 A F))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	62.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (log.f64 (pow.f64 (exp.f64 F) (fma.f64 B B (.f64 C (.f64 A -4))))) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.7b	(/.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))))
	63.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 2) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 8 (.f64 C (.f64 F (pow.f64 B 2)))) (.f64 16 (.f64 A (.f64 (pow.f64 C 2) F)))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	62.3b	(/.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))))
	63.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 3) 1/3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	47.0b	(/.f64 (neg.f64 (exp.f64 (log.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))))
	56.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	50.3b	(/.f64 (neg.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))))) 3/2))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 4 (.f64 C (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 4 (.f64 A (.f64 F (pow.f64 B 2)))) (.f64 16 (.f64 A (.f64 (pow.f64 C 2) F))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.5b	(-.f64 (.f64 (.f64 2 (/.f64 (.f64 (.f64 A C) (sqrt.f64 2)) (pow.f64 B 3))) (sqrt.f64 (/.f64 F (/.f64 (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (+.f64 (.f64 A A) (.f64 B B)))))) (fma.f64 2 (.f64 (/.f64 (.f64 (.f64 (.f64 A A) C) (sqrt.f64 2)) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 1/2 (.f64 (/.f64 C (/.f64 B (sqrt.f64 2))) (sqrt.f64 (/.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 (.f64 1/2 (/.f64 A (/.f64 B (.f64 C (sqrt.f64 2))))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))))))
	63.6b	(pow.f64 (/.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))))) 1/4) (hypot.f64 B (sqrt.f64 (.f64 C (*.f64 A -4))))) 2)
▶	45.9b	(/.f64 (neg.f64 (pow.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))))) 1/4) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))

Compiler

Compiled 53848 to 30496 computations (43.4% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.3b	(.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) (*.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))
	5.5b	(.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)
✓	21.3b	(/.f64 (neg.f64 (pow.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))))) 1/4) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
✓	27.5b	(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))))) 1/4)

series5.6s (12.6%)

Counts

3 → 116

Calls

36 calls:

1.5s	(/.f64 (neg.f64 (pow.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))))) 1/4) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))	F	-inf
1.2s	(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))))) 1/4)	F	0
403.0ms	(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))))) 1/4)	F	inf
402.0ms	(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))))) 1/4)	F	-inf
362.0ms	(/.f64 (neg.f64 (pow.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))))) 1/4) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))	A	0

rewrite44.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	117
1	500	116

Stop Event

1×	node limit

Counts

3 → 51

simplify265.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-def_binary64`
255×	`associate-/l*_binary64`
182×	`associate-/r*_binary64`
165×	`associate-*l/_binary64`
148×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2427	38366

Stop Event

1×	node limit

Counts

167 → 239

prune946.0ms (2.1%)

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	248	13	261
Fresh	7	21	28
Picked	1	0	1
Done	1	0	1
Total	257	34	291

Error

23.2b

Counts

291 → 34

Alt Table

Status	Error	Program
	58.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.4b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 F)) (.f64 3 (log.f64 (/.f64 -1 B)))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.2b	(/.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))))
	54.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	60.7b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -2 F)) (.f64 -3 (neg.f64 (log.f64 B))))) 2)) (fma.f64 B B (.f64 C (.f64 A -4))))
	51.0b	(/.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))))
	55.7b	(/.f64 (neg.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 C (*.f64 A -4))))
	60.6b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 F)) (.f64 3 (log.f64 (/.f64 1 B)))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	55.5b	(/.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))))
	55.9b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 F (.f64 B B)) (.f64 2 (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) 1/4) 2)) (fma.f64 B B (.f64 C (.f64 A -4))))
	58.2b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))) 1/4) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	63.6b	(pow.f64 (/.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))))) 1/4) (hypot.f64 B (sqrt.f64 (.f64 C (*.f64 A -4))))) 2)
	56.9b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))) 1/4) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	55.3b	(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 F (/.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 (sqrt.f64 2) (.f64 B B))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 -2 (*.f64 A C))))) C)))) (sqrt.f64 2)))
	62.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (log.f64 (pow.f64 (exp.f64 F) (fma.f64 B B (.f64 C (.f64 A -4))))) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.7b	(/.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))))
	58.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 8 (.f64 C (.f64 F (pow.f64 B 2)))) (.f64 16 (.f64 A (.f64 (pow.f64 C 2) F)))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	62.3b	(/.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))))
	60.4b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (-.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)))))))) (log.f64 (/.f64 1 F))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	63.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 3) 1/3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.7b	(pow.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 C (*.f64 A -4)))) 3) 1/3)
▶	45.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	58.0b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 16 (.f64 (pow.f64 C 2) F)))) (log.f64 (/.f64 1 A))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	47.0b	(/.f64 (neg.f64 (exp.f64 (log.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))))
	56.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	58.7b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 16 (.f64 (pow.f64 A 2) F)))) (log.f64 (/.f64 1 C))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	50.3b	(/.f64 (neg.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))))) 3/2))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 4 (.f64 C (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 4 (.f64 A (.f64 F (pow.f64 B 2)))) (.f64 16 (.f64 A (.f64 (pow.f64 C 2) F))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	47.5b	(/.f64 (neg.f64 (pow.f64 (.f64 (pow.f64 (fma.f64 B B (.f64 C (.f64 A -4))) 1/4) (pow.f64 (.f64 F (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) 1/4)) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.5b	(-.f64 (.f64 (.f64 2 (/.f64 (.f64 (.f64 A C) (sqrt.f64 2)) (pow.f64 B 3))) (sqrt.f64 (/.f64 F (/.f64 (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (+.f64 (.f64 A A) (.f64 B B)))))) (fma.f64 2 (.f64 (/.f64 (.f64 (.f64 (.f64 A A) C) (sqrt.f64 2)) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 1/2 (.f64 (/.f64 C (/.f64 B (sqrt.f64 2))) (sqrt.f64 (/.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 (.f64 1/2 (/.f64 A (/.f64 B (.f64 C (sqrt.f64 2))))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))))))
	59.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	59.5b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -2 F)) (.f64 -3 (log.f64 (/.f64 -1 B))))) 2)) (fma.f64 B B (.f64 C (.f64 A -4))))

Compiler

Compiled 56663 to 33710 computations (40.5% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))
	5.5b	(.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)
✓	15.5b	(sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))
✓	22.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))

series7.5s (16.8%)

Counts

3 → 88

Calls

36 calls:

1.6s	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))	F	-inf
1.3s	(sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))	F	-inf
1.3s	(sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))	F	0
1.1s	(sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))	F	inf
352.0ms	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))	A	0

rewrite52.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`add-sqr-sqrt_binary64`
241×	`pow1_binary64`
240×	`*-un-lft-identity_binary64`
230×	`add-cbrt-cube_binary64`
230×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	115
1	489	115

Stop Event

1×	node limit

Counts

3 → 54

simplify274.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
490×	`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	2077	36136

Stop Event

1×	node limit

Counts

142 → 206

prune1.0s (2.2%)

Pruning

36 alts after pruning (35 fresh and 1 done)

	Pruned	Kept	Total
New	222	6	228
Fresh	4	29	33
Picked	0	1	1
Done	0	0	0
Total	226	36	262

Error

23.2b

Counts

262 → 36

Alt Table

Status	Error	Program
	58.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.4b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 F)) (.f64 3 (log.f64 (/.f64 -1 B)))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	54.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	60.7b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -2 F)) (.f64 -3 (neg.f64 (log.f64 B))))) 2)) (fma.f64 B B (.f64 C (.f64 A -4))))
	51.0b	(/.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))))
	55.6b	(.f64 (neg.f64 (.f64 -1 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	55.7b	(/.f64 (neg.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 C (*.f64 A -4))))
	60.6b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 F)) (.f64 3 (log.f64 (/.f64 1 B)))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.5b	(-.f64 (.f64 (.f64 2 (/.f64 (.f64 (.f64 A C) (sqrt.f64 2)) (pow.f64 B 3))) (sqrt.f64 (/.f64 F (/.f64 (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (+.f64 (.f64 A A) (.f64 B B)))))) (fma.f64 2 (.f64 (/.f64 (.f64 (.f64 (.f64 A A) C) (sqrt.f64 2)) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 1/2 (.f64 (/.f64 C (/.f64 B (sqrt.f64 2))) (sqrt.f64 (/.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 (.f64 1/2 (/.f64 A (/.f64 B (.f64 C (sqrt.f64 2))))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))))))
▶	45.5b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	55.5b	(/.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))))
	58.2b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))) 1/4) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	57.0b	(.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	59.7b	(.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	59.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	63.6b	(pow.f64 (/.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))))) 1/4) (hypot.f64 B (sqrt.f64 (.f64 C (*.f64 A -4))))) 2)
	56.0b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 F (.f64 B B)) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (*.f64 A -4)))))
	55.3b	(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 F (/.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 (sqrt.f64 2) (.f64 B B))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (.f64 (/.f64 F A) (/.f64 (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 -2 (*.f64 A C))))) C)))) (sqrt.f64 2)))
	62.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (log.f64 (pow.f64 (exp.f64 F) (fma.f64 B B (.f64 C (.f64 A -4))))) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.7b	(/.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))))
	58.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 8 (.f64 C (.f64 F (pow.f64 B 2)))) (.f64 16 (.f64 A (.f64 (pow.f64 C 2) F)))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	60.4b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (-.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)))))))) (log.f64 (/.f64 1 F))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	63.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 3) 1/3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.7b	(pow.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 C (*.f64 A -4)))) 3) 1/3)
✓	45.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	58.0b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 16 (.f64 (pow.f64 C 2) F)))) (log.f64 (/.f64 1 A))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	47.0b	(/.f64 (neg.f64 (exp.f64 (log.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))))
	62.4b	(.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))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	56.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	58.7b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 16 (.f64 (pow.f64 A 2) F)))) (log.f64 (/.f64 1 C))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	50.3b	(/.f64 (neg.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))))) 3/2))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 4 (.f64 C (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 4 (.f64 A (.f64 F (pow.f64 B 2)))) (.f64 16 (.f64 A (.f64 (pow.f64 C 2) F))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	47.5b	(/.f64 (neg.f64 (pow.f64 (.f64 (pow.f64 (fma.f64 B B (.f64 C (.f64 A -4))) 1/4) (pow.f64 (.f64 F (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) 1/4)) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.5b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -2 F)) (.f64 -3 (log.f64 (/.f64 -1 B))))) 2)) (fma.f64 B B (.f64 C (.f64 A -4))))

Compiler

Compiled 54107 to 30983 computations (42.7% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.5b	(.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)
✓	15.5b	(sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))
✓	22.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
✓	24.0b	(cbrt.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F))

series6.0s (13.4%)

Counts

3 → 52

Calls

36 calls:

1.3s	(sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))	F	0
1.2s	(sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))	F	-inf
1.1s	(sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (*.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))	F	inf
368.0ms	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))	A	0
285.0ms	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))	B	0

rewrite57.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

267×	`add-sqr-sqrt_binary64`
257×	`pow1_binary64`
255×	`*-un-lft-identity_binary64`
248×	`add-cbrt-cube_binary64`
248×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	99
1	555	99

Stop Event

1×	node limit

Counts

3 → 36

simplify261.0ms (0.6%)

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

88 → 132

prune748.0ms (1.7%)

Pruning

36 alts after pruning (34 fresh and 2 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	2	32	34
Picked	0	1	1
Done	0	1	1
Total	154	36	190

Error

23.2b

Counts

190 → 36

Alt Table

Status	Error	Program
	58.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.4b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 F)) (.f64 3 (log.f64 (/.f64 -1 B)))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.1b	(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)))
	54.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	60.7b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -2 F)) (.f64 -3 (neg.f64 (log.f64 B))))) 2)) (fma.f64 B B (.f64 C (.f64 A -4))))
	51.0b	(/.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))))
	55.7b	(/.f64 (neg.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 C (*.f64 A -4))))
	60.6b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 F)) (.f64 3 (log.f64 (/.f64 1 B)))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	60.5b	(-.f64 (.f64 (.f64 2 (/.f64 (.f64 (.f64 A C) (sqrt.f64 2)) (pow.f64 B 3))) (sqrt.f64 (/.f64 F (/.f64 (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (+.f64 (.f64 A A) (.f64 B B)))))) (fma.f64 2 (.f64 (/.f64 (.f64 (.f64 (.f64 A A) C) (sqrt.f64 2)) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 1/2 (.f64 (/.f64 C (/.f64 B (sqrt.f64 2))) (sqrt.f64 (/.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 (.f64 1/2 (/.f64 A (/.f64 B (.f64 C (sqrt.f64 2))))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))))))
✓	45.5b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F)) 3) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	55.5b	(/.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))))
	58.2b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 A A) (/.f64 C (.f64 F (.f64 B B)))) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))) 1/4) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	57.0b	(.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	59.7b	(.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	59.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	63.6b	(pow.f64 (/.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))))) 1/4) (hypot.f64 B (sqrt.f64 (.f64 C (*.f64 A -4))))) 2)
	56.0b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 F (.f64 B B)) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (*.f64 A -4)))))
	62.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (log.f64 (pow.f64 (exp.f64 F) (fma.f64 B B (.f64 C (.f64 A -4))))) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	54.7b	(/.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))))
	58.2b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 8 (.f64 C (.f64 F (pow.f64 B 2)))) (.f64 16 (.f64 A (.f64 (pow.f64 C 2) F)))))) (fma.f64 B B (.f64 C (.f64 A -4))))
	60.4b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (-.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)))))))) (log.f64 (/.f64 1 F))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	63.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 3) 1/3) (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	59.7b	(pow.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (fma.f64 B B (.f64 C (*.f64 A -4)))) 3) 1/3)
✓	45.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (.f64 (fma.f64 B B (.f64 C (.f64 A -4))) F) 2) (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	58.0b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 16 (.f64 (pow.f64 C 2) F)))) (log.f64 (/.f64 1 A))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	47.0b	(/.f64 (neg.f64 (exp.f64 (log.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))))
	62.4b	(.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))))))) (/.f64 1 (fma.f64 B B (.f64 C (.f64 A -4)))))
	56.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	58.7b	(/.f64 (neg.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (neg.f64 (.f64 16 (.f64 (pow.f64 A 2) F)))) (log.f64 (/.f64 1 C))))) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	50.3b	(/.f64 (neg.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))))) 3/2))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	58.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 4 (.f64 C (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 4 (.f64 A (.f64 F (pow.f64 B 2)))) (.f64 16 (.f64 A (.f64 (pow.f64 C 2) F))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))
	47.5b	(/.f64 (neg.f64 (pow.f64 (.f64 (pow.f64 (fma.f64 B B (.f64 C (.f64 A -4))) 1/4) (pow.f64 (.f64 F (.f64 2 (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C)))))) 1/4)) 2)) (fma.f64 B B (.f64 C (*.f64 A -4))))
	55.6b	(.f64 (neg.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 -8 C) F)))))) (/.f64 1 (fma.f64 B B (.f64 C (*.f64 A -4)))))
	59.5b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 -2 F)) (.f64 -3 (log.f64 (/.f64 -1 B))))) 2)) (fma.f64 B B (.f64 C (.f64 A -4))))
	55.3b	(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 F (/.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 (sqrt.f64 2) (.f64 B B))))))) (fma.f64 B B (.f64 C (*.f64 A -4))))

Compiler

Compiled 47486 to 27714 computations (41.6% saved)

regimes2.1s (4.7%)

Accuracy

Total 17.8b remaining (42.6%)

Threshold costs 0b (0%)

Counts

132 → 4

Compiler

Compiled 33106 to 22134 computations (33.1% saved)

bsearch289.0ms (0.6%)

Algorithm

3×	binary-search

Calls

3 calls:

118.0ms	A
115.0ms	A
48.0ms	A

Steps

Iters	Point		Range
7.86622038382639e+31	∈ [	7.791760514814636e+31	,	5.478803703326545e+34	]
-5.45911078926389e-135	∈ [	-7.538577753376542e-130	,	-3.2135562798623948e-136	]
-8.618866089292812e+101	∈ [	-1.903394752541349e+102	,	-4.151310679380862e+101	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

125×	`distribute-rgt-neg-in_binary64`
84×	`distribute-lft-neg-in_binary64`
81×	`cancel-sign-sub-inv_binary64`
76×	`neg-sub0_binary64`
75×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	172
1	99	169
2	139	169
3	190	169
4	226	169
5	270	169
6	318	169
7	358	169
8	393	169
9	419	169
10	442	169
11	479	169
12	531	169
13	581	169
14	634	169
15	688	169
16	758	169
17	825	169
18	871	169
19	896	169
20	904	169

Stop Event

1×

saturated

end693.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 1611 to 1065 computations (33.9% saved)

Iter	Nodes	Cost
0	56	172
1	99	169
2	139	169
3	190	169
4	226	169
5	270	169
6	318	169
7	358	169
8	393	169
9	419	169
10	442	169
11	479	169
12	531	169
13	581	169
14	634	169
15	688	169
16	758	169
17	825	169
18	871	169
19	896	169
20	904	169

Iter	Nodes	Cost
0	56	172
1	99	169
2	139	169
3	190	169
4	226	169
5	270	169
6	318	169
7	358	169
8	393	169
9	419	169
10	442	169
11	479	169
12	531	169
13	581	169
14	634	169
15	688	169
16	758	169
17	825	169
18	871	169
19	896	169
20	904	169

Details

analyze3.2s (7.2%)

sample6.3s (14.2%)

preprocess34.0ms (0.1%)

simplify25.0ms (0.1%)

prune6.0ms (0%)

localize17.0ms (0%)

series7.8s (17.5%)

rewrite46.0ms (0.1%)

simplify271.0ms (0.6%)

prune979.0ms (2.2%)

localize19.0ms (0%)

series5.6s (12.6%)

rewrite44.0ms (0.1%)

simplify265.0ms (0.6%)

prune946.0ms (2.1%)

localize18.0ms (0%)

series7.5s (16.8%)

rewrite52.0ms (0.1%)

simplify274.0ms (0.6%)

prune1.0s (2.2%)

localize21.0ms (0%)

series6.0s (13.4%)

rewrite57.0ms (0.1%)

simplify261.0ms (0.6%)

prune748.0ms (1.7%)

regimes2.1s (4.7%)

bsearch289.0ms (0.6%)

simplify29.0ms (0.1%)

end693.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	56	172
1	99	169
2	139	169
3	190	169
4	226	169
5	270	169
6	318	169
7	358	169
8	393	169
9	419	169
10	442	169
11	479	169
12	531	169
13	581	169
14	634	169
15	688	169
16	758	169
17	825	169
18	871	169
19	896	169
20	904	169