Details

analyze3.6s (6.6%)

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)

sample7.2s (13.2%)

Results

1.7s	5733×	body	128	valid
902.0ms	660×	body	2048	valid
858.0ms	905×	body	1024	valid
817.0ms	2892×	body	128	invalid
787.0ms	831×	body	1024	invalid
715.0ms	637×	body	2048	invalid
469.0ms	620×	body	512	invalid
449.0ms	621×	body	512	valid
267.0ms	364×	body	256	invalid
164.0ms	336×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1006×	`rules-43_binary64`
751×	`rules-40_binary64`
751×	`rules-41_binary64`
751×	`rules-42_binary64`
223×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	137	53
2	496	53
3	2478	53
4	4159	53
5	4877	53
6	4988	53

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

49.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	49.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	52.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))

Status

Error

Program

▶

49.6b

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

52.1b

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

Compiler

Compiled 245 to 162 computations (33.9% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.6b	(.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))
✓	7.0b	(.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)
✓	17.6b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))
✓	23.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))

series17.2s (31.5%)

Counts

4 → 136

Calls

4 calls:

9.2s	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))
7.7s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
203.0ms	(.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))
27.0ms	(.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)

rewrite87.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

226×	`add-sqr-sqrt_binary64`
219×	`log1p-expm1-u_binary64`
219×	`expm1-log1p-u_binary64`
212×	`add-cbrt-cube_binary64`
212×	`add-exp-log_binary64`

Counts

4 → 105

Calls

4 calls:

84.0ms	(.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))
84.0ms	(.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)
84.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))
84.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	139
1	518	139
2	4860	139
3	4996	139
0	0	0
1	0	0

simplify329.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2029×	`rules-42_binary64`
2029×	`rules-43_binary64`
538×	`fma-def_binary64`
17×	`cube-mult_binary64`
17×	`unpow3_binary64`

Counts

241 → 258

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2069	36755
1	6737	36755

prune883.0ms (1.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	236	22	258
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	238	22	260

Error

27.3b

Counts

260 → 22

Alt Table

Status	Error	Program
	51.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (+.f64 (pow.f64 B 2) (pow.f64 C 2))) (.f64 2 (.f64 A C))))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (fma.f64 (.f64 A A) (.f64 F B) (.f64 (.f64 C C) (.f64 F B)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.4b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	50.5b	(/.f64 (neg.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (fma.f64 2 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))) (.f64 F (.f64 B B))) (.f64 2 (.f64 A (.f64 F (.f64 B B)))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 4 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 8 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.4b	(/.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))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	49.6b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) 1/4) 2)) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	59.6b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.1b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
	58.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	56.3b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	56.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) (.f64 F (pow.f64 B 2)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.4b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) F)) (/.f64 (sqrt.f64 2) B)))
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F) 3))) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	49.8b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))) 2) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))))
	55.6b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))))
	49.8b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 A C) (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.0b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
▶	45.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	60.1b	(.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))))))

Compiler

Compiled 54888 to 31011 computations (43.5% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	7.0b	(.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)
✓	20.1b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)) F)))
✓	21.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))

series3.7s (6.8%)

Counts

3 → 76

Calls

3 calls:

3.5s

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

193.0ms

(sqrt.f64 (*.f64 2 (*.f64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)) F)))

51.0ms

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

rewrite76.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

232×	`add-sqr-sqrt_binary64`
225×	`log1p-expm1-u_binary64`
225×	`expm1-log1p-u_binary64`
218×	`add-cbrt-cube_binary64`
218×	`add-exp-log_binary64`

Counts

3 → 80

Calls

3 calls:

74.0ms

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

74.0ms

(sqrt.f64 (*.f64 2 (*.f64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)) F)))

74.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	87
1	538	87
2	4797	87
3	4956	87
0	0	0
1	0	0

simplify190.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1278×	`rules-41_binary64`
1278×	`rules-42_binary64`
1278×	`rules-43_binary64`
298×	`fma-def_binary64`
15×	`cube-mult_binary64`

Counts

156 → 199

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1313	20348
1	5515	20348

prune609.0ms (1.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	222	8	230
Fresh	4	17	21
Picked	1	0	1
Done	0	0	0
Total	227	25	252

Error

25.4b

Counts

252 → 25

Alt Table

Status	Error	Program
	51.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (+.f64 (pow.f64 B 2) (pow.f64 C 2))) (.f64 2 (.f64 A C))))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	55.1b	(cbrt.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C))) 3))
	55.3b	(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (sqrt.f64 F) (.f64 (sqrt.f64 2) B)) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 F)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (fma.f64 (.f64 A A) (.f64 F B) (.f64 (.f64 C C) (.f64 F B)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.4b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	45.1b	(/.f64 (neg.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)))) 2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (fma.f64 2 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))) (.f64 F (.f64 B B))) (.f64 2 (.f64 A (.f64 F (.f64 B B)))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 4 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 8 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.4b	(/.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))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	61.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (fma.f64 1/2 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (.f64 1/2 (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.1b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	54.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))) 3) 1/3)))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	56.3b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
▶	45.0b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.0b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	57.9b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	56.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) (.f64 F (pow.f64 B 2)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.4b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) F)) (/.f64 (sqrt.f64 2) B)))
	55.6b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))))
	49.6b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) 1/4) 2)) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	49.8b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 A C) (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	56.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	60.1b	(.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))))))

Compiler

Compiled 35297 to 20143 computations (42.9% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))
	1.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	20.8b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
✓	24.2b	(pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)

series9.6s (17.6%)

Counts

3 → 76

Calls

3 calls:

6.3s

(*.f64 (*.f64 (sqrt.f64 F) (pow.f64 (*.f64 2 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))

3.2s

(/.f64 (neg.f64 (*.f64 (*.f64 (sqrt.f64 F) (pow.f64 (*.f64 2 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))

54.0ms

(pow.f64 (*.f64 2 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) 1/2)

rewrite45.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

248×	`add-sqr-sqrt_binary64`
242×	`log1p-expm1-u_binary64`
242×	`expm1-log1p-u_binary64`
232×	`add-cbrt-cube_binary64`
232×	`add-exp-log_binary64`

Counts

3 → 66

Calls

3 calls:

42.0ms

(*.f64 (*.f64 (sqrt.f64 F) (pow.f64 (*.f64 2 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))

42.0ms

(/.f64 (neg.f64 (*.f64 (*.f64 (sqrt.f64 F) (pow.f64 (*.f64 2 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)))

42.0ms

(pow.f64 (*.f64 2 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C))) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	115
1	583	113
2	4947	113
0	0	0
1	0	0

simplify316.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1923×	`rules-42_binary64`
1923×	`rules-43_binary64`
467×	`fma-def_binary64`
17×	`cube-mult_binary64`
17×	`unpow3_binary64`

Counts

142 → 200

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1960	33888
1	6365	33888

prune907.0ms (1.7%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	284	7	291
Fresh	2	22	24
Picked	0	1	1
Done	0	0	0
Total	286	30	316

Error

25.4b

Counts

316 → 30

Alt Table

Status	Error	Program
	51.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (+.f64 (pow.f64 B 2) (pow.f64 C 2))) (.f64 2 (.f64 A C))))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	55.1b	(cbrt.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C))) 3))
	57.2b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (fma.f64 (.f64 A A) (.f64 F B) (.f64 (.f64 C C) (.f64 F B)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.4b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
▶	45.1b	(/.f64 (neg.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)))) 2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (fma.f64 2 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))) (.f64 F (.f64 B B))) (.f64 2 (.f64 A (.f64 F (.f64 B B)))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 4 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 8 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.4b	(/.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))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	49.8b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 A C) (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	45.4b	(/.f64 (neg.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) F) 1/2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) 3)) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	61.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (fma.f64 1/2 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (.f64 1/2 (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.1b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	57.0b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (.f64 2 A)))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	54.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))) 3) 1/3)))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	56.3b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
✓	45.0b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.0b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	56.6b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (.f64 B B) A)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	55.3b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (-.f64 (.f64 (sqrt.f64 2) B) (.f64 2 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	56.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) (.f64 F (pow.f64 B 2)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.4b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) F)) (/.f64 (sqrt.f64 2) B)))
	58.0b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 B))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	55.6b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))))
	49.6b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) 1/4) 2)) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	56.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	60.1b	(.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))))))
	60.9b	(pow.f64 (sqrt.f64 (/.f64 (neg.f64 (.f64 (pow.f64 (.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) F) 1/2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))) 2)

Compiler

Compiled 57276 to 33002 computations (42.4% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.4b	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)) F))))
	7.0b	(.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)
	20.1b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)) F)))
✓	21.7b	(/.f64 (neg.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)))) 2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))

series4.2s (7.7%)

Counts

2 → 64

Calls

2 calls:

3.6s

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

618.0ms

(sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)) F))))

rewrite77.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

238×	`add-sqr-sqrt_binary64`
233×	`log1p-expm1-u_binary64`
233×	`expm1-log1p-u_binary64`
225×	`add-cbrt-cube_binary64`
225×	`add-exp-log_binary64`

Counts

2 → 48

Calls

2 calls:

75.0ms

(sqrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (-.f64 (*.f64 B B) (*.f64 (*.f64 4 A) C)) F))))

75.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	78
1	563	76
2	4957	76
3	5111	76
0	0	0
1	0	0

simplify204.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1302×	`rules-41_binary64`
1302×	`rules-42_binary64`
1302×	`rules-43_binary64`
271×	`fma-def_binary64`
28×	`fma-neg_binary64`

Counts

112 → 148

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1341	20874
1	5649	20874

prune622.0ms (1.1%)

Pruning

33 alts after pruning (31 fresh and 2 done)

	Pruned	Kept	Total
New	225	3	228
Fresh	0	28	28
Picked	0	1	1
Done	0	1	1
Total	225	33	258

Error

25.2b

Counts

258 → 33

Alt Table

Status	Error	Program
	51.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 4 (.f64 A C))) (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (+.f64 (pow.f64 B 2) (pow.f64 C 2))) (.f64 2 (.f64 A C))))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	55.1b	(cbrt.f64 (pow.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C))) 3))
	57.2b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (fma.f64 (.f64 A A) (.f64 F B) (.f64 (.f64 C C) (.f64 F B)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.4b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
✓	45.1b	(/.f64 (neg.f64 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)))) 2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (fma.f64 2 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))) (.f64 F (.f64 B B))) (.f64 2 (.f64 A (.f64 F (.f64 B B)))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 4 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 8 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.4b	(/.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))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.3b	(/.f64 (neg.f64 (.f64 (pow.f64 (.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 -4 (.f64 C F))) (neg.f64 (log.f64 A)))) (sqrt.f64 (sqrt.f64 2))) 2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	49.8b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 A C) (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	45.4b	(/.f64 (neg.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) F) 1/2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) 3)) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	61.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (fma.f64 1/2 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (.f64 1/2 (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.1b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
	58.1b	(/.f64 (neg.f64 (.f64 (pow.f64 (.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -4 (.f64 C F))) (log.f64 (/.f64 1 A))))) (sqrt.f64 (sqrt.f64 2))) 2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	57.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	57.0b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (.f64 2 A)))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	54.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))) 3) 1/3)))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	56.3b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
✓	45.0b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	58.0b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	56.6b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (.f64 B B) A)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	55.3b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (-.f64 (.f64 (sqrt.f64 2) B) (.f64 2 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	56.0b	(/.f64 (neg.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (exp.f64 (.f64 1/4 (-.f64 (log.f64 F) (.f64 2 (log.f64 (/.f64 1 B))))))) 2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	56.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F))) (sqrt.f64 (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	56.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) (.f64 F (pow.f64 B 2)))))) (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)))
	58.4b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) F)) (/.f64 (sqrt.f64 2) B)))
	58.0b	(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 F) (pow.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) 1/2)) (sqrt.f64 B))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	55.6b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 -1/2 (/.f64 F A)))))
	49.6b	(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (.f64 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) 1/4) 2)) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))
	60.1b	(.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))))))
	60.9b	(pow.f64 (sqrt.f64 (/.f64 (neg.f64 (.f64 (pow.f64 (.f64 (.f64 2 (-.f64 (.f64 B B) (.f64 (.f64 4 A) C))) F) 1/2) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (-.f64 (.f64 B B) (.f64 (*.f64 4 A) C)))) 2)

Compiler

Compiled 35823 to 20832 computations (41.8% saved)

regimes3.3s (6%)

Accuracy

Total 17.7b remaining (42.8%)

Threshold costs 0b (0%)

Counts

191 → 6

Compiler

Compiled 56654 to 36276 computations (36% saved)

bsearch483.0ms (0.9%)

Steps

Iters	Range		Point
6	5.4880541512515054e+172	6.098023762335932e+173	3.718423827809515e+173
5	6.3096734433383285e+53	2.0161045823309827e+54	1.1150151595515204e+54
9	3.211081560272966e-270	2.9914885296432184e-262	1.9811684140282612e-269
5	-2.1635952194332943e-134	-8.974520102303552e-135	-2.1406366566139761e-134
7	-5.522448650465628e-16	-2.371396959971025e-17	-2.592644457333761e-17

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	270
1	71	270
2	70	270

end790.0ms (1.5%)

Compiler: Compiled 1797 to 1149 computations (36.1% saved)

Details

analyze3.6s (6.6%)

sample7.2s (13.2%)

simplify79.0ms (0.1%)

prune6.0ms (0%)

localize18.0ms (0%)

series17.2s (31.5%)

rewrite87.0ms (0.2%)

simplify329.0ms (0.6%)

prune883.0ms (1.6%)

localize18.0ms (0%)

series3.7s (6.8%)

rewrite76.0ms (0.1%)

simplify190.0ms (0.3%)

prune609.0ms (1.1%)

localize21.0ms (0%)

series9.6s (17.6%)

rewrite45.0ms (0.1%)

simplify316.0ms (0.6%)

prune907.0ms (1.7%)

localize21.0ms (0%)

series4.2s (7.7%)

rewrite77.0ms (0.1%)

simplify204.0ms (0.4%)

prune622.0ms (1.1%)

regimes3.3s (6%)

bsearch483.0ms (0.9%)

simplify5.0ms (0%)

end790.0ms (1.5%)

Profiling