Details

analyze654.0ms (8.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.3s (28.8%)

Results

721.0ms	5412×	body	128	valid
632.0ms	1191×	body	2048	valid
320.0ms	725×	body	1024	valid
252.0ms	403×	body	4096	valid
156.0ms	1133×	body	128	invalid
144.0ms	364×	body	512	valid
35.0ms	161×	body	256	valid

Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess45.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

807×	`fma-def_binary64`
679×	`div-sub_binary64`
295×	`fma-neg_binary64`
214×	`associate-/l*_binary64`
209×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	104
1	98	88
2	198	88
3	446	88
4	768	88
5	1261	88
6	2236	88
7	4458	88
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 20 to 14 computations (30% saved)

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
619×	`times-frac_binary64`
338×	`fma-def_binary64`
314×	`associate-/l*_binary64`
262×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	69	22
3	161	22
4	259	22
5	417	22
6	734	22
7	1326	22
8	2618	22
9	3877	22

Stop Event

1×	node limit

Counts

1 → 2

prune9.0ms (0.1%)

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

31.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	31.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
▶	31.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.6b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series121.0ms (1.5%)

Counts

4 → 96

Calls

36 calls:

12.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	a	inf
9.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	a	-inf
7.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	c	-inf
7.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	c	inf
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))	a	-inf

rewrite75.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

277×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	343	62
2	4859	62

Stop Event

1×	node limit

Counts

4 → 158

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
430×	`fma-def_binary64`
422×	`associate-/r*_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	402	2164
2	1403	2078

Stop Event

1×	node limit

Counts

254 → 232

prune170.0ms (2.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	222	10	232
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	222	12	234

Error

5.7b

Counts

234 → 12

Alt Table

Status	Error	Program
	54.3b	(cbrt.f64 (pow.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a)) 3))
	57.9b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	43.2b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	45.7b	(/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (.f64 2 a))
	45.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.3b	(/.f64 (neg.f64 b) a)
▶	31.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	42.8b	(/.f64 (neg.f64 c) b)
	41.4b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
✓	31.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	50.9b	(.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (cbrt.f64 (.f64 4 (.f64 a a)))) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (cbrt.f64 (.f64 a 2))))
	43.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) 2))

Compiler

Compiled 6242 to 3634 computations (41.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
✓	0.6b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
✓	1.2b	(fma.f64 b b (.f64 a (.f64 c -4)))
✓	22.0b	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))

series123.0ms (1.6%)

Counts

4 → 96

Calls

36 calls:

10.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))	a	inf
9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))	a	-inf
9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))	c	inf
7.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))	c	-inf
6.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)	c	-inf

rewrite73.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

737×	`prod-diff_binary64`
158×	`egg-rr`
139×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	281	59
2	3626	59

Stop Event

1×	node limit

Counts

4 → 158

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
430×	`fma-def_binary64`
422×	`associate-/r*_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	402	2164
2	1403	2078

Stop Event

1×	node limit

Counts

254 → 232

prune167.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	228	4	232
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	234	10	244

Error

5.7b

Counts

244 → 10

Alt Table

Status	Error	Program
▶	33.3b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))
	41.4b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
	45.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.3b	(/.f64 (neg.f64 b) a)
	42.8b	(/.f64 (neg.f64 c) b)
✓	31.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	45.7b	(/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (.f64 2 a))
	57.9b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	46.3b	(/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))

Compiler

Compiled 5906 to 3671 computations (37.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))
✓	0.2b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))
✓	2.8b	(exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)))
✓	13.3b	(sqrt.f64 (.f64 a (.f64 c -4)))

series398.0ms (5%)

Counts

4 → 36

Calls

33 calls:

41.0ms	(log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))	c	inf
29.0ms	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))	a	inf
28.0ms	(log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))	a	-inf
28.0ms	(log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))	c	-inf
27.0ms	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))	a	-inf

rewrite72.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`prod-diff_binary64`
148×	`add-sqr-sqrt_binary64`
144×	`egg-rr`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	306	62
2	3826	62

Stop Event

1×	node limit

Counts

4 → 144

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-/l*_binary64`
486×	`associate-/r*_binary64`
377×	`fma-def_binary64`
242×	`cancel-sign-sub-inv_binary64`
233×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1541
1	451	1401
2	1531	1318

Stop Event

1×	node limit

Counts

180 → 215

prune179.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	216	9	225

Error

3.5b

Counts

225 → 9

Alt Table

Status	Error	Program
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
▶	41.4b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	45.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.3b	(/.f64 (neg.f64 b) a)
	42.8b	(/.f64 (neg.f64 c) b)
	48.6b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b))) (/.f64 1/2 a))
✓	31.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	45.7b	(/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (.f64 2 a))
	46.3b	(/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))

Compiler

Compiled 5855 to 3876 computations (33.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 b b (.f64 (.f64 a c) -4))
✓	6.9b	(/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))))
✓	17.1b	(-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (*.f64 b b))
✓	22.0b	(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))

series167.0ms (2.1%)

Counts

4 → 112

Calls

36 calls:

23.0ms	(/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))))	c	inf
22.0ms	(/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))))	a	inf
22.0ms	(/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))))	a	-inf
21.0ms	(/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))))	c	-inf
9.0ms	(/.f64 (-.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))))	b	0

rewrite75.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

265×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`
144×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	76
1	294	74
2	4251	74

Stop Event

1×	node limit

Counts

4 → 127

simplify46.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/l*_binary64`
530×	`associate-/r*_binary64`
413×	`associate-r_binary64`
345×	`associate-l_binary64`
297×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	2007
1	333	1917
2	1174	1847

Stop Event

1×	node limit

Counts

239 → 180

prune166.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	210	10	220

Error

3.5b

Counts

220 → 10

Alt Table

Status	Error	Program
	45.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.3b	(/.f64 (neg.f64 b) a)
	42.8b	(/.f64 (neg.f64 c) b)
	48.6b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b))) (/.f64 1/2 a))
	42.5b	(/.f64 (.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	31.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	45.7b	(/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (.f64 2 a))
	46.5b	(/.f64 (.f64 (/.f64 (.f64 -2 c) b) a) (*.f64 2 a))
	46.3b	(/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
	32.0b	(/.f64 (/.f64 (.f64 -4 (.f64 c a)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (*.f64 2 a))

Compiler

Compiled 7699 to 4363 computations (43.3% saved)

regimes2.7s (33.5%)

Accuracy

Total 7.0b remaining (69.6%)

Threshold costs 0b (0%)

Counts

172 → 3

Compiler

Compiled 14544 to 10222 computations (29.7% saved)

bsearch91.0ms (1.1%)

Algorithm

2×	binary-search

Calls

2 calls:

56.0ms	b
28.0ms	b

Steps

Iters	Point		Range
1.0751418463289444e-13	∈ [	1.0587309006830297e-13	,	8.70282333907846e-5	]
-5.119040201792971e+152	∈ [	-1.3003633266935404e+155	,	-4.921711966814816e+152	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	51
1	35	51
2	44	51
3	51	51
4	55	51
5	56	51

Stop Event

1×

saturated

end130.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 254 to 168 computations (33.9% saved)

Details

analyze654.0ms (8.3%)

sample2.3s (28.8%)

preprocess45.0ms (0.6%)

simplify29.0ms (0.4%)

prune9.0ms (0.1%)

localize11.0ms (0.1%)

series121.0ms (1.5%)

rewrite75.0ms (0.9%)

simplify50.0ms (0.6%)

prune170.0ms (2.1%)

localize12.0ms (0.2%)

series123.0ms (1.6%)

rewrite73.0ms (0.9%)

simplify49.0ms (0.6%)

prune167.0ms (2.1%)

localize13.0ms (0.2%)

series398.0ms (5%)

rewrite72.0ms (0.9%)

simplify40.0ms (0.5%)

prune179.0ms (2.3%)

localize14.0ms (0.2%)

series167.0ms (2.1%)

rewrite75.0ms (0.9%)

simplify46.0ms (0.6%)

prune166.0ms (2.1%)

regimes2.7s (33.5%)

bsearch91.0ms (1.1%)

simplify4.0ms (0.1%)

end130.0ms (1.6%)

Profiling