Details

analyze645.0ms (9.8%)

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 (34.4%)

Results

693.0ms	5307×	body	128	valid
623.0ms	1194×	body	2048	valid
315.0ms	770×	body	1024	valid
263.0ms	430×	body	4096	valid
148.0ms	1140×	body	128	invalid
120.0ms	364×	body	512	valid
42.0ms	191×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% 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

prune3.0ms (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

36.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	36.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	36.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize12.0ms (0.2%)

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))
✓	1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series117.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

49.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
32.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite76.0ms (1.2%)

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

Calls

4 calls:

73.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
73.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
73.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
73.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
432×	`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

prune159.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	222	10	232
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	223	11	234

Error

5.2b

Counts

234 → 11

Alt Table

Status	Error	Program
	46.2b	(.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))) a))
	56.1b	(.f64 (/.f64 1 (sqrt.f64 (.f64 a 2))) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (sqrt.f64 (*.f64 a 2))))
▶	36.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	42.7b	(-.f64 (/.f64 c b) (/.f64 b a))
	40.2b	(/.f64 (neg.f64 c) b)
	48.4b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	56.7b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	48.5b	(.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))
	37.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) 3)) (*.f64 2 a))
	42.5b	(/.f64 (neg.f64 b) a)
	48.8b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))

Compiler

Compiled 6192 to 3606 computations (41.8% saved)

localize9.0ms (0.1%)

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))
✓	1.3b	(fma.f64 b b (.f64 a (.f64 c -4)))
✓	1.7b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
✓	23.4b	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))

series119.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

51.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
33.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
26.0ms	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))
9.0ms	(fma.f64 b b (.f64 a (.f64 c -4)))

rewrite70.0ms (1.1%)

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

Calls

4 calls:

66.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
66.0ms	(fma.f64 b b (.f64 a (.f64 c -4)))
66.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
66.0ms	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
432×	`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

prune156.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	226	6	232
Fresh	7	3	10
Picked	0	1	1
Done	0	0	0
Total	233	10	243

Error

5.2b

Counts

243 → 10

Alt Table

Status	Error	Program
✓	36.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	42.7b	(-.f64 (/.f64 c b) (/.f64 b a))
▶	31.9b	(/.f64 1 (/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2)))
	42.5b	(/.f64 (neg.f64 b) a)
	40.2b	(/.f64 (neg.f64 c) b)
	42.6b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	33.9b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))
	56.7b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	47.5b	(.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 1/2 a))
	48.7b	(/.f64 (/.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2) (sqrt.f64 a)) (sqrt.f64 a))

Compiler

Compiled 5850 to 3643 computations (37.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2))
✓	0.2b	(/.f64 1 (/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2)))
✓	1.0b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
✓	12.8b	(sqrt.f64 (.f64 a (.f64 c -4)))

series436.0ms (6.6%)

Counts

4 → 36

Calls

4 calls:

207.0ms	(/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2))
132.0ms	(/.f64 1 (/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2)))
85.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
12.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite79.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

593×	`prod-diff_binary64`
165×	`egg-rr`
158×	`add-sqr-sqrt_binary64`
149×	`add-cbrt-cube_binary64`
149×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	69
1	324	66
2	4218	66

Stop Event

1×	node limit

Counts

4 → 165

Calls

4 calls:

75.0ms	(/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2))
75.0ms	(/.f64 1 (/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2)))
75.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
75.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

585×	`associate-/l*_binary64`
560×	`associate-/r*_binary64`
397×	`fma-def_binary64`
218×	`cancel-sign-sub-inv_binary64`
212×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1518
1	450	1376
2	1509	1333

Stop Event

1×	node limit

Counts

201 → 237

prune177.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	235	2	237
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	237	10	247

Error

2.9b

Counts

247 → 10

Alt Table

Status	Error	Program
	47.5b	(.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 1/2 a))
	47.7b	(/.f64 1 (/.f64 a (.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b) 1/2)))
✓	36.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	42.7b	(-.f64 (/.f64 c b) (/.f64 b a))
✓	31.9b	(/.f64 1 (/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2)))
	42.5b	(/.f64 (neg.f64 b) a)
▶	40.2b	(/.f64 (neg.f64 c) b)
	42.6b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	48.7b	(/.f64 (/.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2) (sqrt.f64 a)) (sqrt.f64 a))
	44.3b	(/.f64 1 (fma.f64 4 (/.f64 a (/.f64 c (/.f64 b (*.f64 a -4)))) (/.f64 a b)))

Compiler

Compiled 6221 to 4216 computations (32.2% saved)

localize3.0ms (0%)

prune7.0ms (0.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	2	2
Total	10	10

Error

2.9b

Counts

10 → 10

Alt Table

Status	Error	Program
	47.5b	(.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 1/2 a))
	47.7b	(/.f64 1 (/.f64 a (.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b) 1/2)))
✓	36.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	42.7b	(-.f64 (/.f64 c b) (/.f64 b a))
✓	31.9b	(/.f64 1 (/.f64 a (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2)))
	42.5b	(/.f64 (neg.f64 b) a)
✓	40.2b	(/.f64 (neg.f64 c) b)
	42.6b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	48.7b	(/.f64 (/.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) 1/2) (sqrt.f64 a)) (sqrt.f64 a))
	44.3b	(/.f64 1 (fma.f64 4 (/.f64 a (/.f64 c (/.f64 b (*.f64 a -4)))) (/.f64 a b)))

Compiler

Compiled 161 to 111 computations (31.1% saved)

regimes1.9s (28.4%)

Accuracy

Total 7.6b remaining (73%)

Threshold costs 0b (0%)

Counts

137 → 3

Compiler

Compiled 11184 to 7974 computations (28.7% saved)

bsearch89.0ms (1.3%)

Steps

Iters	Range		Point
9	6.967160121756309e-24	9.911213757936085e-18	4.287267979175193e-23
8	-4.256315156865985e+122	-2.602874292754627e+114	-3.547150473588976e+120

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`*-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	54
1	46	52
2	65	52
3	80	52
4	87	52
5	90	52
6	91	52

Stop Event

1×

saturated

end126.0ms (1.9%)

Compiler: Compiled 237 to 159 computations (32.9% saved)

Details

analyze645.0ms (9.8%)

sample2.3s (34.4%)

simplify29.0ms (0.4%)

prune3.0ms (0.1%)

localize12.0ms (0.2%)

series117.0ms (1.8%)

rewrite76.0ms (1.2%)

simplify44.0ms (0.7%)

prune159.0ms (2.4%)

localize9.0ms (0.1%)

series119.0ms (1.8%)

rewrite70.0ms (1.1%)

simplify45.0ms (0.7%)

prune156.0ms (2.4%)

localize10.0ms (0.1%)

series436.0ms (6.6%)

rewrite79.0ms (1.2%)

simplify38.0ms (0.6%)

prune177.0ms (2.7%)

localize3.0ms (0%)

prune7.0ms (0.1%)

regimes1.9s (28.4%)

bsearch89.0ms (1.3%)

simplify6.0ms (0.1%)

end126.0ms (1.9%)

Profiling