Details

analyze666.0ms (6.3%)

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)

sample2.4s (22.4%)

Results

753.0ms	5359×	body	128	valid
646.0ms	1185×	body	2048	valid
294.0ms	684×	body	1024	valid
289.0ms	444×	body	4096	valid
140.0ms	1044×	body	128	invalid
124.0ms	378×	body	512	valid
56.0ms	206×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify30.0ms (0.3%)

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

prune4.0ms (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

34.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
▶	34.5b	(/.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
✓	0.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.2b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series127.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

58.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite76.0ms (0.7%)

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:

72.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
72.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
72.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
72.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify48.0ms (0.5%)

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

prune170.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	221	11	232
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	222	12	234

Error

6.3b

Counts

234 → 12

Alt Table

Status	Error	Program
	47.0b	(/.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))
	47.1b	(/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (.f64 2 a))
	36.5b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
▶	34.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	47.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	47.0b	(/.f64 (neg.f64 b) a)
	45.3b	(/.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a))) (*.f64 2 a))
	46.6b	(.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)))
	42.9b	(/.f64 (.f64 (/.f64 -2 b) (.f64 c a)) (*.f64 2 a))
	45.3b	(/.f64 (-.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) (*.f64 2 a))
	53.9b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	38.5b	(/.f64 (neg.f64 c) b)

Compiler

Compiled 6212 to 3614 computations (41.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
✓	0.8b	(fma.f64 b b (.f64 a (.f64 c -4)))
✓	1.2b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
✓	23.7b	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))

series127.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

56.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
35.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
27.0ms	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))
9.0ms	(fma.f64 b b (.f64 a (.f64 c -4)))

rewrite79.0ms (0.8%)

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:

76.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
76.0ms	(fma.f64 b b (.f64 a (.f64 c -4)))
76.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
76.0ms	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))

simplify48.0ms (0.5%)

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

prune192.0ms (1.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	226	6	232
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	230	14	244

Error

6.3b

Counts

244 → 14

Alt Table

Status	Error	Program
	36.5b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
✓	34.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	47.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	33.4b	(pow.f64 (cbrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)
	47.0b	(/.f64 (neg.f64 b) a)
	44.8b	(/.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))))))
	45.3b	(/.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a))) (*.f64 2 a))
▶	33.0b	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
	53.9b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	47.1b	(/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (.f64 2 a))
	46.3b	(exp.f64 (log.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))))
	42.9b	(/.f64 (.f64 (/.f64 -2 b) (.f64 c a)) (*.f64 2 a))
	38.5b	(/.f64 (neg.f64 c) b)
	47.0b	(.f64 (.f64 -2 b) (/.f64 1/2 a))

Compiler

Compiled 5998 to 3747 computations (37.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))
✓	0.0b	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
✓	0.4b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
✓	14.2b	(sqrt.f64 (.f64 a (.f64 c -4)))

series297.0ms (2.8%)

Counts

4 → 38

Calls

4 calls:

134.0ms	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
82.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
68.0ms	(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))
12.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite177.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

937×	`prod-diff_binary64`
461×	`egg-rr`
143×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	57
1	287	57
2	3914	57

Stop Event

1×	node limit

Counts

4 → 461

Calls

4 calls:

158.0ms	(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))
158.0ms	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
158.0ms	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
158.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

764×	`times-frac_binary64`
415×	`associate-/l*_binary64`
381×	`associate-/r*_binary64`
340×	`fma-def_binary64`
205×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	1403
1	385	1291
2	1238	1256

Stop Event

1×	node limit

Counts

499 → 530

prune552.0ms (5.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	525	5	530
Fresh	6	6	12
Picked	1	0	1
Done	0	1	1
Total	532	12	544

Error

3.9b

Counts

544 → 12

Alt Table

Status	Error	Program
✓	34.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	47.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	33.4b	(pow.f64 (cbrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 3)
	38.5b	(/.f64 (neg.f64 c) b)
	47.1b	(/.f64 (fma.f64 b -2 (.f64 (/.f64 a (/.f64 b (.f64 -4 c))) -1/2)) (*.f64 a 2))
▶	33.1b	(/.f64 (-.f64 (hypot.f64 b (pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)) b) (*.f64 a 2))
	41.6b	(/.f64 (.f64 1/2 (/.f64 a (/.f64 b (.f64 -4 c)))) (*.f64 a 2))
	47.0b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	53.9b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	46.9b	(/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))) b) (*.f64 a 2))
	44.8b	(/.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))))))
	53.4b	(/.f64 (-.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3)))) (*.f64 a 2))

Compiler

Compiled 24751 to 16032 computations (35.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (hypot.f64 b (pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)) b) (*.f64 a 2))
✓	0.4b	(-.f64 (hypot.f64 b (pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)) b)
✓	0.4b	(pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)
✓	15.0b	(pow.f64 (.f64 -4 (.f64 a c)) 1/4)

series1.6s (15.3%)

Counts

4 → 120

Calls

4 calls:

489.0ms	(/.f64 (-.f64 (hypot.f64 b (pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)) b) (*.f64 a 2))
404.0ms	(-.f64 (hypot.f64 b (pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)) b)
362.0ms	(pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)
354.0ms	(pow.f64 (.f64 -4 (.f64 a c)) 1/4)

rewrite175.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

916×	`prod-diff_binary64`
468×	`egg-rr`
161×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	58
1	339	55
2	4456	55

Stop Event

1×	node limit

Counts

4 → 468

Calls

4 calls:

158.0ms	(/.f64 (-.f64 (hypot.f64 b (pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)) b) (*.f64 a 2))
158.0ms	(-.f64 (hypot.f64 b (pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)) b)
158.0ms	(pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)
158.0ms	(pow.f64 (.f64 -4 (.f64 a c)) 1/4)

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

786×	`times-frac_binary64`
421×	`associate-/l*_binary64`
347×	`fma-def_binary64`
187×	`cancel-sign-sub-inv_binary64`
150×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	3516
1	556	3188
2	1632	2901

Stop Event

1×	node limit

Counts

588 → 552

prune525.0ms (5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	549	3	552
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	554	10	564

Error

0.1b

Counts

564 → 10

Alt Table

Status	Error	Program
	45.5b	(/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (.f64 -4 a)) (sqrt.f64 c))) b) (*.f64 a 2))
	53.4b	(/.f64 (fma.f64 1/2 (/.f64 (.f64 -4 (.f64 a c)) b) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 a c))) 4) (pow.f64 b 3)) -1/8)) (.f64 a 2))
	44.8b	(/.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))))))
	38.5b	(/.f64 (neg.f64 c) b)
	47.1b	(/.f64 (fma.f64 b -2 (.f64 (/.f64 a (/.f64 b (.f64 -4 c))) -1/2)) (*.f64 a 2))
✓	33.1b	(/.f64 (-.f64 (hypot.f64 b (pow.f64 (pow.f64 (.f64 -4 (.f64 a c)) 1/4) 2)) b) (*.f64 a 2))
	41.6b	(/.f64 (.f64 1/2 (/.f64 a (/.f64 b (.f64 -4 c)))) (*.f64 a 2))
	45.6b	(/.f64 (-.f64 (hypot.f64 b (pow.f64 (.f64 (pow.f64 (.f64 -4 a) 1/4) (pow.f64 c 1/4)) 2)) b) (*.f64 a 2))
	46.9b	(/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))) b) (*.f64 a 2))
✓	34.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))

Compiler

Compiled 24978 to 16352 computations (34.5% saved)

regimes2.9s (27.4%)

Accuracy

Total 10.2b remaining (98.2%)

Threshold costs 0b (0%)

Counts

192 → 3

Compiler

Compiled 15928 to 11306 computations (29% saved)

bsearch45.0ms (0.4%)

Steps

Iters	Range		Point
3	1.255660612360325e-46	1.5332762383966197e-46	1.4118194020057405e-46
6	-6.70581043318833e+82	-1.3219327474019394e+82	-6.593756766636855e+82

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	62
1	46	62
2	57	62
3	64	62
4	67	62

Stop Event

1×

saturated

end155.0ms (1.5%)

Compiler: Compiled 288 to 200 computations (30.6% saved)

Details

analyze666.0ms (6.3%)

sample2.4s (22.4%)

simplify30.0ms (0.3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series127.0ms (1.2%)

rewrite76.0ms (0.7%)

simplify48.0ms (0.5%)

prune170.0ms (1.6%)

localize11.0ms (0.1%)

series127.0ms (1.2%)

rewrite79.0ms (0.8%)

simplify48.0ms (0.5%)

prune192.0ms (1.8%)

localize10.0ms (0.1%)

series297.0ms (2.8%)

rewrite177.0ms (1.7%)

simplify58.0ms (0.6%)

prune552.0ms (5.2%)

localize13.0ms (0.1%)

series1.6s (15.3%)

rewrite175.0ms (1.7%)

simplify83.0ms (0.8%)

prune525.0ms (5%)

regimes2.9s (27.4%)

bsearch45.0ms (0.4%)

simplify3.0ms (0%)

end155.0ms (1.5%)

Profiling