Details

analyze648.0ms (8.4%)

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 (30.7%)

Results

696.0ms	5341×	body	128	valid
668.0ms	1232×	body	2048	valid
315.0ms	743×	body	1024	valid
268.0ms	416×	body	4096	valid
151.0ms	1158×	body	128	invalid
107.0ms	338×	body	512	valid
43.0ms	186×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify377.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

2009×	`fma-neg_binary64`
1508×	`div-sub_binary64`
1334×	`associate-/l*_binary64`
1156×	`fma-def_binary64`
685×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	64	22
3	132	22
4	198	22
5	325	22
6	552	22
7	918	22
8	1352	22
9	1554	22
10	2359	22
11	3158	22
12	2565	22
13	2653	22
14	3219	22
15	3361	22
16	3461	22
17	3985	22
18	4171	22
19	4439	22
20	4659	22
21	4701	22
22	4757	22
23	4941	22
24	4941	22
25	3365	22
26	3059	22
27	2983	22
28	2985	22
29	2997	22
30	2997	22
31	2997	22
32	2997	22
33	2736	22

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

31.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	32.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	32.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	0.9b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	20.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series176.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

77.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
50.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
39.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
9.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify184.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
338×	`distribute-rgt-in_binary64`
273×	`cancel-sign-sub-inv_binary64`
155×	`associate-l_binary64`
153×	`associate-r_binary64`

Counts

205 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5424
1	673	4468
2	2524	4293
3	4550	4293
4	4991	4293
5	4994	4293
6	4884	4293

prune176.0ms (2.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	220	11	231
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	221	12	233

Error

5.1b

Counts

233 → 12

Alt Table

Status	Error	Program
	36.5b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
	43.6b	(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
	30.6b	(.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
	47.9b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	38.6b	(neg.f64 (/.f64 c b))
	36.3b	(.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) b) (/.f64 1/2 a))
✓	32.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	55.0b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	48.2b	(-.f64 (/.f64 c b) (/.f64 b a))
▶	28.8b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	45.5b	(-.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))))) (.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) a))) (.f64 1/2 (/.f64 b a)))
	32.3b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))

Compiler

Compiled 6419 to 3778 computations (41.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 c (.f64 a -4))
✓	1.0b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	13.5b	(.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
	20.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series54.0ms (0.7%)

Counts

3 → 68

Calls

3 calls:

46.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
4.0ms	(.f64 c (.f64 a -4))
3.0ms	(.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
14×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`

Counts

3 → 78

Calls

3 calls:

8.0ms	(.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
3.0ms	(.f64 c (.f64 a -4))
3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

395×	`fma-neg_binary64`
331×	`associate-l_binary64`
303×	`distribute-rgt-in_binary64`
281×	`associate-r_binary64`
240×	`distribute-rgt-neg-out_binary64`

Counts

146 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2057
1	518	1882
2	2479	1846
3	4280	1846
4	4918	1846

prune146.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	185	11	196

Error

5.1b

Counts

196 → 11

Alt Table

Status	Error	Program
	30.6b	(.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))) b) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
	47.9b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	43.6b	(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
	38.6b	(neg.f64 (/.f64 c b))
	36.3b	(.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) b) (/.f64 1/2 a))
✓	32.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	46.1b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 -2 (.f64 c a)) a) 3)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	48.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.5b	(-.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))))) (.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) a))) (.f64 1/2 (/.f64 b a)))
	32.3b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
▶	25.6b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 6249 to 3985 computations (36.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	1.0b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	20.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series240.0ms (3.1%)

Counts

1 → 20

Calls

1 calls:

240.0ms

(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

5.0ms

(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

769×	`times-frac_binary64`
615×	`associate-/l*_binary64`
357×	`associate-/r*_binary64`
352×	`fma-neg_binary64`
235×	`fma-def_binary64`

Counts

47 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1488
1	366	1333
2	1180	1254
3	4844	1254
4	5078	1254

prune406.0ms (5.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	178	7	185
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	184	12	196

Error

5.1b

Counts

196 → 12

Alt Table

Status	Error	Program
	48.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	25.7b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
	25.8b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) b))
	38.6b	(neg.f64 (/.f64 c b))
	32.0b	(/.f64 (.f64 -2 c) (+.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) b))
	47.9b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
	36.3b	(.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) b) (/.f64 1/2 a))
✓	32.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	25.6b	(.f64 (.f64 -2 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
▶	25.3b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
	32.5b	(/.f64 (.f64 -2 c) (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4))))))))
	36.3b	(/.f64 (.f64 -2 c) (/.f64 (.f64 c (.f64 a -4)) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)))

Compiler

Compiled 4911 to 2982 computations (39.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	0.1b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
✓	14.2b	(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) b)
	20.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series357.0ms (4.6%)

Counts

3 → 108

Calls

3 calls:

217.0ms

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

91.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b)

48.0ms

(sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-prod_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 54

Calls

3 calls:

3.0ms

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

1.0ms

(sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))

0.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b)

simplify166.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
332×	`fma-def_binary64`
205×	`*-commutative_binary64`
174×	`fma-neg_binary64`
136×	`distribute-neg-in_binary64`

Counts

162 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	610	8925
1	2099	8542
2	4978	8534
3	5076	8534

prune460.0ms (6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	408	2	410
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	412	10	422

Error

0.5b

Counts

422 → 10

Alt Table

Status	Error	Program
	48.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	25.7b	(/.f64 -2 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) c))
	25.8b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) b))
	38.6b	(neg.f64 (/.f64 c b))
	50.9b	(/.f64 (.f64 -2 c) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 a)) (log.f64 (/.f64 -1 c))))) 2) b))
	50.2b	(/.f64 (.f64 -2 c) (+.f64 b (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (*.f64 4 c)) (log.f64 (/.f64 -1 a))))) 2)))
✓	32.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	25.6b	(.f64 (.f64 -2 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
✓	25.3b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
	36.3b	(/.f64 (.f64 -2 c) (/.f64 (.f64 c (.f64 a -4)) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))) b)))

Compiler

Compiled 20187 to 13475 computations (33.2% saved)

regimes1.4s (18.5%)

Accuracy

Total 5.8b remaining (88.7%)

Threshold costs 0b (0%)

Counts

149 → 4

Compiler

Compiled 14576 to 10034 computations (31.2% saved)

bsearch117.0ms (1.5%)

Steps

Iters	Range	Point
7	3.4304305144586265e+115	6.939013140447918e+116	4.463908774462876e+115
8	-1.80742604944651e-296	-1.0061779700790181e-299	-2.5674198272216355e-298
6	-6.322179816249959e+81	-4.5698229433821705e+80	-6.211339473848772e+81

Iters

Range

Point

3.4304305144586265e+115

6.939013140447918e+116

4.463908774462876e+115

-1.80742604944651e-296

-1.0061779700790181e-299

-2.5674198272216355e-298

-6.322179816249959e+81

-4.5698229433821705e+80

-6.211339473848772e+81

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-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	31	78
1	45	78
2	56	78
3	63	78
4	66	78
5	66	78

end144.0ms (1.9%)

Compiler: Compiled 301 to 199 computations (33.9% saved)

Details

analyze648.0ms (8.4%)

sample2.4s (30.7%)

simplify377.0ms (4.9%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series176.0ms (2.3%)

rewrite21.0ms (0.3%)

simplify184.0ms (2.4%)

prune176.0ms (2.3%)

localize13.0ms (0.2%)

series54.0ms (0.7%)

rewrite18.0ms (0.2%)

simplify83.0ms (1.1%)

prune146.0ms (1.9%)

localize9.0ms (0.1%)

series240.0ms (3.1%)

rewrite7.0ms (0.1%)

simplify68.0ms (0.9%)

prune406.0ms (5.3%)

localize11.0ms (0.1%)

series357.0ms (4.6%)

rewrite8.0ms (0.1%)

simplify166.0ms (2.2%)

prune460.0ms (6%)

regimes1.4s (18.5%)

bsearch117.0ms (1.5%)

simplify4.0ms (0%)

end144.0ms (1.9%)

Profiling