Details

analyze624.0ms (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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample360.0ms (4.9%)

Algorithm

1×

intervals

Results

11.0ms	183×	body	128	valid
9.0ms	25×	body	2048	valid
6.0ms	25×	body	1024	valid
2.0ms	6×	body	4096	valid
2.0ms	33×	body	128	nan
2.0ms	10×	body	512	valid
1.0ms	7×	body	256	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
428×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
205×	`fma-def_binary64`
183×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	54	20
3	115	20
4	179	20
5	291	20
6	417	20
7	528	20
8	602	20
9	854	20
10	1802	20
11	1043	20
12	1027	20
13	1035	20
14	1043	20
15	1043	20
16	1101	20
17	1137	20
18	1139	20
19	1151	20
20	1046	20

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.5b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	19.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series596.0ms (8.1%)

Counts

4 → 96

Calls

4 calls:

302.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
149.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
135.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
61×	`prod-diff_binary64`
60×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 176

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
8.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify307.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
181×	`unswap-sqr_binary64`
169×	`sub-neg_binary64`
135×	`associate-r_binary64`

Counts

272 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	8791
1	779	6792
2	2682	5750
3	4584	5750
4	4974	5750

prune181.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	280	12	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	281	12	293

Error

6.5b

Counts

293 → 12

Alt Table

Status	Error	Program
	40.6b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	44.4b	(*.f64 -1/2 (/.f64 c b_2))
▶	30.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
	53.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a) 3))
	31.1b	(/.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (cbrt.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (/.f64 a (cbrt.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
	36.0b	(/.f64 (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	53.2b	(/.f64 (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b_2 5)) -1/16 (fma.f64 (/.f64 (.f64 c a) b_2) -1/2 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) -1/8))) a)
	41.2b	(/.f64 (*.f64 -2 b_2) a)
	33.1b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)
	33.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (cbrt.f64 a)))
	60.4b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)

Compiler

Compiled 9200 to 2064 computations (77.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	19.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series76.0ms (1%)

Counts

1 → 20

Calls

1 calls:

76.0ms

(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
121×	`*-un-lft-identity_binary64`
121×	`add-sqr-sqrt_binary64`
73×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`

Counts

1 → 134

Calls

1 calls:

11.0ms

(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))))

simplify172.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

858×	`times-frac_binary64`
427×	`associate-/l*_binary64`
377×	`fma-neg_binary64`
298×	`fma-def_binary64`
204×	`associate-/r/_binary64`

Counts

154 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	5683
1	445	5239
2	1427	4890
3	4833	4890
4	5033	4890

prune273.0ms (3.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	364	4	368
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	369	11	380

Error

6.5b

Counts

380 → 11

Alt Table

Status	Error	Program
▶	32.5b	(.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (.f64 a c))))) a))
	36.0b	(/.f64 (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)
	33.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (.f64 a c))))))) (cbrt.f64 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (.f64 a c))))))))) (/.f64 1 (cbrt.f64 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c)))))))))
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	44.4b	(*.f64 -1/2 (/.f64 c b_2))
✓	30.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
	41.3b	(/.f64 1 (/.f64 a (*.f64 b_2 -2)))
	36.2b	(/.f64 (/.f64 (.f64 a c) a) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
	41.2b	(/.f64 (*.f64 -2 b_2) a)
	33.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (cbrt.f64 a)))
	60.4b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)

Compiler

Compiled 12267 to 3071 computations (75% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))) a)
✓	0.7b	(-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c)))))
✓	14.3b	(sqrt.f64 (neg.f64 (*.f64 a c)))

series652.0ms (8.8%)

Counts

4 → 42

Calls

4 calls:

375.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))) a)
151.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c)))))
108.0ms	(hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))
17.0ms	(sqrt.f64 (neg.f64 (*.f64 a c)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
50×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
18×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

7.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))) a)
5.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c)))))
2.0ms	(sqrt.f64 (neg.f64 (*.f64 a c)))
0.0ms	(hypot.f64 b_2 (sqrt.f64 (neg.f64 (*.f64 a c))))

simplify153.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
389×	`fma-neg_binary64`
314×	`div-sub_binary64`
285×	`cancel-sign-sub-inv_binary64`
176×	`sub-neg_binary64`

Counts

175 → 257

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	285	5362
1	667	4289
2	2182	3828
3	4432	3824
4	4922	3824

prune199.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	254	3	257
Fresh	6	3	9
Picked	0	1	1
Done	0	1	1
Total	260	8	268

Error

0.1b

Counts

268 → 8

Alt Table

Status	Error	Program
	43.8b	(.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 c))))) a))
✓	32.5b	(.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (.f64 a c))))) a))
	44.4b	(*.f64 -1/2 (/.f64 c b_2))
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	54.0b	(.f64 1 (/.f64 (+.f64 (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 (neg.f64 (.f64 c a)) 3) (pow.f64 b_2 5)) (/.f64 (.f64 -1/2 (.f64 c a)) b_2))) (/.f64 -5/128 (/.f64 (pow.f64 b_2 7) (pow.f64 (neg.f64 (.f64 c a)) 4)))) a))
✓	30.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
▶	36.2b	(/.f64 (/.f64 (.f64 a c) a) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
	46.6b	(.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (.f64 (sqrt.f64 (neg.f64 a)) (sqrt.f64 c)))) a))

Compiler

Compiled 7706 to 2271 computations (70.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.4b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	15.2b	(/.f64 (*.f64 a c) a)
	19.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series56.0ms (0.8%)

Counts

2 → 44

Calls

2 calls:

53.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
2.0ms	(/.f64 (*.f64 a c) a)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`fma-def_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

9.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.0ms	(/.f64 (*.f64 a c) a)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

484×	`associate-/r*_binary64`
399×	`associate-l_binary64`
380×	`fma-neg_binary64`
296×	`associate-*l/_binary64`
284×	`fma-def_binary64`

Counts

94 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1367
1	387	1179
2	1366	1103
3	4741	1103
4	4945	1103

prune86.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	174	8	182

Error

0.1b

Counts

182 → 8

Alt Table

Status	Error	Program
	33.7b	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
	44.4b	(*.f64 -1/2 (/.f64 c b_2))
	43.8b	(.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 c))))) a))
✓	32.5b	(.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (.f64 a c))))) a))
	41.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
✓	30.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
✓	36.2b	(/.f64 (/.f64 (.f64 a c) a) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
	46.6b	(.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (.f64 (sqrt.f64 (neg.f64 a)) (sqrt.f64 c)))) a))

Compiler

Compiled 4347 to 1193 computations (72.6% saved)

regimes1.6s (21.1%)

Accuracy

Total 6.5b remaining (98.7%)

Threshold costs 0b (0%)

Counts

130 → 4

Compiler

Compiled 10797 to 6285 computations (41.8% saved)

bsearch83.0ms (1.1%)

Steps

Iters	Range	Point
6	1.2801692910942717e+92	8.413209116405939e+92	8.089389794080142e+92
8	2.848439522607429e-308	7.326547088866894e-306	3.794720303511745e-306
4	-2.4639643721163906e+168	-3.1329246665015342e+147	-6.619515284789695e+148

Iters

Range

Point

1.2801692910942717e+92

8.413209116405939e+92

8.089389794080142e+92

2.848439522607429e-308

7.326547088866894e-306

3.794720303511745e-306

-2.4639643721163906e+168

-3.1329246665015342e+147

-6.619515284789695e+148

Compiler

Compiled 4 to 3 computations (25% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-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	30	77
1	46	75
2	61	75
3	73	75
4	81	75
5	85	75
6	86	75
7	85	75

end1.0ms (0%)

Compiler: Compiled 53 to 28 computations (47.2% saved)

sample1.7s (22.9%)

Algorithm

1×

intervals

Results

369.0ms	5220×	body	128	valid
329.0ms	1118×	body	2048	valid
227.0ms	395×	body	4096	valid
169.0ms	735×	body	1024	valid
59.0ms	347×	body	512	valid
43.0ms	787×	body	128	nan
21.0ms	185×	body	256	valid
17.0ms	271×	body	128	invalid

Compiler

Compiled 201 to 128 computations (36.3% saved)

Details

analyze624.0ms (8.4%)

sample360.0ms (4.9%)

simplify85.0ms (1.2%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series596.0ms (8.1%)

rewrite44.0ms (0.6%)

simplify307.0ms (4.2%)

prune181.0ms (2.4%)

localize10.0ms (0.1%)

series76.0ms (1%)

rewrite32.0ms (0.4%)

simplify172.0ms (2.3%)

prune273.0ms (3.7%)

localize11.0ms (0.1%)

series652.0ms (8.8%)

rewrite24.0ms (0.3%)

simplify153.0ms (2.1%)

prune199.0ms (2.7%)

localize10.0ms (0.1%)

series56.0ms (0.8%)

rewrite14.0ms (0.2%)

simplify66.0ms (0.9%)

prune86.0ms (1.2%)

regimes1.6s (21.1%)

bsearch83.0ms (1.1%)

simplify13.0ms (0.2%)

end1.0ms (0%)

sample1.7s (22.9%)

Profiling