Details

analyze673.0ms (7.7%)

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)

sample2.6s (29.9%)

Results

708.0ms	5331×	body	128	valid
568.0ms	1131×	body	2048	valid
392.0ms	742×	body	1024	valid
261.0ms	437×	body	4096	valid
143.0ms	1108×	body	128	invalid
124.0ms	399×	body	512	valid
48.0ms	216×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify85.0ms (1%)

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

37.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.7b	(/.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)
✓	1.9b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	2.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	24.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series231.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

114.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
58.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
44.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
14.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite137.0ms (1.6%)

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:

13.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.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))

simplify204.0ms (2.3%)

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	7693
1	779	6304
2	2682	5750
3	4584	5750
4	4974	5750

prune166.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	281	11	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	282	11	293

Error

5.2b

Counts

293 → 11

Alt Table

Status	Error	Program
	48.0b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (sqrt.f64 a)) (sqrt.f64 a))
	46.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	39.2b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 c a)))))) a)
	57.1b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
▶	35.5b	(*.f64 -1/2 (/.f64 c b_2))
	46.7b	(/.f64 (*.f64 -2 b_2) a)
	37.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	37.9b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	52.2b	(/.f64 (-.f64 (pow.f64 (neg.f64 b_2) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3)) (.f64 a (fma.f64 b_2 b_2 (fma.f64 b_2 (neg.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (-.f64 (.f64 b_2 b_2) (.f64 c a))))))
	51.9b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	38.7b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)

Compiler

Compiled 9120 to 2034 computations (77.7% saved)

localize3.0ms (0%)

prune10.0ms (0.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	10	10
Picked	1	1
Done	0	0
Total	11	11

Error

5.2b

Counts

11 → 11

Alt Table

Status	Error	Program
	48.0b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (sqrt.f64 a)) (sqrt.f64 a))
	46.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	39.2b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 c a)))))) a)
	57.1b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
✓	35.5b	(*.f64 -1/2 (/.f64 c b_2))
	46.7b	(/.f64 (*.f64 -2 b_2) a)
▶	37.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	37.9b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	52.2b	(/.f64 (-.f64 (pow.f64 (neg.f64 b_2) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3)) (.f64 a (fma.f64 b_2 b_2 (fma.f64 b_2 (neg.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (-.f64 (.f64 b_2 b_2) (.f64 c a))))))
	51.9b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	38.7b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)

Compiler

Compiled 388 to 234 computations (39.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
✓	1.2b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	13.6b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series467.0ms (5.4%)

Counts

3 → 28

Calls

3 calls:

242.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
207.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
18.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
18×	`times-frac_binary64`

Counts

3 → 123

Calls

3 calls:

11.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
6.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
2.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify139.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
451×	`fma-neg_binary64`
296×	`div-sub_binary64`
232×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-in_binary64`

Counts

151 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	4852
1	599	3789
2	1923	3346
3	4316	3342
4	4897	3342

prune92.0ms (1.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	173	10	183

Error

0.2b

Counts

183 → 10

Alt Table

Status	Error	Program
	48.0b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (sqrt.f64 a)) (sqrt.f64 a))
	46.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
✓	37.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	37.9b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	52.2b	(/.f64 (-.f64 (pow.f64 (neg.f64 b_2) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3)) (.f64 a (fma.f64 b_2 b_2 (fma.f64 b_2 (neg.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (-.f64 (.f64 b_2 b_2) (.f64 c a))))))
	46.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	51.8b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
▶	37.6b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2)) a)
	38.7b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
✓	35.5b	(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 5450 to 1314 computations (75.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))
✓	0.2b	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
✓	1.2b	(-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))
✓	16.6b	(cbrt.f64 (neg.f64 (*.f64 c a)))

series2.1s (24.3%)

Counts

4 → 108

Calls

4 calls:

756.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))
469.0ms	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
451.0ms	(cbrt.f64 (neg.f64 (*.f64 c a)))
436.0ms	(sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
38×	`cbrt-prod_binary64`
36×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`

Counts

4 → 157

Calls

4 calls:

10.0ms	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
5.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))
2.0ms	(sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))
1.0ms	(cbrt.f64 (neg.f64 (*.f64 c a)))

simplify217.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

934×	`times-frac_binary64`
615×	`fma-def_binary64`
450×	`fma-neg_binary64`
211×	`associate-l_binary64`
204×	`associate-r_binary64`

Counts

265 → 276

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	369	10035
1	826	7446
2	2167	6243
3	4792	6243
4	4970	6243

prune171.0ms (2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	310	0	310
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	310	10	320

Error

0.2b

Counts

320 → 10

Alt Table

Status	Error	Program
	48.0b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (sqrt.f64 a)) (sqrt.f64 a))
	46.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
✓	37.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	37.9b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	52.2b	(/.f64 (-.f64 (pow.f64 (neg.f64 b_2) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 3)) (.f64 a (fma.f64 b_2 b_2 (fma.f64 b_2 (neg.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (-.f64 (.f64 b_2 b_2) (.f64 c a))))))
	46.5b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	51.8b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
✓	37.6b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2)) a)
	38.7b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
✓	35.5b	(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 11097 to 2952 computations (73.4% saved)

regimes1.1s (12.5%)

Accuracy

Total 10.4b remaining (97.9%)

Threshold costs 0b (0%)

Counts

66 → 3

Compiler

Compiled 5747 to 3245 computations (43.5% saved)

bsearch72.0ms (0.8%)

Steps

Iters	Range		Point
6	1.07416270065108e+33	1.608110291590463e+34	1.5765221083297083e+34
9	-1.2673641327254137e-109	-1.6452565235323379e-115	-4.3712533615696105e-110

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
11×	`*-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	56
1	42	56
2	61	56
3	78	56
4	88	56
5	91	56
6	91	56

end135.0ms (1.6%)

Compiler: Compiled 273 to 168 computations (38.5% saved)

Details

analyze673.0ms (7.7%)

sample2.6s (29.9%)

simplify85.0ms (1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series231.0ms (2.7%)

rewrite137.0ms (1.6%)

simplify204.0ms (2.3%)

prune166.0ms (1.9%)

localize3.0ms (0%)

prune10.0ms (0.1%)

localize10.0ms (0.1%)

series467.0ms (5.4%)

rewrite28.0ms (0.3%)

simplify139.0ms (1.6%)

prune92.0ms (1.1%)

localize12.0ms (0.1%)

series2.1s (24.3%)

rewrite39.0ms (0.4%)

simplify217.0ms (2.5%)

prune171.0ms (2%)

regimes1.1s (12.5%)

bsearch72.0ms (0.8%)

simplify4.0ms (0%)

end135.0ms (1.6%)

Profiling