Details

analyze2.0s (16.6%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	93.6%	6.4%	7
0%	93.6%	6.4%	8
0%	91.3%	8.7%	9
0%	86.6%	13.4%	10
0%	85%	15%	11
0%	82.3%	17.7%	12
0%	79.9%	20.1%	13
0%	78.8%	21.2%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample3.1s (26.2%)

Results

858.0ms	5346×	body	128	valid
719.0ms	1163×	body	2048	valid
383.0ms	783×	body	1024	valid
332.0ms	385×	body	8192	exit
306.0ms	418×	body	4096	valid
143.0ms	364×	body	512	valid
129.0ms	905×	body	128	invalid
53.0ms	182×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify145.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

35.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.8b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	1.6b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	24.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series166.0ms (1.4%)

Counts

3 → 60

Calls

3 calls:

72.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
50.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
43.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
5×	`distribute-lft-out_binary64`

Counts

3 → 67

Calls

3 calls:

4.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
2.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify103.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
539×	`associate-/l*_binary64`
458×	`fma-def_binary64`
246×	`fma-neg_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

127 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3311
1	510	3170
2	1534	3008
3	4840	3008
4	4954	3008

prune127.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Error

7.0b

Counts

170 → 10

Alt Table

Status	Error	Program
	35.8b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	55.0b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.8b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	46.5b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	46.9b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
▶	33.9b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	34.3b	(.f64 -1/2 (.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) a)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	46.2b	(.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a) 3)))

Compiler

Compiled 4764 to 2886 computations (39.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	0.1b	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
✓	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	14.7b	(sqrt.f64 (.f64 a (.f64 c -4)))

series730.0ms (6.2%)

Counts

4 → 42

Calls

4 calls:

370.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
198.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
142.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
20.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
99×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
65×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

4 → 164

Calls

4 calls:

6.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
4.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
3.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))

simplify163.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

500×	`associate-*l/_binary64`
496×	`fma-def_binary64`
478×	`fma-neg_binary64`
422×	`associate-/r/_binary64`
308×	`cancel-sign-sub-inv_binary64`

Counts

206 → 291

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	6330
1	644	5816
2	2163	5690
3	4938	5684
4	5187	5684

prune239.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	285	6	291
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	292	9	301

Error

3.6b

Counts

301 → 9

Alt Table

Status	Error	Program
	33.9b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
▶	33.9b	(.f64 -1/2 (/.f64 1 (/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))))
	46.9b	(.f64 -1/2 (/.f64 1 (/.f64 a (.f64 2 b))))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	46.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	34.2b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 a (.f64 c -4)))) (cbrt.f64 (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 (sqrt.f64 (.f64 a (*.f64 c -4))))))))))
	46.5b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	38.6b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))

Compiler

Compiled 9075 to 6009 computations (33.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a))
	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
	14.7b	(sqrt.f64 (.f64 a (.f64 c -4)))

series567.0ms (4.8%)

Counts

2 → 28

Calls

2 calls:

370.0ms	(/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a))
198.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
92×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 125

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a))
4.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)

simplify108.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

802×	`associate-/l*_binary64`
758×	`associate-/r*_binary64`
364×	`associate-/r/_binary64`
345×	`fma-def_binary64`
181×	`associate-/l/_binary64`

Counts

153 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	5134
1	528	4626
2	1764	4570
3	5161	4570

prune230.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	280	10	290

Error

3.6b

Counts

290 → 10

Alt Table

Status	Error	Program
	46.4b	(.f64 -1/2 (/.f64 1 (/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c))))) a))))
	46.5b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
▶	33.9b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
✓	33.9b	(.f64 -1/2 (/.f64 1 (/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))))
	46.9b	(.f64 -1/2 (/.f64 1 (/.f64 a (.f64 2 b))))
	43.4b	(.f64 -1/2 (/.f64 1 (fma.f64 (/.f64 (.f64 a b) (.f64 -4 (.f64 a c))) -2 (*.f64 (/.f64 a b) -1/2))))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	38.6b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))
	34.3b	(.f64 -1/2 (/.f64 1 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (/.f64 a (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))))))))))

Compiler

Compiled 9197 to 6252 computations (32% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (.f64 c a))
✓	0.2b	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
✓	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
✓	14.7b	(sqrt.f64 (.f64 -4 (.f64 c a)))

series621.0ms (5.2%)

Counts

4 → 28

Calls

4 calls:

459.0ms	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
137.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
20.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
5.0ms	(.f64 -4 (.f64 c a))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-exp-log_binary64`
17×	`pow1_binary64`
16×	`associate-l_binary64`

Counts

4 → 95

Calls

4 calls:

7.0ms	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (*.f64 c a))))))
4.0ms	(.f64 -4 (.f64 c a))
3.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
3.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/r*_binary64`
447×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
234×	`distribute-lft-in_binary64`
157×	`associate-r_binary64`

Counts

123 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	2765
1	587	2488
2	1863	2447
3	4942	2447
4	4995	2447
5	4936	2447

prune445.0ms (3.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	167	10	177

Error

3.6b

Counts

177 → 10

Alt Table

Status	Error	Program
	46.4b	(.f64 -1/2 (/.f64 1 (/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c))))) a))))
	46.5b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
✓	33.9b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))))
✓	33.9b	(.f64 -1/2 (/.f64 1 (/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))))
	46.9b	(.f64 -1/2 (.f64 (/.f64 1 a) (*.f64 2 b)))
	43.4b	(.f64 -1/2 (/.f64 1 (fma.f64 (/.f64 (.f64 a b) (.f64 -4 (.f64 a c))) -2 (*.f64 (/.f64 a b) -1/2))))
	38.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	38.6b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))
	34.3b	(.f64 -1/2 (/.f64 1 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (/.f64 a (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 a c)))))))))))

Compiler

Compiled 4654 to 2971 computations (36.2% saved)

regimes2.6s (22.3%)

Accuracy

Total 7.1b remaining (70.4%)

Threshold costs 0b (0%)

Counts

166 → 3

Compiler

Compiled 17016 to 12118 computations (28.8% saved)

bsearch77.0ms (0.6%)

Steps

Iters	Range		Point
5	4.4348519765763406e+80	8.989866643635864e+80	8.609944247882453e+80
9	-5.0836839403424875e-76	-4.330419631663822e-83	-2.177667226285847e-76

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	54
1	34	54
2	34	54

end158.0ms (1.3%)

Compiler: Compiled 296 to 214 computations (27.7% saved)

Details

analyze2.0s (16.6%)

sample3.1s (26.2%)

simplify145.0ms (1.2%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series166.0ms (1.4%)

rewrite13.0ms (0.1%)

simplify103.0ms (0.9%)

prune127.0ms (1.1%)

localize11.0ms (0.1%)

series730.0ms (6.2%)

rewrite31.0ms (0.3%)

simplify163.0ms (1.4%)

prune239.0ms (2%)

localize11.0ms (0.1%)

series567.0ms (4.8%)

rewrite23.0ms (0.2%)

simplify108.0ms (0.9%)

prune230.0ms (1.9%)

localize10.0ms (0.1%)

series621.0ms (5.2%)

rewrite22.0ms (0.2%)

simplify112.0ms (0.9%)

prune445.0ms (3.8%)

regimes2.6s (22.3%)

bsearch77.0ms (0.6%)

simplify3.0ms (0%)

end158.0ms (1.3%)

Profiling