Details

analyze1.3s (9.7%)

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
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)

sample92.0ms (0.7%)

Algorithm

1×

intervals

Results

22.0ms	171×	body	128	valid
18.0ms	29×	body	2048	valid
13.0ms	24×	body	1024	valid
10.0ms	13×	body	4096	valid
5.0ms	13×	body	512	valid
2.0ms	15×	body	128	nan
2.0ms	6×	body	256	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify165.0ms (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

prune6.0ms (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

33.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	33.9b	(.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)

localize19.0ms (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)
✓	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	23.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series324.0ms (2.4%)

Counts

3 → 60

Calls

3 calls:

141.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
98.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
84.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite27.0ms (0.2%)

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:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
6.0ms	(+.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)))

simplify186.0ms (1.4%)

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

prune280.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	161	8	169
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	161	9	170

Error

6.8b

Counts

170 → 9

Alt Table

Status	Error	Program
	34.1b	(.f64 -1/2 (.f64 (/.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 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 a))))
	34.0b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	41.3b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.3b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	49.3b	(.f64 -1/2 (/.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) (sqrt.f64 a)) (sqrt.f64 a)))
▶	34.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	43.9b	(.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))
	46.5b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
✓	33.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 4728 to 2856 computations (39.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
✓	0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	23.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series568.0ms (4.1%)

Counts

2 → 40

Calls

2 calls:

429.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
139.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

rewrite57.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 133

Calls

2 calls:

16.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
8.0ms	(/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

simplify237.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

712×	`associate-/l*_binary64`
631×	`associate-/r*_binary64`
411×	`fma-def_binary64`
324×	`associate-/r/_binary64`
172×	`cancel-sign-sub-inv_binary64`

Counts

173 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	5780
1	538	5307
2	1750	5032
3	5356	5032

prune473.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	310	4	314
Fresh	4	3	7
Picked	0	1	1
Done	1	0	1
Total	315	8	323

Error

6.7b

Counts

323 → 8

Alt Table

Status	Error	Program
	41.3b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.3b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	34.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	34.3b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))))
	43.9b	(.f64 -1/2 (.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) a) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
▶	33.6b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
	41.2b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
	46.5b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 9658 to 5973 computations (38.2% saved)

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))
✓	0.6b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	13.4b	(sqrt.f64 (.f64 a (.f64 c -4)))

series696.0ms (5.1%)

Counts

3 → 28

Calls

3 calls:

393.0ms	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))
264.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
39.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
12×	`add-cube-cbrt_binary64`
12×	`add-exp-log_binary64`

Counts

3 → 75

Calls

3 calls:

14.0ms	(.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))
6.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
5.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

simplify119.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

783×	`associate-/l*_binary64`
648×	`associate-/r*_binary64`
447×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
234×	`distribute-lft-in_binary64`

Counts

103 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	2558
1	521	2340
2	1584	2281
3	5289	2281

prune258.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	161	9	170

Error

4.3b

Counts

170 → 9

Alt Table

Status	Error	Program
	47.0b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (.f64 c -4)))))))
✓	34.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	41.3b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.3b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
▶	34.3b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))))
	43.9b	(.f64 -1/2 (.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) a) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	33.6b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
	41.2b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
	46.5b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 4664 to 3098 computations (33.6% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (+.f64 b (.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))))
✓	0.3b	(.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))
✓	5.7b	(+.f64 b (.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
	13.4b	(sqrt.f64 (.f64 a (.f64 c -4)))

series883.0ms (6.4%)

Counts

3 → 42

Calls

3 calls:

394.0ms

(/.f64 1 (/.f64 a (+.f64 b (*.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))

274.0ms

(+.f64 b (*.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))

215.0ms

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

rewrite69.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`times-frac_binary64`
72×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`

Counts

3 → 155

Calls

3 calls:

12.0ms

(/.f64 1 (/.f64 a (+.f64 b (*.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))))

10.0ms

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

4.0ms

(+.f64 b (*.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))

simplify312.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

972×	`times-frac_binary64`
502×	`fma-def_binary64`
383×	`fma-neg_binary64`
232×	`cancel-sign-sub-inv_binary64`
131×	`neg-mul-1_binary64`

Counts

197 → 276

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	257	5919
1	616	5344
2	1784	5156
3	4559	5134
4	4979	5134

prune561.0ms (4.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	316	9	325

Error

4.3b

Counts

325 → 9

Alt Table

Status	Error	Program
	47.0b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (.f64 c -4)))))))
✓	34.0b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))
	41.3b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.3b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	34.3b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (.f64 (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (sqrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))))
	43.9b	(.f64 -1/2 (.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) a) (/.f64 1 (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	33.6b	(.f64 -1/2 (.f64 (/.f64 1 a) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
	41.2b	(.f64 -1/2 (/.f64 1 (.f64 1/2 (-.f64 (/.f64 b c) (/.f64 a b)))))
	46.5b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 12345 to 8489 computations (31.2% saved)

regimes3.6s (26.2%)

Accuracy

Total 7.9b remaining (74.9%)

Threshold costs 0b (0%)

Counts

160 → 3

Compiler

Compiled 16712 to 11562 computations (30.8% saved)

bsearch131.0ms (1%)

Steps

Iters	Range		Point
12	2.1782511974788453e+115	6.303904232635134e+154	1.1835654396951589e+120
9	-28500765.1627402	-0.013955724964173901	-0.01419156820443832

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
13×	`+-commutative_binary64`
12×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	64
1	51	64
2	69	64
3	91	64
4	104	64
5	111	64
6	113	64
7	112	64

end1.0ms (0%)

Compiler: Compiled 46 to 31 computations (32.6% saved)

sample3.2s (23.4%)

Algorithm

1×

intervals

Results

986.0ms	1068×	body	2048	valid
627.0ms	5184×	body	128	valid
329.0ms	758×	body	1024	valid
288.0ms	409×	body	4096	valid
136.0ms	393×	body	512	valid
73.0ms	652×	body	128	nan
41.0ms	188×	body	256	valid
39.0ms	359×	body	128	invalid

Compiler

Compiled 241 to 171 computations (29% saved)

Details

analyze1.3s (9.7%)

sample92.0ms (0.7%)

simplify165.0ms (1.2%)

prune6.0ms (0%)

localize19.0ms (0.1%)

series324.0ms (2.4%)

rewrite27.0ms (0.2%)

simplify186.0ms (1.4%)

prune280.0ms (2%)

localize22.0ms (0.2%)

series568.0ms (4.1%)

rewrite57.0ms (0.4%)

simplify237.0ms (1.7%)

prune473.0ms (3.4%)

localize20.0ms (0.1%)

series696.0ms (5.1%)

rewrite34.0ms (0.2%)

simplify119.0ms (0.9%)

prune258.0ms (1.9%)

localize26.0ms (0.2%)

series883.0ms (6.4%)

rewrite69.0ms (0.5%)

simplify312.0ms (2.3%)

prune561.0ms (4.1%)

regimes3.6s (26.2%)

bsearch131.0ms (1%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample3.2s (23.4%)

Profiling