Details

analyze1.6s (17.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.7s (18.8%)

Results

1.2s	8256×	body	128	valid
481.0ms	3193×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

preprocess57.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

545×	`associate-/l*_binary64`
326×	`fma-def_binary64`
308×	`associate-/r*_binary64`
295×	`distribute-rgt-in_binary64`
248×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	231
1	171	231
2	370	231
3	674	231
4	1021	231
5	1421	231
6	1800	231
7	2804	231
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort x y)

(sort t a)

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1034×	`fma-def_binary64`
336×	`fma-neg_binary64`
138×	`distribute-rgt-in_binary64`
131×	`cancel-sign-sub-inv_binary64`
126×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	26	21
2	56	21
3	95	21
4	143	21
5	199	21
6	267	21
7	343	21
8	603	21
9	1383	21
10	2682	21
11	3425	21
12	3539	21
13	3669	21
14	3749	21
15	3749	21

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

24.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	27.3b	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
▶	26.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 109 to 63 computations (42.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	3.9b	(.f64 (.f64 x y) z)
✓	10.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
✓	28.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series206.0ms (2.3%)

Counts

4 → 136

Calls

42 calls:

15.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))	x	-inf
15.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))	x	0
14.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))	y	-inf
14.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))	y	inf
14.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))	y	0

rewrite103.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`prod-diff_binary64`
256×	`egg-rr`
145×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	288	50
2	4022	50

Stop Event

1×	node limit

Counts

4 → 256

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-def_binary64`
330×	`associate-/r/_binary64`
224×	`times-frac_binary64`
205×	`associate-r_binary64`
140×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	2730
1	574	2726
2	2727	2703

Stop Event

1×	node limit

Counts

392 → 312

prune217.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	306	6	312
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	306	8	314

Error

2.2b

Counts

314 → 8

Alt Table

Status	Error	Program
	27.3b	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
✓	26.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	35.6b	(*.f64 y (neg.f64 x))
	34.5b	(*.f64 y x)
	27.9b	(.f64 y (.f64 z (.f64 x (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 a t)))))))
	28.1b	(.f64 (/.f64 x (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (/.f64 (.f64 z y) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
▶	26.6b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
	34.2b	(/.f64 (.f64 (.f64 x y) z) (fma.f64 (/.f64 t (/.f64 z a)) -1/2 z))

Compiler

Compiled 9314 to 2771 computations (70.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	1.8b	(/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
✓	9.8b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)
	28.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series332.0ms (3.7%)

Counts

2 → 88

Calls

30 calls:

26.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) z)	z	0
18.0ms	(/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))	x	-inf
17.0ms	(/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))	x	0
14.0ms	(/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))	y	-inf
14.0ms	(/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))	y	0

rewrite65.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`prod-diff_binary64`
145×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`
136×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	288	39
2	4015	39

Stop Event

1×	node limit

Counts

2 → 70

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-def_binary64`
417×	`times-frac_binary64`
232×	`associate-/r*_binary64`
231×	`associate-r_binary64`
215×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	3231
1	671	3217
2	3642	3203

Stop Event

1×	node limit

Counts

158 → 121

prune276.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	340	4	344
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	342	10	352

Error

2.1b

Counts

352 → 10

Alt Table

Status	Error	Program
	41.9b	(*.f64 (neg.f64 (/.f64 x (/.f64 z y))) z)
✓	26.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	34.2b	(/.f64 (.f64 (.f64 x y) z) (fma.f64 (/.f64 t (/.f64 z a)) -1/2 z))
	34.8b	(.f64 (/.f64 (.f64 x y) (fma.f64 (/.f64 t (/.f64 z a)) -1/2 z)) z)
▶	27.3b	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	35.6b	(*.f64 y (neg.f64 x))
	34.5b	(*.f64 y x)
	27.8b	(.f64 (.f64 x (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) y))) z)
	27.9b	(.f64 y (.f64 z (.f64 x (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 a t)))))))
	35.6b	(.f64 (/.f64 (.f64 x y) (-.f64 (*.f64 1/2 (/.f64 t (/.f64 z a))) z)) z)

Compiler

Compiled 10569 to 3708 computations (64.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	1.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	9.3b	(/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))
	28.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series266.0ms (2.9%)

Counts

2 → 76

Calls

27 calls:

16.0ms	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))	x	-inf
16.0ms	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))	y	0
16.0ms	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))	x	0
15.0ms	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))	y	-inf
14.0ms	(/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))	y	inf

rewrite69.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`prod-diff_binary64`
145×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`
136×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	288	39
2	4011	39

Stop Event

1×	node limit

Counts

2 → 69

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

831×	`fma-def_binary64`
354×	`times-frac_binary64`
246×	`associate-r_binary64`
223×	`associate-/r*_binary64`
198×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2780
1	713	2761
2	3592	2753

Stop Event

1×	node limit

Counts

145 → 119

prune262.0ms (2.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	339	3	342
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	341	11	352

Error

2.1b

Counts

352 → 11

Alt Table

Status	Error	Program
	41.9b	(*.f64 (neg.f64 (/.f64 x (/.f64 z y))) z)
✓	26.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	27.9b	(.f64 y (.f64 z (.f64 x (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 a t)))))))
	36.2b	(.f64 x (/.f64 (.f64 y z) (fma.f64 (/.f64 t (/.f64 z a)) -1/2 z)))
	34.2b	(/.f64 (.f64 (.f64 x y) z) (fma.f64 (/.f64 t (/.f64 z a)) -1/2 z))
▶	25.0b	(/.f64 (.f64 y x) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	34.8b	(.f64 (/.f64 (.f64 x y) (fma.f64 (/.f64 t (/.f64 z a)) -1/2 z)) z)
✓	27.3b	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	35.6b	(*.f64 y (neg.f64 x))
	27.8b	(.f64 (.f64 x (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) y))) z)
	34.4b	(.f64 x (/.f64 (.f64 y z) (-.f64 (*.f64 1/2 (/.f64 t (/.f64 z a))) z)))

Compiler

Compiled 10441 to 3652 computations (65% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) z)
	1.6b	(-.f64 (.f64 z z) (.f64 t a))
✓	2.1b	(/.f64 (.f64 y x) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))
	28.1b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series203.0ms (2.3%)

Counts

2 → 64

Calls

24 calls:

16.0ms	(/.f64 (.f64 y x) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))	x	-inf
16.0ms	(/.f64 (.f64 y x) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))	y	-inf
15.0ms	(/.f64 (.f64 y x) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))	x	0
15.0ms	(/.f64 (.f64 y x) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))	a	inf
14.0ms	(/.f64 (.f64 y x) (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a))) z))	t	inf

rewrite69.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
140×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	294	36
2	4287	36

Stop Event

1×	node limit

Counts

2 → 88

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-def_binary64`
329×	`associate-/r/_binary64`
225×	`times-frac_binary64`
205×	`associate-r_binary64`
138×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	2203
1	567	2193
2	2714	2166

Stop Event

1×	node limit

Counts

152 → 135

prune261.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	356	2	358
Fresh	4	4	8
Picked	1	0	1
Done	0	2	2
Total	361	8	369

Error

2.1b

Counts

369 → 8

Alt Table

Status	Error	Program
	30.1b	(/.f64 (.f64 y x) (fma.f64 (/.f64 a (.f64 (/.f64 z t) z)) -1/2 1))
✓	27.3b	(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
	27.9b	(.f64 y (.f64 z (.f64 x (sqrt.f64 (/.f64 1 (-.f64 (.f64 z z) (*.f64 a t)))))))
	36.2b	(.f64 x (/.f64 (.f64 y z) (fma.f64 (/.f64 t (/.f64 z a)) -1/2 z)))
	31.4b	(/.f64 (.f64 y x) (fma.f64 1/2 (/.f64 a (.f64 (/.f64 z t) z)) -1))
✓	26.0b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
	27.8b	(.f64 (.f64 x (/.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))) y))) z)
	34.4b	(.f64 x (/.f64 (.f64 y z) (-.f64 (*.f64 1/2 (/.f64 t (/.f64 z a))) z)))

Compiler

Compiled 10304 to 3262 computations (68.3% saved)

regimes2.7s (30.4%)

Accuracy

Total 4.3b remaining (56.1%)

Threshold costs 0b (0%)

Counts

114 → 3

Compiler

Compiled 17231 to 11410 computations (33.8% saved)

bsearch94.0ms (1%)

Algorithm

2×	binary-search

Calls

2 calls:

49.0ms	z
42.0ms	z

Steps

Iters	Point		Range
4.861570841540991e-16	∈ [	1.7391235840553186e-19	,	4.961431557437777e-16	]
-4.2219193410772696e+73	∈ [	-2.0950397854341149e+74	,	-2.54757807405747e+73	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	73
1	42	73
2	50	73
3	56	73
4	59	73
5	60	73

Stop Event

1×

saturated

end148.0ms (1.6%)

Stop Event

1×

fuel

Remove

(sort t a)

(sort x y)

Compiler

Compiled 487 to 277 computations (43.1% saved)

Details

analyze1.6s (17.8%)

sample1.7s (18.8%)

preprocess57.0ms (0.6%)

simplify44.0ms (0.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series206.0ms (2.3%)

rewrite103.0ms (1.1%)

simplify66.0ms (0.7%)

prune217.0ms (2.4%)

localize10.0ms (0.1%)

series332.0ms (3.7%)

rewrite65.0ms (0.7%)

simplify72.0ms (0.8%)

prune276.0ms (3.1%)

localize11.0ms (0.1%)

series266.0ms (2.9%)

rewrite69.0ms (0.8%)

simplify69.0ms (0.8%)

prune262.0ms (2.9%)

localize10.0ms (0.1%)

series203.0ms (2.3%)

rewrite69.0ms (0.8%)

simplify54.0ms (0.6%)

prune261.0ms (2.9%)

regimes2.7s (30.4%)

bsearch94.0ms (1%)

simplify4.0ms (0%)

end148.0ms (1.6%)

Profiling