Metrics for Linear.Quaternion:$ccos from linear-1.19.1.3

analyze19.0ms (0.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 10 to 7 computations (30% saved)

sample2.9s (80.6%)

Results

913.0ms	1038×	body	1024	valid
654.0ms	2557×	body	256	valid
484.0ms	2534×	body	256	infinite
390.0ms	1051×	body	1024	infinite
189.0ms	541×	body	512	valid
179.0ms	532×	body	512	infinite
2.0ms	3×	body	2048	valid

Bogosity

preprocess201.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

996×	`fma-neg`
956×	`div-sub`
774×	`sub-neg`
718×	`times-frac`
696×	`fma-def`

Problems

256×

No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	218
1	68	218
2	175	218
3	588	218
4	2825	218
5	6601	218

Stop Event

1×	node limit

Calls

Call 1

Inputs
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
(*.f64 (sin.f64 (neg.f64 x)) (/.f64 (sinh.f64 y) y))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 (neg.f64 y)) (neg.f64 y)))
(neg.f64 (*.f64 (sin.f64 (neg.f64 x)) (/.f64 (sinh.f64 y) y)))
(neg.f64 (*.f64 (sin.f64 x) (/.f64 (sinh.f64 (neg.f64 y)) (neg.f64 y))))
(*.f64 (sin.f64 y) (/.f64 (sinh.f64 x) x))

Outputs
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
(*.f64 (sin.f64 (neg.f64 x)) (/.f64 (sinh.f64 y) y))
(*.f64 (/.f64 (sinh.f64 y) y) (neg.f64 (sin.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) (neg.f64 y))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) (neg.f64 y)))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 (neg.f64 y)) (neg.f64 y)))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
(neg.f64 (*.f64 (sin.f64 (neg.f64 x)) (/.f64 (sinh.f64 y) y)))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
(neg.f64 (*.f64 (sin.f64 x) (/.f64 (sinh.f64 (neg.f64 y)) (neg.f64 y))))
(*.f64 (/.f64 (sinh.f64 y) y) (neg.f64 (sin.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (sinh.f64 y)) (neg.f64 y))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) (neg.f64 y)))
(*.f64 (sin.f64 y) (/.f64 (sinh.f64 x) x))
(*.f64 (sinh.f64 x) (/.f64 (sin.f64 y) x))

Symmetry

(abs y)

(negabs x)

Compiler

Compiled 29 to 13 computations (55.2% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
▶	100.0%	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize78.0ms (2.2%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(sinh.f64 y)

Compiler

Compiled 20 to 7 computations (65% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(sinh.f64 y)
1.0ms	y	@	-inf	(sinh.f64 y)
0.0ms	y	@	0	(sinh.f64 y)

rewrite83.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

496×	`associate-r`
392×	`associate-l`
244×	`unpow-prod-down`
210×	`cbrt-prod`
208×	`log-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	49	8
2	551	8

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(sinh.f64 y)

Outputs
-8
-4
-2
-1
-1/2
0
1/9
1/8
1/6
1/4
1/3
1/2
2/3
1
4/3
3/2
2
5/2
3
4
5
6
8
9
16

simplify88.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2008×	`fma-def`
1248×	`unswap-sqr`
1240×	`distribute-rgt-neg-in`
1140×	`distribute-lft-neg-in`
614×	`neg-mul-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	403
1	85	399
2	165	375
3	384	375
4	710	375
5	1539	375
6	2368	375
7	3614	375
8	4613	375
9	7257	375

Stop Event

1×	node limit

Counts

37 → 43

Calls

Call 1

Inputs
y
(+.f64 y (*.f64 1/6 (pow.f64 y 3)))
(+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 1/6 (pow.f64 y 3))))
(+.f64 y (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (*.f64 1/6 (pow.f64 y 3)))))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
-8
-4
-2
-1
-1/2
0
1/9
1/8
1/6
1/4
1/3
1/2
2/3
1
4/3
3/2
2
5/2
3
4
5
6
8
9
16

Outputs
y
(+.f64 y (*.f64 1/6 (pow.f64 y 3)))
(fma.f64 1/6 (pow.f64 y 3) y)
(+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 1/6 (pow.f64 y 3))))
(+.f64 y (fma.f64 1/120 (pow.f64 y 5) (*.f64 1/6 (pow.f64 y 3))))
(+.f64 y (fma.f64 1/6 (pow.f64 y 3) (*.f64 1/120 (pow.f64 y 5))))
(fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/6 (pow.f64 y 3) y))
(fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y))
(+.f64 y (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (*.f64 1/6 (pow.f64 y 3)))))
(+.f64 y (fma.f64 1/5040 (pow.f64 y 7) (fma.f64 1/120 (pow.f64 y 5) (*.f64 1/6 (pow.f64 y 3)))))
(+.f64 y (fma.f64 1/5040 (pow.f64 y 7) (fma.f64 1/6 (pow.f64 y 3) (*.f64 1/120 (pow.f64 y 5)))))
(fma.f64 1/5040 (pow.f64 y 7) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/6 (pow.f64 y 3) y)))
(fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) y)))
(fma.f64 1/120 (pow.f64 y 5) (fma.f64 1/5040 (pow.f64 y 7) (fma.f64 1/6 (pow.f64 y 3) y)))
(fma.f64 1/6 (pow.f64 y 3) (fma.f64 1/5040 (pow.f64 y 7) (fma.f64 1/120 (pow.f64 y 5) y)))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (exp.f64 (neg.f64 y))))
(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (exp.f64 (neg.f64 y))))
(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (exp.f64 (neg.f64 y))))
(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (exp.f64 (neg.f64 y))))
(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (exp.f64 (neg.f64 y))))
(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (exp.f64 (neg.f64 y))))
(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (exp.f64 (neg.f64 y))))
(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
(*.f64 1/2 (-.f64 (exp.f64 y) (/.f64 1 (exp.f64 y))))
(*.f64 1/2 (-.f64 (exp.f64 y) (exp.f64 (neg.f64 y))))
(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
-8
-4
-2
-1
-1/2
0
1/9
1/8
1/6
1/4
1/3
1/2
2/3
1
4/3
3/2
2
5/2
3
4
5
6
8
9
16

eval14.0ms (0.4%)

Compiler: Compiled 457 to 271 computations (40.7% saved)

prune7.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	2	44

Accuracy

100.0%

Counts

44 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
▶	57.9%	(*.f64 (sin.f64 x) (/.f64 y y))
✓	100.0%	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
▶	57.9%	(*.f64 (sin.f64 x) (/.f64 y y))

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize52.0ms (1.4%)

Compiler: Compiled 16 to 6 computations (62.5% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Accuracy

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
✓	57.9%	(*.f64 (sin.f64 x) (/.f64 y y))

Compiler

Compiled 32 to 19 computations (40.6% saved)

regimes18.0ms (0.5%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 (sin.f64 x) (/.f64 y y))
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))

Outputs
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))

Calls

5 calls:

6.0ms	(sin.f64 x)
3.0ms	x
3.0ms	y
3.0ms	(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
2.0ms	(/.f64 (sinh.f64 y) y)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))`
100.0%	1	`(sin.f64 x)`
100.0%	1	`(/.f64 (sinh.f64 y) y)`

Compiler

Compiled 40 to 25 computations (37.5% saved)

regimes10.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 (sin.f64 x) (/.f64 y y))

Outputs
(*.f64 (sin.f64 x) (/.f64 y y))

Calls

3 calls:

4.0ms	(sin.f64 x)
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
57.9%	1	`x`
57.9%	1	`y`
57.9%	1	`(sin.f64 x)`

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	16	56

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
(*.f64 (sin.f64 x) (/.f64 y y))

Outputs
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) y))
(*.f64 (sin.f64 x) (/.f64 y y))

Compiler

Compiled 17 to 11 computations (35.3% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess114.0ms (3.2%)

Remove

(negabs x)

(abs y)

Compiler

Compiled 84 to 52 computations (38.1% saved)

analyze19.0ms (0.5%)

sample2.9s (80.6%)

preprocess201.0ms (5.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize78.0ms (2.2%)

series2.0ms (0.1%)

rewrite83.0ms (2.3%)

simplify88.0ms (2.5%)

eval14.0ms (0.4%)

prune7.0ms (0.2%)

localize52.0ms (1.4%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes18.0ms (0.5%)

regimes10.0ms (0.3%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess114.0ms (3.2%)

Profiling