Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample793.0ms (70.7%)

Results

680.0ms	7220×	body	256	valid
104.0ms	1036×	body	256	infinite

Bogosity

preprocess97.0ms (8.7%)

Algorithm

2×	egg-herbie

Rules

2340×	`fma-def`
234×	`fma-neg`
216×	`distribute-lft-neg-in`
192×	`associate-/l*`
192×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	100
1	39	100
2	65	100
3	103	100
4	185	84
5	296	84
6	645	84
7	1263	84
8	2054	84
9	2713	84
10	2803	84
11	2809	84
12	2809	84
13	2813	84
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2

Call 2

Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 y x) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 z y) 2) (/.f64 x 8))
(-.f64 (/.f64 (*.f64 x z) 2) (/.f64 y 8))

Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(-.f64 (*.f64 x (/.f64 y 2)) (/.f64 z 8))
(fma.f64 x (/.f64 y 2) (*.f64 -1/8 z))
(fma.f64 -1/8 z (/.f64 x (/.f64 2 y)))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (.f64 1/2 y) (.f64 z -1/8))
(fma.f64 x (.f64 y 1/2) (.f64 z -1/8))
(-.f64 (/.f64 (*.f64 y x) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(-.f64 (*.f64 x (/.f64 y 2)) (/.f64 z 8))
(fma.f64 x (/.f64 y 2) (*.f64 -1/8 z))
(fma.f64 -1/8 z (/.f64 x (/.f64 2 y)))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (.f64 1/2 y) (.f64 z -1/8))
(fma.f64 x (.f64 y 1/2) (.f64 z -1/8))
(-.f64 (/.f64 (*.f64 z y) 2) (/.f64 x 8))
(-.f64 (/.f64 z (/.f64 2 y)) (/.f64 x 8))
(-.f64 (*.f64 (/.f64 z 2) y) (/.f64 x 8))
(-.f64 (*.f64 y (/.f64 z 2)) (/.f64 x 8))
(-.f64 (*.f64 z (/.f64 y 2)) (/.f64 x 8))
(fma.f64 y (/.f64 z 2) (*.f64 -1/8 x))
(fma.f64 y (/.f64 z 2) (*.f64 x -1/8))
(fma.f64 y (.f64 1/2 z) (.f64 x -1/8))
(fma.f64 y (.f64 z 1/2) (.f64 x -1/8))
(-.f64 (/.f64 (*.f64 x z) 2) (/.f64 y 8))
(-.f64 (*.f64 (/.f64 x 2) z) (/.f64 y 8))
(-.f64 (*.f64 z (/.f64 x 2)) (/.f64 y 8))
(fma.f64 x (/.f64 z 2) (*.f64 -1/8 y))
(fma.f64 -1/8 y (/.f64 (*.f64 x z) 2))
(fma.f64 x (/.f64 z 2) (*.f64 y -1/8))
(fma.f64 x (.f64 1/2 z) (.f64 y -1/8))
(fma.f64 x (.f64 z 1/2) (.f64 y -1/8))

Symmetry

(sort x y)

Compiler

Compiled 15 to 12 computations (20% saved)

simplify43.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def`
92×	`distribute-lft-neg-in`
86×	`cancel-sign-sub-inv`
68×	`distribute-rgt-in`
68×	`associate-r`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	17	25
2	28	25
3	42	25
4	72	21
5	119	21
6	232	21
7	419	21
8	668	21
9	966	21
10	1079	21
11	1105	21
12	1108	21

Stop Event

1×

saturated

Counts

1 → 11

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(fma.f64 (/.f64 x 2) y (/.f64 (neg.f64 z) 8))
(fma.f64 (/.f64 y 2) x (/.f64 (neg.f64 z) 8))
(fma.f64 x (/.f64 y 2) (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 z -1/8 (/.f64 y (/.f64 2 x)))
(fma.f64 z -1/8 (.f64 1/2 (.f64 x y)))
(fma.f64 z -1/8 (.f64 (.f64 x y) 1/2))
(fma.f64 (.f64 x y) 1/2 (.f64 z -1/8))

eval2.0ms (0.2%)

Compiler: Compiled 96 to 59 computations (38.5% saved)

prune2.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	10	1	11
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	10	2	12

Accurracy

100.0%

Counts

12 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
▶	100.0%	(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Compiler

Compiled 24 to 18 computations (25% saved)

localize34.0ms (3.1%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(/.f64 (*.f64 x y) 2)

Compiler

Compiled 29 to 16 computations (44.8% saved)

series3.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(/.f64 (*.f64 x y) 2)
1.0ms	x	@	inf	(/.f64 (*.f64 x y) 2)
1.0ms	x	@	0	(/.f64 (*.f64 x y) 2)
0.0ms	y	@	inf	(/.f64 (*.f64 x y) 2)
0.0ms	x	@	-inf	(/.f64 (*.f64 x y) 2)

rewrite53.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1434×	`pow1`
1330×	`add-exp-log`
1330×	`log1p-expm1-u`
1330×	`expm1-log1p-u`
1302×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	149	13
2	1811	13

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

Inputs
(/.f64 (*.f64 x y) 2)

Outputs
(-.f64 (+.f64 1 (.f64 x (.f64 y 1/2))) 1)
(*.f64 x (/.f64 1 (/.f64 2 y)))
(.f64 x (.f64 y 1/2))
(.f64 y (.f64 x 1/2))
(.f64 (.f64 x y) 1/2)
(.f64 (.f64 x (*.f64 y 1/2)) 1)
(.f64 1 (.f64 x (*.f64 y 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) 1/2))
(.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) (pow.f64 (cbrt.f64 (.f64 x (*.f64 y 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 2) (cbrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 (sqrt.f64 (.f64 x y)) (.f64 (sqrt.f64 (.f64 x y)) 1/2))
(.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) (sqrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 (.f64 x (neg.f64 y)) -1/2)
(.f64 1/2 (.f64 x y))
(*.f64 (/.f64 x 2) y)
(pow.f64 (.f64 x (.f64 y 1/2)) 1)
(pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) 2)
(pow.f64 (/.f64 2 (*.f64 x y)) -1)
(neg.f64 (/.f64 (*.f64 x y) -2))
(sqrt.f64 (.f64 (pow.f64 (.f64 x y) 2) 1/4))
(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 y 1/2))))
(exp.f64 (log.f64 (.f64 x (.f64 y 1/2))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 y 1/2))))

simplify44.0ms (4%)

Algorithm

1×	egg-herbie

Rules

920×	`fma-def`
872×	`associate-*r/`
786×	`associate-/l*`
722×	`associate-+r+`
662×	`log-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	669
1	157	669
2	583	669
3	2098	669

Stop Event

1×	node limit

Counts

51 → 28

Calls

Call 1

Inputs
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(-.f64 (+.f64 1 (.f64 x (.f64 y 1/2))) 1)
(*.f64 x (/.f64 1 (/.f64 2 y)))
(.f64 x (.f64 y 1/2))
(.f64 y (.f64 x 1/2))
(.f64 (.f64 x y) 1/2)
(.f64 (.f64 x (*.f64 y 1/2)) 1)
(.f64 1 (.f64 x (*.f64 y 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) 1/2))
(.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) (pow.f64 (cbrt.f64 (.f64 x (*.f64 y 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 2) (cbrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 (sqrt.f64 (.f64 x y)) (.f64 (sqrt.f64 (.f64 x y)) 1/2))
(.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) (sqrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 (.f64 x (neg.f64 y)) -1/2)
(.f64 1/2 (.f64 x y))
(*.f64 (/.f64 x 2) y)
(pow.f64 (.f64 x (.f64 y 1/2)) 1)
(pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 3)
(pow.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) 2)
(pow.f64 (/.f64 2 (*.f64 x y)) -1)
(neg.f64 (/.f64 (*.f64 x y) -2))
(sqrt.f64 (.f64 (pow.f64 (.f64 x y) 2) 1/4))
(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3))
(expm1.f64 (log1p.f64 (.f64 x (.f64 y 1/2))))
(exp.f64 (log.f64 (.f64 x (.f64 y 1/2))))
(log1p.f64 (expm1.f64 (.f64 x (.f64 y 1/2))))

Outputs
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 y x))
(-.f64 (+.f64 1 (.f64 x (.f64 y 1/2))) 1)
(.f64 1/2 (.f64 y x))
(*.f64 x (/.f64 1 (/.f64 2 y)))
(.f64 1/2 (.f64 y x))
(.f64 x (.f64 y 1/2))
(.f64 1/2 (.f64 y x))
(.f64 y (.f64 x 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 x y) 1/2)
(.f64 1/2 (.f64 y x))
(.f64 (.f64 x (*.f64 y 1/2)) 1)
(.f64 1/2 (.f64 y x))
(.f64 1 (.f64 x (*.f64 y 1/2)))
(.f64 1/2 (.f64 y x))
(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) (pow.f64 (cbrt.f64 (.f64 x (*.f64 y 1/2))) 2))
(.f64 1/2 (.f64 y x))
(.f64 (pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 2) (cbrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 1/2 (.f64 y x))
(.f64 (sqrt.f64 (.f64 x y)) (.f64 (sqrt.f64 (.f64 x y)) 1/2))
(.f64 1/2 (.f64 y x))
(.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) (sqrt.f64 (.f64 x (*.f64 y 1/2))))
(.f64 1/2 (.f64 y x))
(.f64 (.f64 x (neg.f64 y)) -1/2)
(.f64 1/2 (.f64 y x))
(.f64 1/2 (.f64 x y))
(.f64 1/2 (.f64 y x))
(*.f64 (/.f64 x 2) y)
(.f64 1/2 (.f64 y x))
(pow.f64 (.f64 x (.f64 y 1/2)) 1)
(.f64 1/2 (.f64 y x))
(pow.f64 (cbrt.f64 (.f64 x (.f64 y 1/2))) 3)
(.f64 1/2 (.f64 y x))
(pow.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3) 1/3)
(.f64 1/2 (.f64 y x))
(pow.f64 (sqrt.f64 (.f64 x (.f64 y 1/2))) 2)
(.f64 1/2 (.f64 y x))
(pow.f64 (/.f64 2 (*.f64 x y)) -1)
(.f64 1/2 (.f64 y x))
(neg.f64 (/.f64 (*.f64 x y) -2))
(.f64 1/2 (.f64 y x))
(sqrt.f64 (.f64 (pow.f64 (.f64 x y) 2) 1/4))
(.f64 1/2 (.f64 y x))
(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))
(cbrt.f64 (pow.f64 (.f64 x (.f64 y 1/2)) 3))
(.f64 1/2 (.f64 y x))
(expm1.f64 (log1p.f64 (.f64 x (.f64 y 1/2))))
(.f64 1/2 (.f64 y x))
(exp.f64 (log.f64 (.f64 x (.f64 y 1/2))))
(.f64 1/2 (.f64 y x))
(log1p.f64 (expm1.f64 (.f64 x (.f64 y 1/2))))
(.f64 1/2 (.f64 y x))

eval6.0ms (0.6%)

Compiler: Compiled 336 to 232 computations (31% saved)

prune5.0ms (0.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	1	29

Accurracy

100.0%

Counts

29 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Compiler

Compiled 24 to 18 computations (25% saved)

simplify11.0ms (1%)

Algorithm

1×	egg-herbie

Rules

6×	`sub-neg`
6×	`+-commutative`
6×	`*-commutative`
4×	`neg-mul-1`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	15	25
2	22	25
3	26	25
4	29	25
5	30	25

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))

Compiler

Compiled 12 to 9 computations (25% saved)

soundness0.0ms (0%)

end27.0ms (2.4%)

Remove: (sort x y)
Compiler: Compiled 72 to 54 computations (25% saved)

Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Details

analyze0.0ms (0%)

sample793.0ms (70.7%)

preprocess97.0ms (8.7%)

simplify43.0ms (3.8%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

localize34.0ms (3.1%)

series3.0ms (0.3%)

rewrite53.0ms (4.8%)

simplify44.0ms (4%)

eval6.0ms (0.6%)

prune5.0ms (0.4%)

simplify11.0ms (1%)

soundness0.0ms (0%)

end27.0ms (2.4%)

Profiling