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

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)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-div: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample722.0ms (13.4%)

Results

522.0ms	8255×	0	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 263.0ms

ival-div: 120.0ms (45.6% of total)

ival-mult: 79.0ms (30% of total)

ival-sub: 47.0ms (17.9% of total)

const: 15.0ms (5.7% of total)

backward-pass: 2.0ms (0.8% of total)

Bogosity

preprocess121.0ms (2.3%)

Algorithm

2×	egg-herbie

Rules

1890×	`fnmadd-define`
1322×	`fma-define`
1158×	`fmsub-define`
1152×	`fnmsub-define`
1104×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	96
1	76	83
2	171	80
3	404	80
4	1119	80
5	2503	80
6	4710	80
7	5306	80
8	5330	80
9	5330	80
0	9	9
1	14	8
2	29	8
3	43	8
4	75	8
5	136	8
6	275	8
7	622	8
8	1068	8
9	1577	8
10	1892	8
11	1951	8
12	1959	8
0	1959	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

Outputs
(- (/ (* x y) 2) (/ z 8))
(+.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal -8 binary64)))

Call 2

Inputs
(- (/ (* x y) 2) (/ z 8))
(- (/ (* (neg x) y) 2) (/ z 8))
(- (/ (* x (neg y)) 2) (/ z 8))
(- (/ (* x y) 2) (/ (neg z) 8))
(neg (- (/ (* (neg x) y) 2) (/ z 8)))
(neg (- (/ (* x (neg y)) 2) (/ z 8)))
(neg (- (/ (* x y) 2) (/ (neg z) 8)))
(- (/ (* y x) 2) (/ z 8))
(- (/ (* z y) 2) (/ x 8))
(- (/ (* x z) 2) (/ y 8))

Outputs
(- (/ (* x y) 2) (/ z 8))
(fnmsub x (* y -1/2) (* z 1/8))
(- (/ (* (neg x) y) 2) (/ z 8))
(fnmsub x (* y 1/2) (* z 1/8))
(- (/ (* x (neg y)) 2) (/ z 8))
(fnmsub x (* y 1/2) (* z 1/8))
(- (/ (* x y) 2) (/ (neg z) 8))
(fnmsub x (* y -1/2) (* z -1/8))
(neg (- (/ (* (neg x) y) 2) (/ z 8)))
(fnmsub x (* y -1/2) (* z -1/8))
(neg (- (/ (* x (neg y)) 2) (/ z 8)))
(fnmsub x (* y -1/2) (* z -1/8))
(neg (- (/ (* x y) 2) (/ (neg z) 8)))
(fnmsub x (* y 1/2) (* z 1/8))
(- (/ (* y x) 2) (/ z 8))
(fnmsub x (* y -1/2) (* z 1/8))
(- (/ (* z y) 2) (/ x 8))
(fnmsub x 1/8 (* y (* z -1/2)))
(- (/ (* x z) 2) (/ y 8))
(fnmsub y 1/8 (* z (* x -1/2)))

Symmetry

(sort x y)

explain71.0ms (1.3%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(/.f64 z #s(literal 8 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`y`
-	-	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
-	-	`(*.f64 x y)`
-	-	`z`
-	-	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
-	-	`#s(literal 8 binary64)`

Results

41.0ms

512×

valid

Compiler

Compiled 70 to 29 computations (58.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-div: 7.0ms (46.2% of total)

ival-mult: 5.0ms (33% of total)

ival-sub: 3.0ms (19.8% of total)

const: 1.0ms (6.6% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Compiler

Compiled 12 to 9 computations (25% saved)

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 z #s(literal 8 binary64))
✓	cost-diff	(*.f64 x y)
✓	cost-diff	(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓	cost-diff	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Rules

676×	`fnmadd-define`
424×	`fma-define`
416×	`fmsub-define`
400×	`fnmsub-define`
392×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	14	24
2	29	24
3	43	24
4	75	24
5	136	24
6	275	24
7	622	24
8	1068	24
9	1577	24
10	1892	24
11	1951	24
12	1959	24
0	1959	24

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

Outputs
(- (/ (* x y) 2) (/ z 8))
(+.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal -8 binary64)))
(/ (* x y) 2)
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(* x y)
(*.f64 x y)
x
y
2
#s(literal 2 binary64)
(/ z 8)
(/.f64 z #s(literal 8 binary64))
z
8
#s(literal 8 binary64)

localize32.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 z #s(literal 8 binary64))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Results

22.0ms

256×

valid

Compiler

Compiled 29 to 10 computations (65.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 3.0ms (39.2% of total)

ival-mult: 2.0ms (26.2% of total)

ival-sub: 1.0ms (13.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series7.0ms (0.1%)

Counts

4 → 96

Calls

Call 1

Inputs
#<alt (- (/ (* x y) 2) (/ z 8))>
#<alt (/ (* x y) 2)>
#<alt (* x y)>
#<alt (/ z 8)>

Outputs
#<alt (* -1/8 z)>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1/8 z)>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* 1/2 (* x y))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* -1/8 z)>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* -1/8 z)>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (* x y) 2)
1.0ms	x	@	0	(- (/ (* x y) 2) (/ z 8))
1.0ms	y	@	inf	(- (/ (* x y) 2) (/ z 8))
0.0ms	x	@	inf	(- (/ (* x y) 2) (/ z 8))
0.0ms	y	@	0	(- (/ (* x y) 2) (/ z 8))

rewrite327.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4654×	`-lowering-.f32`
4654×	`-lowering-.f64`
3062×	`/-lowering-/.f32`
3062×	`/-lowering-/.f64`
1682×	`frac-add`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	52	19
2	513	19
0	9018	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 219

Calls

Call 1

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

Outputs
(+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64)))
(+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (+.f64 (/.f64 z #s(literal -8 binary64)) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64)))))
(+.f64 (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64))) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64))))
(+.f64 (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64))) (fma.f64 (/.f64 z #s(literal -8 binary64)) #s(literal 1 binary64) (/.f64 z #s(literal 8 binary64))))
(+.f64 (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64))) (fma.f64 (-.f64 #s(literal 0 binary64) z) #s(literal 1/8 binary64) (/.f64 z #s(literal 8 binary64))))
(+.f64 (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64))) (+.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64))) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64)))))
(+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal 2 binary64) y)))
(+.f64 (/.f64 z #s(literal -8 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64)))))
(+.f64 (/.f64 (.f64 x (.f64 y #s(literal 8 binary64))) #s(literal 16 binary64)) (neg.f64 (/.f64 (*.f64 z #s(literal -2 binary64)) #s(literal -16 binary64))))
(+.f64 (/.f64 (/.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) #s(literal 8 binary64)) (+.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (.f64 (/.f64 z #s(literal 8 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))))) (neg.f64 (/.f64 (/.f64 (.f64 z (.f64 z z)) #s(literal 512 binary64)) (+.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (*.f64 (/.f64 z #s(literal 8 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64))))))))
(+.f64 (/.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))) (neg.f64 (/.f64 (/.f64 (*.f64 z z) #s(literal 64 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64))))))
(+.f64 (fma.f64 x (/.f64 y #s(literal 2 binary64)) (neg.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z)))) (fma.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) z) (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z))))
(+.f64 (fma.f64 y (/.f64 x #s(literal 2 binary64)) (neg.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z)))) (fma.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) z) (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z))))
(+.f64 (fma.f64 (.f64 x y) #s(literal 1/2 binary64) (neg.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z)))) (fma.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) z) (*.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z))))
(+.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x y)) #s(literal -1/2 binary64) (neg.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z)))) (fma.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) z) (*.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 2 binary64) y)) (neg.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z)))) (fma.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) z) (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z))))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x y) (neg.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z)))) (fma.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) z) (*.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z))))
(+.f64 (fma.f64 (/.f64 y #s(literal 2 binary64)) x (neg.f64 (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z)))) (fma.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) z) (.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) z))))
(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (-.f64 (/.f64 z #s(literal 8 binary64)) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64)))))
(-.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 z #s(literal 8 binary64)) (/.f64 x (/.f64 #s(literal 2 binary64) y))))
(-.f64 (/.f64 (.f64 x (.f64 y #s(literal 8 binary64))) #s(literal 16 binary64)) (/.f64 (*.f64 z #s(literal -2 binary64)) #s(literal -16 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 y #s(literal 8 binary64))) #s(literal 16 binary64)) (-.f64 (/.f64 (*.f64 z #s(literal -2 binary64)) #s(literal -16 binary64)) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) #s(literal 8 binary64)) (+.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (.f64 (/.f64 z #s(literal 8 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))))) (/.f64 (/.f64 (.f64 z (.f64 z z)) #s(literal 512 binary64)) (+.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (*.f64 (/.f64 z #s(literal 8 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) #s(literal 8 binary64)) (+.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (.f64 (/.f64 z #s(literal 8 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))))) (-.f64 (/.f64 (/.f64 (.f64 z (.f64 z z)) #s(literal 512 binary64)) (+.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (*.f64 (/.f64 z #s(literal 8 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))))) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))) (/.f64 (/.f64 (*.f64 z z) #s(literal 64 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 y (.f64 #s(literal 1/4 binary64) (.f64 x y)))) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))) (-.f64 (/.f64 (/.f64 (*.f64 z z) #s(literal 64 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x y) #s(literal -8 binary64)) #s(literal -16 binary64)) (/.f64 (*.f64 z #s(literal -2 binary64)) #s(literal -16 binary64)))
(-.f64 (/.f64 (/.f64 (*.f64 x y) (/.f64 z #s(literal 8 binary64))) (/.f64 #s(literal 2 binary64) (/.f64 z #s(literal 8 binary64)))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (/.f64 z #s(literal 8 binary64)))))
(-.f64 (/.f64 (neg.f64 (.f64 (.f64 x y) #s(literal -8 binary64))) #s(literal 16 binary64)) (/.f64 (*.f64 z #s(literal -2 binary64)) #s(literal -16 binary64)))
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(-.f64 (/.f64 #s(literal 8 binary64) (.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal 8 binary64))) (/.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) z) (.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal 8 binary64))))
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(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x y))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
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(*.f64 #s(literal 1 binary64) (/.f64 z #s(literal 8 binary64)))
(*.f64 #s(literal 1/8 binary64) z)
(*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) z) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 z #s(literal -8 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) z) #s(literal -1/8 binary64))
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simplify241.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

2038×	`-lowering-.f32`
2038×	`-lowering-.f64`
1994×	`fmsub-define`
1834×	`fmm-def`
1278×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	481
1	132	481
2	400	481
3	1073	481
4	2981	481
5	5790	481
0	8174	481

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)

Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(- (* 1/2 (* x y)) (* 1/8 z))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(- (* 1/2 (* x y)) (* 1/8 z))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))
(* 1/8 z)
(*.f64 z #s(literal 1/8 binary64))

eval51.0ms (1%)

Compiler: Compiled 5713 to 637 computations (88.8% saved)

prune50.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	310	5	315
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	310	6	316

Accuracy

100.0%

Counts

316 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal -8 binary64)))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64)))))
✓	100.0%	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
▶	99.8%	(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
▶	49.8%	(.f64 #s(literal 1/2 binary64) (.f64 x y))
▶	51.5%	(*.f64 #s(literal -1/8 binary64) z)

Compiler

Compiled 118 to 89 computations (24.6% saved)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 x (/.f64 #s(literal 2 binary64) y))
✓	cost-diff	0	(+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64))))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64)))))
✓	cost-diff	0	(/.f64 z #s(literal 8 binary64))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) y)
✓	cost-diff	0	(/.f64 x (/.f64 #s(literal 2 binary64) y))
✓	cost-diff	0	(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x y))
✓	cost-diff	0	(*.f64 #s(literal -1/8 binary64) z)
✓	cost-diff	0	(/.f64 z #s(literal -8 binary64))
✓	cost-diff	0	(/.f64 y #s(literal 2 binary64))
✓	cost-diff	6272	(fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal -8 binary64)))

Rules

744×	`fnmadd-define`
582×	`fmsub-define`
564×	`fma-define`
524×	`fnmsub-define`
420×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	102
1	44	101
2	73	101
3	134	101
4	217	101
5	412	101
6	690	101
7	1216	101
8	1818	101
9	2401	101
10	2571	101
11	2587	101
0	2587	101

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* (/ y 2) x) (/ z -8))
(/ y 2)
y
2
x
(/ z -8)
z
-8
(* -1/8 z)
-1/8
z
(* 1/2 (* x y))
1/2
(* x y)
x
y
(- (/ x (/ 2 y)) (/ z 8))
(/ x (/ 2 y))
x
(/ 2 y)
2
y
(/ z 8)
z
8
(/ 1 (/ 1 (+ (/ x (/ 2 y)) (/ z -8))))
1
(/ 1 (+ (/ x (/ 2 y)) (/ z -8)))
(+ (/ x (/ 2 y)) (/ z -8))
(/ x (/ 2 y))
x
(/ 2 y)
2
y
(/ z -8)
z
-8

Outputs
(+ (* (/ y 2) x) (/ z -8))
(+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 y x) #s(literal 2 binary64)))
(/ y 2)
(/.f64 y #s(literal 2 binary64))
y
2
#s(literal 2 binary64)
x
(/ z -8)
(/.f64 z #s(literal -8 binary64))
z
-8
#s(literal -8 binary64)
(* -1/8 z)
(/.f64 z #s(literal -8 binary64))
-1/8
#s(literal -1/8 binary64)
z
(* 1/2 (* x y))
(/.f64 (*.f64 y x) #s(literal 2 binary64))
1/2
#s(literal 1/2 binary64)
(* x y)
(*.f64 y x)
x
y
(- (/ x (/ 2 y)) (/ z 8))
(+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 y x) #s(literal 2 binary64)))
(/ x (/ 2 y))
(/.f64 (*.f64 y x) #s(literal 2 binary64))
x
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
2
#s(literal 2 binary64)
y
(/ z 8)
(/.f64 z #s(literal 8 binary64))
z
8
#s(literal 8 binary64)
(/ 1 (/ 1 (+ (/ x (/ 2 y)) (/ z -8))))
(+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 y x) #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(/ 1 (+ (/ x (/ 2 y)) (/ z -8)))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 y x) #s(literal 2 binary64))))
(+ (/ x (/ 2 y)) (/ z -8))
(+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 y x) #s(literal 2 binary64)))
(/ x (/ 2 y))
(/.f64 (*.f64 y x) #s(literal 2 binary64))
x
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
2
#s(literal 2 binary64)
y
(/ z -8)
(/.f64 z #s(literal -8 binary64))
z
-8
#s(literal -8 binary64)

localize135.0ms (2.5%)

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64)))
✓	accuracy	99.7%	(/.f64 x (/.f64 #s(literal 2 binary64) y))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64)))))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64))))
✓	accuracy	100.0%	(/.f64 z #s(literal 8 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) y)
✓	accuracy	100.0%	(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
✓	accuracy	99.7%	(/.f64 x (/.f64 #s(literal 2 binary64) y))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x y))
✓	accuracy	100.0%	(*.f64 #s(literal -1/8 binary64) z)
✓	accuracy	100.0%	(fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal -8 binary64)))
✓	accuracy	100.0%	(/.f64 z #s(literal -8 binary64))
✓	accuracy	100.0%	(/.f64 y #s(literal 2 binary64))

Results

99.0ms

256×

valid

Compiler

Compiled 114 to 23 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-div: 13.0ms (43.4% of total)

ival-mult: 7.0ms (23.3% of total)

compiled-spec: 4.0ms (13.3% of total)

ival-add: 3.0ms (10% of total)

ival-sub: 1.0ms (3.3% of total)

const: 1.0ms (3.3% of total)

backward-pass: 0.0ms (0% of total)

series12.0ms (0.2%)

Counts

13 → 312

Calls

Call 1

Inputs
#<alt (+ (* (/ y 2) x) (/ z -8))>
#<alt (/ y 2)>
#<alt (/ z -8)>
#<alt (* -1/8 z)>
#<alt (* 1/2 (* x y))>
#<alt (* x y)>
#<alt (- (/ x (/ 2 y)) (/ z 8))>
#<alt (/ x (/ 2 y))>
#<alt (/ 2 y)>
#<alt (/ z 8)>
#<alt (/ 1 (/ 1 (+ (/ x (/ 2 y)) (/ z -8))))>
#<alt (/ 1 (+ (/ x (/ 2 y)) (/ z -8)))>
#<alt (+ (/ x (/ 2 y)) (/ z -8))>

Outputs
#<alt (* -1/8 z)>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1/8 z)>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* 1/2 (* x y))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* -1/8 z)>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* -1/8 z)>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* -1/8 z)>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* -1/8 z)>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1/8 z)>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (- (* 1/2 (* x y)) (* 1/8 z))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* 1/2 (* x y))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* -1/8 z)>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* -1/8 z)>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* 1/8 z)>
#<alt (* -1/8 z)>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1/8 z)>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* 1/2 (* x y))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* -1/8 z)>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* -1/8 z)>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (/ -8 z)>
#<alt (- (* -32 (/ (* x y) (pow z 2))) (* 8 (/ 1 z)))>
#<alt (- (* x (- (* -128 (/ (* x (pow y 2)) (pow z 3))) (* 32 (/ y (pow z 2))))) (* 8 (/ 1 z)))>
#<alt (- (* x (- (* x (- (* -512 (/ (* x (pow y 3)) (pow z 4))) (* 128 (/ (pow y 2) (pow z 3))))) (* 32 (/ y (pow z 2))))) (* 8 (/ 1 z)))>
#<alt (/ 2 (* x y))>
#<alt (/ (+ (* 1/2 (/ z (* x (pow y 2)))) (* 2 (/ 1 y))) x)>
#<alt (/ (- (+ (* 1/8 (/ (pow z 2) (* (pow x 2) (pow y 3)))) (* 2 (/ 1 y))) (* -1/2 (/ z (* x (pow y 2))))) x)>
#<alt (/ (- (+ (* 1/32 (/ (pow z 3) (* (pow x 3) (pow y 4)))) (* 2 (/ 1 y))) (+ (* -1/2 (/ z (* x (pow y 2)))) (* -1/8 (/ (pow z 2) (* (pow x 2) (pow y 3)))))) x)>
#<alt (/ 2 (* x y))>
#<alt (* -1 (/ (- (* -1/2 (/ z (* x (pow y 2)))) (* 2 (/ 1 y))) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow z 2) (* x (pow y 3)))) (* -1/2 (/ z (pow y 2)))) x)) (* 2 (/ 1 y))) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/32 (/ (pow z 3) (* x (pow y 4)))) (* 1/8 (/ (pow z 2) (pow y 3)))) x)) (* -1/2 (/ z (pow y 2)))) x)) (* 2 (/ 1 y))) x))>
#<alt (/ -8 z)>
#<alt (- (* -32 (/ (* x y) (pow z 2))) (* 8 (/ 1 z)))>
#<alt (- (* y (- (* -128 (/ (* (pow x 2) y) (pow z 3))) (* 32 (/ x (pow z 2))))) (* 8 (/ 1 z)))>
#<alt (- (* y (- (* y (- (* -512 (/ (* (pow x 3) y) (pow z 4))) (* 128 (/ (pow x 2) (pow z 3))))) (* 32 (/ x (pow z 2))))) (* 8 (/ 1 z)))>
#<alt (/ 2 (* x y))>
#<alt (/ (+ (* 1/2 (/ z (* (pow x 2) y))) (* 2 (/ 1 x))) y)>
#<alt (/ (- (+ (* 1/8 (/ (pow z 2) (* (pow x 3) (pow y 2)))) (* 2 (/ 1 x))) (* -1/2 (/ z (* (pow x 2) y)))) y)>
#<alt (/ (- (+ (* 1/32 (/ (pow z 3) (* (pow x 4) (pow y 3)))) (* 2 (/ 1 x))) (+ (* -1/2 (/ z (* (pow x 2) y))) (* -1/8 (/ (pow z 2) (* (pow x 3) (pow y 2)))))) y)>
#<alt (/ 2 (* x y))>
#<alt (* -1 (/ (- (* -1/2 (/ z (* (pow x 2) y))) (* 2 (/ 1 x))) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow z 2) (* (pow x 3) y))) (* -1/2 (/ z (pow x 2)))) y)) (* 2 (/ 1 x))) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/32 (/ (pow z 3) (* (pow x 4) y))) (* 1/8 (/ (pow z 2) (pow x 3)))) y)) (* -1/2 (/ z (pow x 2)))) y)) (* 2 (/ 1 x))) y))>
#<alt (/ 2 (* x y))>
#<alt (+ (* 1/2 (/ z (* (pow x 2) (pow y 2)))) (* 2 (/ 1 (* x y))))>
#<alt (+ (* z (+ (* 1/8 (/ z (* (pow x 3) (pow y 3)))) (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))))) (* 2 (/ 1 (* x y))))>
#<alt (+ (* z (+ (* z (+ (* 1/32 (/ z (* (pow x 4) (pow y 4)))) (* 1/8 (/ 1 (* (pow x 3) (pow y 3)))))) (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))))) (* 2 (/ 1 (* x y))))>
#<alt (/ -8 z)>
#<alt (/ (- (* -32 (/ (* x y) z)) 8) z)>
#<alt (/ (- (* -128 (/ (* (pow x 2) (pow y 2)) (pow z 2))) (+ 8 (* 32 (/ (* x y) z)))) z)>
#<alt (/ (- (* -512 (/ (* (pow x 3) (pow y 3)) (pow z 3))) (+ 8 (+ (* 32 (/ (* x y) z)) (* 128 (/ (* (pow x 2) (pow y 2)) (pow z 2)))))) z)>
#<alt (/ -8 z)>
#<alt (* -1 (/ (+ 8 (* 32 (/ (* x y) z))) z))>
#<alt (* -1 (/ (+ 8 (* -1 (/ (- (* -128 (/ (* (pow x 2) (pow y 2)) z)) (* 32 (* x y))) z))) z))>
#<alt (* -1 (/ (+ 8 (* -1 (/ (- (* -1 (/ (- (* 512 (/ (* (pow x 3) (pow y 3)) z)) (* -128 (* (pow x 2) (pow y 2)))) z)) (* 32 (* x y))) z))) z))>
#<alt (* -1/8 z)>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1/8 z)>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* 1/2 (* x y))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* -1/8 z)>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* -1/8 z)>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>

Calls

78 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/ 1 (+ (/ x (/ 2 y)) (/ z -8)))
0.0ms	y	@	inf	(/ 1 (+ (/ x (/ 2 y)) (/ z -8)))
0.0ms	z	@	0	(/ 1 (+ (/ x (/ 2 y)) (/ z -8)))
0.0ms	x	@	inf	(/ 1 (+ (/ x (/ 2 y)) (/ z -8)))
0.0ms	x	@	-inf	(/ 1 (+ (/ x (/ 2 y)) (/ z -8)))

rewrite409.0ms (7.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3056×	`/-lowering-/.f32`
3056×	`/-lowering-/.f64`
2802×	`-lowering-.f32`
2802×	`-lowering-.f64`
1496×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	69
1	132	69
2	1155	69
0	8805	69

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 1206

Calls

Call 1

Inputs
(+ (* (/ y 2) x) (/ z -8))
(/ y 2)
(/ z -8)
(* -1/8 z)
(* 1/2 (* x y))
(* x y)
(- (/ x (/ 2 y)) (/ z 8))
(/ x (/ 2 y))
(/ 2 y)
(/ z 8)
(/ 1 (/ 1 (+ (/ x (/ 2 y)) (/ z -8))))
(/ 1 (+ (/ x (/ 2 y)) (/ z -8)))
(+ (/ x (/ 2 y)) (/ z -8))

Outputs
(+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x))
(+.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal -8 binary64)))
(+.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) x) (neg.f64 (/.f64 (/.f64 z (/.f64 y #s(literal 2 binary64))) (/.f64 #s(literal 16 binary64) y))))
(+.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x)) (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 z #s(literal 8 binary64))))
(+.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x)) (fma.f64 (/.f64 z #s(literal -8 binary64)) #s(literal 1 binary64) (/.f64 z #s(literal 8 binary64))))
(+.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x)) (fma.f64 #s(literal 1/8 binary64) (-.f64 #s(literal 0 binary64) z) (/.f64 z #s(literal 8 binary64))))
(+.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x)) (fma.f64 (-.f64 #s(literal 0 binary64) z) #s(literal 1/8 binary64) (/.f64 z #s(literal 8 binary64))))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (+.f64 (.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64)))) (neg.f64 (/.f64 (/.f64 (.f64 z z) #s(literal 64 binary64)) (+.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64))))))
(+.f64 (/.f64 (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y y)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))) (/.f64 #s(literal -8 binary64) z)))) (neg.f64 (/.f64 (/.f64 (.f64 z (.f64 z z)) #s(literal -512 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))) (/.f64 #s(literal -8 binary64) z))))))
(exp.f64 (log.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x))))
(exp.f64 (.f64 (log.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (.f64 (/.f64 y #s(literal 2 binary64)) x))) #s(literal 1 binary64)))
(-.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y)))
(-.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64)))
(-.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 (/.f64 z (/.f64 y #s(literal 2 binary64))) (/.f64 #s(literal 16 binary64) y)))
(-.f64 #s(literal 0 binary64) (+.f64 (/.f64 z #s(literal 8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (+.f64 (.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64)))) (/.f64 (/.f64 (.f64 z z) #s(literal 64 binary64)) (+.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y y)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))) (/.f64 #s(literal -8 binary64) z)))) (/.f64 (/.f64 (.f64 z (.f64 z z)) #s(literal -512 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))) (/.f64 #s(literal -8 binary64) z)))))
(-.f64 (/.f64 (*.f64 (/.f64 y #s(literal 2 binary64)) x) #s(literal 1 binary64)) (/.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 1 binary64)))
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(.f64 (pow.f64 (+.f64 (.f64 x #s(literal -8 binary64)) (/.f64 z (/.f64 y #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -16 binary64) y)) #s(literal 1 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 x #s(literal 8 binary64)) (/.f64 z (/.f64 y #s(literal -2 binary64)))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 16 binary64) y)) #s(literal 1 binary64)))
(.f64 (pow.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y y)))) (/.f64 (.f64 z (.f64 z z)) #s(literal -512 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (*.f64 y y) #s(literal 1/4 binary64))) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))) (/.f64 #s(literal -8 binary64) z)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (.f64 (.f64 z z) #s(literal -1/64 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (.f64 (/.f64 y #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (.f64 (/.f64 y #s(literal 2 binary64)) x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (*.f64 (/.f64 y #s(literal 2 binary64)) x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -8 binary64)) (/.f64 z (/.f64 y #s(literal 2 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -16 binary64) y)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y y)))) (/.f64 (.f64 z (.f64 z z)) #s(literal -512 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (*.f64 y y) #s(literal 1/4 binary64))) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))) (/.f64 #s(literal -8 binary64) z)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (.f64 (.f64 z z) #s(literal -1/64 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))) (/.f64 #s(literal -8 binary64) z))) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (.f64 (/.f64 y #s(literal 2 binary64)) x)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 y y) #s(literal 1/4 binary64))) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (/.f64 x (/.f64 #s(literal -2 binary64) y))) (/.f64 #s(literal -8 binary64) z)))))
(.f64 (/.f64 (+.f64 (.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 z #s(literal -8 binary64)) (.f64 (/.f64 y #s(literal 2 binary64)) x)) (+.f64 (.f64 (/.f64 y #s(literal 2 binary64)) x) (/.f64 z #s(literal 8 binary64)))))

simplify444.0ms (8.3%)

Algorithm

1×	egg-herbie

Rules

7470×	`-lowering-.f32`
7470×	`-lowering-.f64`
1848×	`/-lowering-/.f32`
1848×	`/-lowering-/.f64`
1598×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	2379
1	905	2361
2	2878	2341
0	8732	2341

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

Inputs
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* -1/8 z)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1/8 z)
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(- (* 1/2 (* x y)) (* 1/8 z))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* 1/8 z)
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(/ -8 z)
(- (* -32 (/ (* x y) (pow z 2))) (* 8 (/ 1 z)))
(- (* x (- (* -128 (/ (* x (pow y 2)) (pow z 3))) (* 32 (/ y (pow z 2))))) (* 8 (/ 1 z)))
(- (* x (- (* x (- (* -512 (/ (* x (pow y 3)) (pow z 4))) (* 128 (/ (pow y 2) (pow z 3))))) (* 32 (/ y (pow z 2))))) (* 8 (/ 1 z)))
(/ 2 (* x y))
(/ (+ (* 1/2 (/ z (* x (pow y 2)))) (* 2 (/ 1 y))) x)
(/ (- (+ (* 1/8 (/ (pow z 2) (* (pow x 2) (pow y 3)))) (* 2 (/ 1 y))) (* -1/2 (/ z (* x (pow y 2))))) x)
(/ (- (+ (* 1/32 (/ (pow z 3) (* (pow x 3) (pow y 4)))) (* 2 (/ 1 y))) (+ (* -1/2 (/ z (* x (pow y 2)))) (* -1/8 (/ (pow z 2) (* (pow x 2) (pow y 3)))))) x)
(/ 2 (* x y))
(* -1 (/ (- (* -1/2 (/ z (* x (pow y 2)))) (* 2 (/ 1 y))) x))
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow z 2) (* x (pow y 3)))) (* -1/2 (/ z (pow y 2)))) x)) (* 2 (/ 1 y))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/32 (/ (pow z 3) (* x (pow y 4)))) (* 1/8 (/ (pow z 2) (pow y 3)))) x)) (* -1/2 (/ z (pow y 2)))) x)) (* 2 (/ 1 y))) x))
(/ -8 z)
(- (* -32 (/ (* x y) (pow z 2))) (* 8 (/ 1 z)))
(- (* y (- (* -128 (/ (* (pow x 2) y) (pow z 3))) (* 32 (/ x (pow z 2))))) (* 8 (/ 1 z)))
(- (* y (- (* y (- (* -512 (/ (* (pow x 3) y) (pow z 4))) (* 128 (/ (pow x 2) (pow z 3))))) (* 32 (/ x (pow z 2))))) (* 8 (/ 1 z)))
(/ 2 (* x y))
(/ (+ (* 1/2 (/ z (* (pow x 2) y))) (* 2 (/ 1 x))) y)
(/ (- (+ (* 1/8 (/ (pow z 2) (* (pow x 3) (pow y 2)))) (* 2 (/ 1 x))) (* -1/2 (/ z (* (pow x 2) y)))) y)
(/ (- (+ (* 1/32 (/ (pow z 3) (* (pow x 4) (pow y 3)))) (* 2 (/ 1 x))) (+ (* -1/2 (/ z (* (pow x 2) y))) (* -1/8 (/ (pow z 2) (* (pow x 3) (pow y 2)))))) y)
(/ 2 (* x y))
(* -1 (/ (- (* -1/2 (/ z (* (pow x 2) y))) (* 2 (/ 1 x))) y))
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow z 2) (* (pow x 3) y))) (* -1/2 (/ z (pow x 2)))) y)) (* 2 (/ 1 x))) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/32 (/ (pow z 3) (* (pow x 4) y))) (* 1/8 (/ (pow z 2) (pow x 3)))) y)) (* -1/2 (/ z (pow x 2)))) y)) (* 2 (/ 1 x))) y))
(/ 2 (* x y))
(+ (* 1/2 (/ z (* (pow x 2) (pow y 2)))) (* 2 (/ 1 (* x y))))
(+ (* z (+ (* 1/8 (/ z (* (pow x 3) (pow y 3)))) (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))))) (* 2 (/ 1 (* x y))))
(+ (* z (+ (* z (+ (* 1/32 (/ z (* (pow x 4) (pow y 4)))) (* 1/8 (/ 1 (* (pow x 3) (pow y 3)))))) (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))))) (* 2 (/ 1 (* x y))))
(/ -8 z)
(/ (- (* -32 (/ (* x y) z)) 8) z)
(/ (- (* -128 (/ (* (pow x 2) (pow y 2)) (pow z 2))) (+ 8 (* 32 (/ (* x y) z)))) z)
(/ (- (* -512 (/ (* (pow x 3) (pow y 3)) (pow z 3))) (+ 8 (+ (* 32 (/ (* x y) z)) (* 128 (/ (* (pow x 2) (pow y 2)) (pow z 2)))))) z)
(/ -8 z)
(* -1 (/ (+ 8 (* 32 (/ (* x y) z))) z))
(* -1 (/ (+ 8 (* -1 (/ (- (* -128 (/ (* (pow x 2) (pow y 2)) z)) (* 32 (* x y))) z))) z))
(* -1 (/ (+ 8 (* -1 (/ (- (* -1 (/ (- (* 512 (/ (* (pow x 3) (pow y 3)) z)) (* -128 (* (pow x 2) (pow y 2)))) z)) (* 32 (* x y))) z))) z))
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))

Outputs
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* 1/2 (* x y))
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(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(/ -8 z)
(/.f64 #s(literal -8 binary64) z)
(- (* -32 (/ (* x y) (pow z 2))) (* 8 (/ 1 z)))
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (.f64 (.f64 x y) #s(literal -32 binary64)) z)) z)
(- (* x (- (* -128 (/ (* x (pow y 2)) (pow z 3))) (* 32 (/ y (pow z 2))))) (* 8 (/ 1 z)))
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 #s(literal -128 binary64) (.f64 x (.f64 y y)))) z) (.f64 (.f64 x y) #s(literal -32 binary64))) z)) z)
(- (* x (- (* x (- (* -512 (/ (* x (pow y 3)) (pow z 4))) (* 128 (/ (pow y 2) (pow z 3))))) (* 32 (/ y (pow z 2))))) (* 8 (/ 1 z)))
(+.f64 (.f64 (+.f64 (/.f64 (.f64 x (.f64 (.f64 y (.f64 y y)) #s(literal -512 binary64))) (pow.f64 z #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -128 binary64) (.f64 y y)) (.f64 z (.f64 z z)))) (.f64 x x)) (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (.f64 (.f64 x y) #s(literal -32 binary64)) z)) z))
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 x y))
(/ (+ (* 1/2 (/ z (* x (pow y 2)))) (* 2 (/ 1 y))) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x x))) y) (/.f64 #s(literal 2 binary64) x)) y)
(/ (- (+ (* 1/8 (/ (pow z 2) (* (pow x 2) (pow y 3)))) (* 2 (/ 1 y))) (* -1/2 (/ z (* x (pow y 2))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 z (/.f64 z (.f64 y (.f64 y y))))) x) (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 y y)))) x)) x)
(/ (- (+ (* 1/32 (/ (pow z 3) (* (pow x 3) (pow y 4)))) (* 2 (/ 1 y))) (+ (* -1/2 (/ z (* x (pow y 2)))) (* -1/8 (/ (pow z 2) (* (pow x 2) (pow y 3)))))) x)
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 (.f64 #s(literal 1/32 binary64) (.f64 z (.f64 z (/.f64 (/.f64 z (.f64 x x)) x)))) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 z (/.f64 z (.f64 y (.f64 y y))))) x) (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 y y)))) x)) x)
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 x y))
(* -1 (/ (- (* -1/2 (/ z (* x (pow y 2)))) (* 2 (/ 1 y))) x))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x x))) y) (/.f64 #s(literal 2 binary64) x)) y)
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow z 2) (* x (pow y 3)))) (* -1/2 (/ z (pow y 2)))) x)) (* 2 (/ 1 y))) x))
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 z (/.f64 z (.f64 y (.f64 y y))))) x) (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 y y)))) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/32 (/ (pow z 3) (* x (pow y 4)))) (* 1/8 (/ (pow z 2) (pow y 3)))) x)) (* -1/2 (/ z (pow y 2)))) x)) (* 2 (/ 1 y))) x))
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 y y))) (/.f64 (+.f64 (/.f64 (.f64 z (.f64 (.f64 z z) #s(literal -1/32 binary64))) (.f64 x (pow.f64 y #s(literal 4 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 z (/.f64 z (.f64 y (.f64 y y)))))) x)) x)) x)
(/ -8 z)
(/.f64 #s(literal -8 binary64) z)
(- (* -32 (/ (* x y) (pow z 2))) (* 8 (/ 1 z)))
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (.f64 (.f64 x y) #s(literal -32 binary64)) z)) z)
(- (* y (- (* -128 (/ (* (pow x 2) y) (pow z 3))) (* 32 (/ x (pow z 2))))) (* 8 (/ 1 z)))
(+.f64 (.f64 y (+.f64 (/.f64 (.f64 x (.f64 (.f64 x y) #s(literal -128 binary64))) (.f64 z (.f64 z z))) (.f64 #s(literal -32 binary64) (/.f64 x (.f64 z z))))) (/.f64 #s(literal -8 binary64) z))
(- (* y (- (* y (- (* -512 (/ (* (pow x 3) y) (pow z 4))) (* 128 (/ (pow x 2) (pow z 3))))) (* 32 (/ x (pow z 2))))) (* 8 (/ 1 z)))
(+.f64 (.f64 (.f64 y y) (+.f64 (.f64 (.f64 #s(literal -512 binary64) (.f64 x (.f64 x x))) (/.f64 y (pow.f64 z #s(literal 4 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal -128 binary64))) (.f64 z (.f64 z z))))) (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (.f64 (.f64 x y) #s(literal -32 binary64)) z)) z))
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 x y))
(/ (+ (* 1/2 (/ z (* (pow x 2) y))) (* 2 (/ 1 x))) y)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x x))) y) (/.f64 #s(literal 2 binary64) x)) y)
(/ (- (+ (* 1/8 (/ (pow z 2) (* (pow x 3) (pow y 2)))) (* 2 (/ 1 x))) (* -1/2 (/ z (* (pow x 2) y)))) y)
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (/.f64 (.f64 z (.f64 (/.f64 (/.f64 z (.f64 x x)) x) #s(literal 1/8 binary64))) y) (.f64 #s(literal 1/2 binary64) (/.f64 z (*.f64 x x)))) y)) y)
(/ (- (+ (* 1/32 (/ (pow z 3) (* (pow x 4) (pow y 3)))) (* 2 (/ 1 x))) (+ (* -1/2 (/ z (* (pow x 2) y))) (* -1/8 (/ (pow z 2) (* (pow x 3) (pow y 2)))))) y)
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (.f64 (/.f64 (.f64 z (.f64 z z)) (.f64 y (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/32 binary64) (.f64 y y)))) (/.f64 (+.f64 (/.f64 (.f64 z (.f64 (/.f64 (/.f64 z (.f64 x x)) x) #s(literal 1/8 binary64))) y) (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x x)))) y)) y)
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 x y))
(* -1 (/ (- (* -1/2 (/ z (* (pow x 2) y))) (* 2 (/ 1 x))) y))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x x))) y) (/.f64 #s(literal 2 binary64) x)) y)
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow z 2) (* (pow x 3) y))) (* -1/2 (/ z (pow x 2)))) y)) (* 2 (/ 1 x))) y))
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (/.f64 (.f64 z (.f64 (/.f64 (/.f64 z (.f64 x x)) x) #s(literal 1/8 binary64))) y) (.f64 #s(literal 1/2 binary64) (/.f64 z (*.f64 x x)))) y)) y)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/32 (/ (pow z 3) (* (pow x 4) y))) (* 1/8 (/ (pow z 2) (pow x 3)))) y)) (* -1/2 (/ z (pow x 2)))) y)) (* 2 (/ 1 x))) y))
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x x))) (/.f64 (+.f64 (/.f64 (.f64 z (.f64 (.f64 z z) #s(literal -1/32 binary64))) (.f64 y (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 z (/.f64 (/.f64 z (*.f64 x x)) x)))) y)) y)) y)
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 x y))
(+ (* 1/2 (/ z (* (pow x 2) (pow y 2)))) (* 2 (/ 1 (* x y))))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x x))) y) (/.f64 #s(literal 2 binary64) x)) y)
(+ (* z (+ (* 1/8 (/ z (* (pow x 3) (pow y 3)))) (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))))) (* 2 (/ 1 (* x y))))
(+.f64 (/.f64 (.f64 z (.f64 z #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x (.f64 y (.f64 y y)))))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (*.f64 x x))) y) (/.f64 #s(literal 2 binary64) x)) y))
(+ (* z (+ (* z (+ (* 1/32 (/ z (* (pow x 4) (pow y 4)))) (* 1/8 (/ 1 (* (pow x 3) (pow y 3)))))) (* 1/2 (/ 1 (* (pow x 2) (pow y 2)))))) (* 2 (/ 1 (* x y))))
(+.f64 (.f64 (.f64 z z) (+.f64 (/.f64 (/.f64 (.f64 z #s(literal 1/32 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))) (.f64 x (.f64 x x))))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 z (*.f64 x x))) y) (/.f64 #s(literal 2 binary64) x)) y))
(/ -8 z)
(/.f64 #s(literal -8 binary64) z)
(/ (- (* -32 (/ (* x y) z)) 8) z)
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (.f64 (.f64 x y) #s(literal -32 binary64)) z)) z)
(/ (- (* -128 (/ (* (pow x 2) (pow y 2)) (pow z 2))) (+ 8 (* 32 (/ (* x y) z)))) z)
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 #s(literal -128 binary64) (.f64 x (.f64 y y)))) z) (.f64 (.f64 x y) #s(literal -32 binary64))) z)) z)
(/ (- (* -512 (/ (* (pow x 3) (pow y 3)) (pow z 3))) (+ 8 (+ (* 32 (/ (* x y) z)) (* 128 (/ (* (pow x 2) (pow y 2)) (pow z 2)))))) z)
(/.f64 (+.f64 #s(literal -8 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (.f64 x (.f64 #s(literal -128 binary64) (.f64 x (.f64 y y)))) z) (.f64 (.f64 x y) #s(literal -32 binary64))) z) (/.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 y (.f64 y y)))) #s(literal -512 binary64))) (.f64 z (.f64 z z))))) z)
(/ -8 z)
(/.f64 #s(literal -8 binary64) z)
(* -1 (/ (+ 8 (* 32 (/ (* x y) z))) z))
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (.f64 (.f64 x y) #s(literal -32 binary64)) z)) z)
(* -1 (/ (+ 8 (* -1 (/ (- (* -128 (/ (* (pow x 2) (pow y 2)) z)) (* 32 (* x y))) z))) z))
(/.f64 (-.f64 #s(literal 8 binary64) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 #s(literal -128 binary64) (.f64 x (.f64 y y)))) z) (.f64 (.f64 x y) #s(literal -32 binary64))) z)) (-.f64 #s(literal 0 binary64) z))
(* -1 (/ (+ 8 (* -1 (/ (- (* -1 (/ (- (* 512 (/ (* (pow x 3) (pow y 3)) z)) (* -128 (* (pow x 2) (pow y 2)))) z)) (* 32 (* x y))) z))) z))
(/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (-.f64 (.f64 (.f64 x y) #s(literal -32 binary64)) (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 y y) (.f64 (/.f64 y z) #s(literal 512 binary64)))) (.f64 (.f64 (.f64 #s(literal 128 binary64) (.f64 x x)) y) y)) z)) z)) z)
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(.f64 x (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) x) (*.f64 #s(literal 1/2 binary64) y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(.f64 y (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) z) y) (*.f64 #s(literal 1/2 binary64) x)))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+.f64 (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y)))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(* -1/8 z)
(*.f64 #s(literal -1/8 binary64) z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))

eval233.0ms (4.3%)

Compiler: Compiled 31518 to 1965 computations (93.8% saved)

prune191.0ms (3.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1654	3	1657
Fresh	0	0	0
Picked	2	3	5
Done	0	1	1
Total	1656	7	1663

Accuracy

100.0%

Counts

1663 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.7%	(/.f64 y (/.f64 #s(literal 2 binary64) x))
▶	49.6%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) x))
✓	100.0%	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
✓	99.8%	(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
▶	92.2%	(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
✓	49.8%	(.f64 #s(literal 1/2 binary64) (.f64 x y))
✓	51.5%	(*.f64 #s(literal -1/8 binary64) z)

Compiler

Compiled 70 to 53 computations (24.3% saved)

simplify263.0ms (4.9%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(/.f64 y (/.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) y)
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 2 binary64) y) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) x))
✓	cost-diff	0	(/.f64 (*.f64 x y) z)
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x y) z))
✓	cost-diff	0	(+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x y) z)))
✓	cost-diff	128	(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))

Rules

7730×	`-lowering-.f32`
7730×	`-lowering-.f64`
4960×	`associate-/r/`
3952×	`*-commutative`
1940×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	39	66
2	78	66
3	186	64
4	418	64
5	1290	64
6	2635	64
7	2838	64
8	2887	64
9	2887	64
10	4560	64
11	4635	64
12	4635	64
13	5040	64
14	5078	64
15	5078	64
16	6496	64
17	6846	64
18	6880	64
19	6888	64
20	6888	64
0	8190	64

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* z (+ -1/8 (* 1/2 (/ (* x y) z))))
z
(+ -1/8 (* 1/2 (/ (* x y) z)))
-1/8
(* 1/2 (/ (* x y) z))
1/2
(/ (* x y) z)
(* x y)
x
y
(/ 1 (/ (/ 2 y) x))
1
(/ (/ 2 y) x)
(/ 2 y)
2
y
x
(/ y (/ 2 x))
y
(/ 2 x)
2
x

Outputs
(* z (+ -1/8 (* 1/2 (/ (* x y) z))))
(+.f64 (*.f64 z #s(literal -1/8 binary64)) (/.f64 x (/.f64 #s(literal 2 binary64) y)))
z
(+ -1/8 (* 1/2 (/ (* x y) z)))
(+.f64 #s(literal -1/8 binary64) (/.f64 x (/.f64 (*.f64 z #s(literal 2 binary64)) y)))
-1/8
#s(literal -1/8 binary64)
(* 1/2 (/ (* x y) z))
(/.f64 x (/.f64 (*.f64 z #s(literal 2 binary64)) y))
1/2
#s(literal 1/2 binary64)
(/ (* x y) z)
(*.f64 y (/.f64 x z))
(* x y)
(*.f64 x y)
x
y
(/ 1 (/ (/ 2 y) x))
(/.f64 x (/.f64 #s(literal 2 binary64) y))
1
#s(literal 1 binary64)
(/ (/ 2 y) x)
(/.f64 (/.f64 #s(literal 2 binary64) y) x)
(/ 2 y)
(/.f64 #s(literal 2 binary64) y)
2
#s(literal 2 binary64)
y
x
(/ y (/ 2 x))
(/.f64 x (/.f64 #s(literal 2 binary64) y))
y
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x

localize65.0ms (1.2%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	99.7%	(/.f64 y (/.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) y)
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 2 binary64) y) x)
✓	accuracy	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) x))
✓	accuracy	100.0%	(+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x y) z)))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x y) z))
✓	accuracy	92.4%	(/.f64 (*.f64 x y) z)
✓	accuracy	92.1%	(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))

Results

45.0ms

256×

valid

Compiler

Compiled 74 to 18 computations (75.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-div: 15.0ms (63.4% of total)

ival-mult: 7.0ms (29.6% of total)

ival-add: 1.0ms (4.2% of total)

const: 1.0ms (4.2% of total)

backward-pass: 0.0ms (0% of total)

series42.0ms (0.8%)

Counts

9 → 240

Calls

Call 1

Inputs
#<alt (* z (+ -1/8 (* 1/2 (/ (* x y) z))))>
#<alt (+ -1/8 (* 1/2 (/ (* x y) z)))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (/ (* x y) z)>
#<alt (/ 1 (/ (/ 2 y) x))>
#<alt (/ (/ 2 y) x)>
#<alt (/ 2 y)>
#<alt (/ y (/ 2 x))>
#<alt (/ 2 x)>

Outputs
#<alt (* 1/2 (* x y))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* -1/8 z)>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* z (- (* 1/2 (/ (* x y) z)) 1/8))>
#<alt (* -1/8 z)>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))>
#<alt (* -1/8 z)>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* x (+ (* -1/8 (/ z x)) (* 1/2 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))>
#<alt (* -1/8 z)>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (+ (* -1/8 z) (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* y (+ (* -1/8 (/ z y)) (* 1/2 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))>
#<alt -1/8>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* x (- (* 1/2 (/ y z)) (* 1/8 (/ 1 x))))>
#<alt (* x (- (* 1/2 (/ y z)) (* 1/8 (/ 1 x))))>
#<alt (* x (- (* 1/2 (/ y z)) (* 1/8 (/ 1 x))))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* -1 (* x (+ (* -1/2 (/ y z)) (* 1/8 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ y z)) (* 1/8 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ y z)) (* 1/8 (/ 1 x)))))>
#<alt -1/8>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* y (- (* 1/2 (/ x z)) (* 1/8 (/ 1 y))))>
#<alt (* y (- (* 1/2 (/ x z)) (* 1/8 (/ 1 y))))>
#<alt (* y (- (* 1/2 (/ x z)) (* 1/8 (/ 1 y))))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* -1 (* y (+ (* -1/2 (/ x z)) (* 1/8 (/ 1 y)))))>
#<alt (* -1 (* y (+ (* -1/2 (/ x z)) (* 1/8 (/ 1 y)))))>
#<alt (* -1 (* y (+ (* -1/2 (/ x z)) (* 1/8 (/ 1 y)))))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (/ (+ (* -1/8 z) (* 1/2 (* x y))) z)>
#<alt (/ (+ (* -1/8 z) (* 1/2 (* x y))) z)>
#<alt (/ (+ (* -1/8 z) (* 1/2 (* x y))) z)>
#<alt -1/8>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt -1/8>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (- (* 1/2 (/ (* x y) z)) 1/8)>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (* 1/2 (/ (* x y) z))>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (/ (* x y) z)>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 (* x y))>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (/ 2 y)>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>

Calls

60 calls:

Time	Variable		Point	Expression
28.0ms	z	@	0	(* 1/2 (/ (* x y) z))
3.0ms	z	@	inf	(* 1/2 (/ (* x y) z))
1.0ms	z	@	inf	(* z (+ -1/8 (* 1/2 (/ (* x y) z))))
1.0ms	z	@	0	(* z (+ -1/8 (* 1/2 (/ (* x y) z))))
1.0ms	x	@	-inf	(* z (+ -1/8 (* 1/2 (/ (* x y) z))))

rewrite297.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3638×	`-lowering-.f32`
3638×	`-lowering-.f64`
2320×	`/-lowering-/.f32`
2320×	`/-lowering-/.f64`
1584×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	55
1	93	51
2	586	51
3	5828	51
0	8496	51

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 498

Calls

Call 1

Inputs
(* z (+ -1/8 (* 1/2 (/ (* x y) z))))
(+ -1/8 (* 1/2 (/ (* x y) z)))
(* 1/2 (/ (* x y) z))
(/ (* x y) z)
(/ 1 (/ (/ 2 y) x))
(/ (/ 2 y) x)
(/ 2 y)
(/ y (/ 2 x))
(/ 2 x)

Outputs
(+.f64 (.f64 z #s(literal -1/8 binary64)) (/.f64 z (/.f64 z (/.f64 (.f64 x y) #s(literal 2 binary64)))))
(+.f64 (/.f64 z (/.f64 z (/.f64 (.f64 x y) #s(literal 2 binary64)))) (.f64 z #s(literal -1/8 binary64)))
(-.f64 (.f64 z #s(literal -1/8 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (.f64 x y) z)) (.f64 z #s(literal 1/2 binary64))))
(-.f64 (.f64 z #s(literal -1/8 binary64)) (.f64 (.f64 z #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (.f64 x y) z))))
(-.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (.f64 z z)) (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) z)))) (/.f64 (.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 z (.f64 x y))) (/.f64 z (.f64 x y))) (.f64 z z)) (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) z)))))
(fma.f64 z #s(literal -1/8 binary64) (/.f64 z (/.f64 z (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(fma.f64 z (/.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x y))) (.f64 z #s(literal -1/8 binary64)))
(fma.f64 #s(literal -1/8 binary64) z (/.f64 z (/.f64 z (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 z (/.f64 z (.f64 x y))) (.f64 z #s(literal -1/8 binary64)))
(fma.f64 (/.f64 (.f64 x y) z) (.f64 z #s(literal 1/2 binary64)) (*.f64 z #s(literal -1/8 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x y))) z (.f64 z #s(literal -1/8 binary64)))
(fma.f64 (.f64 z #s(literal 1/2 binary64)) (/.f64 (.f64 x y) z) (*.f64 z #s(literal -1/8 binary64)))
(fma.f64 (/.f64 z (/.f64 z (.f64 x y))) #s(literal 1/2 binary64) (.f64 z #s(literal -1/8 binary64)))
(/.f64 z (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 z (*.f64 x y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 z z)) (.f64 (/.f64 z (/.f64 z (/.f64 (.f64 x y) #s(literal 2 binary64)))) (-.f64 (/.f64 z (/.f64 z (/.f64 (.f64 x y) #s(literal 2 binary64)))) (.f64 z #s(literal -1/8 binary64))))) (+.f64 (.f64 #s(literal -1/512 binary64) (.f64 z (.f64 z z))) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 x y) z) (/.f64 (.f64 x y) (.f64 z (/.f64 z (.f64 x y)))))) (.f64 z (.f64 z z))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) z))) (.f64 (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x y))))) (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (*.f64 x y) #s(literal -2 binary64)) z))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (/.f64 (.f64 x y) z) (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 z (.f64 x y))) #s(literal -1/16 binary64)))) (.f64 z (+.f64 #s(literal -1/512 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 x y) z) (/.f64 (.f64 x y) (.f64 z (/.f64 z (.f64 x y))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) z)) (.f64 z (-.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 z (.f64 x y))) (/.f64 z (.f64 x y)))))))
(/.f64 (+.f64 (.f64 #s(literal -1/512 binary64) (.f64 z (.f64 z z))) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 x y) z) (/.f64 (.f64 x y) (.f64 z (/.f64 z (.f64 x y)))))) (.f64 z (.f64 z z)))) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 z z)) (.f64 (/.f64 z (/.f64 z (/.f64 (.f64 x y) #s(literal 2 binary64)))) (-.f64 (/.f64 z (/.f64 z (/.f64 (.f64 x y) #s(literal 2 binary64)))) (.f64 z #s(literal -1/8 binary64))))))
(/.f64 (+.f64 (.f64 #s(literal -1/512 binary64) (.f64 z (.f64 z z))) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 x y) z) (/.f64 (.f64 x y) (.f64 z (/.f64 z (.f64 x y)))))) (.f64 z (.f64 z z)))) (+.f64 (.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 z (.f64 x y))) (/.f64 z (.f64 x y))) (.f64 z z)) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 z z)) (.f64 (.f64 z #s(literal -1/8 binary64)) (/.f64 z (/.f64 z (/.f64 (*.f64 x y) #s(literal 2 binary64))))))))
(/.f64 (.f64 (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x y))))) (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) z)))) (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (*.f64 x y) #s(literal -2 binary64)) z))))
(/.f64 (.f64 z (+.f64 #s(literal -1/512 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 x y) z) (/.f64 (.f64 x y) (.f64 z (/.f64 z (.f64 x y)))))))) (+.f64 #s(literal 1/64 binary64) (.f64 (/.f64 (.f64 x y) z) (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 z (.f64 x y))) #s(literal -1/16 binary64)))))
(/.f64 (.f64 z (-.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 z (.f64 x y))) (/.f64 z (.f64 x y))))) (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) z)))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/512 binary64) (.f64 z (.f64 z z))) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 x y) z) (/.f64 (.f64 x y) (.f64 z (/.f64 z (.f64 x y)))))) (.f64 z (.f64 z z))))) (neg.f64 (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 z z)) (.f64 (/.f64 z (/.f64 z (/.f64 (.f64 x y) #s(literal 2 binary64)))) (-.f64 (/.f64 z (/.f64 z (/.f64 (.f64 x y) #s(literal 2 binary64)))) (.f64 z #s(literal -1/8 binary64)))))))
(/.f64 (neg.f64 (.f64 (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x y))))) (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) z))))) (neg.f64 (.f64 z (+.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (*.f64 x y) #s(literal -2 binary64)) z)))))
(/.f64 (neg.f64 (.f64 z (+.f64 #s(literal -1/512 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (.f64 x y) z) (/.f64 (.f64 x y) (.f64 z (/.f64 z (.f64 x y))))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (/.f64 (.f64 x y) z) (-.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 z (.f64 x y))) #s(literal -1/16 binary64))))))
(/.f64 (neg.f64 (.f64 z (-.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 z (.f64 x y))) (/.f64 z (.f64 x y)))))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 z (.f64 x y)))))
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(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 2 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal -2 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -2 binary64) y))
(.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) x))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) y)) #s(literal -2 binary64))
(.f64 (pow.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -2 binary64) y))
(exp.f64 (*.f64 (log.f64 (/.f64 y #s(literal 2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) y))
(neg.f64 (/.f64 #s(literal -2 binary64) y))
(neg.f64 (/.f64 (/.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal -2 binary64) y) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 y #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) y)
(/.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 y #s(literal -2 binary64)))
(/.f64 (/.f64 #s(literal -2 binary64) y) #s(literal -1 binary64))
(/.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) y))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64))
(pow.f64 (/.f64 y #s(literal 2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) y))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) y) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) y))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) y))
(.f64 #s(literal -2 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)))
(*.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -2 binary64))
(*.f64 (pow.f64 (/.f64 y #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)))))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) x)) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) y)) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(neg.f64 (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 x (/.f64 #s(literal 2 binary64) y))
(/.f64 y (/.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x y)))
(/.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal -2 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -2 binary64) y))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x y)) #s(literal -2 binary64))
(/.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 y #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (*.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))
(/.f64 (/.f64 y #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)) (/.f64 #s(literal -2 binary64) x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal -2 binary64) x))
(/.f64 (/.f64 y (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(/.f64 (/.f64 x (/.f64 #s(literal 1 binary64) y)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) (/.f64 #s(literal 2 binary64) (*.f64 x y))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)))) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal -1 binary64)))
(*.f64 #s(literal 1/2 binary64) (/.f64 y (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) y)))
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x y) #s(literal 1 binary64)))
(*.f64 x (/.f64 y #s(literal 2 binary64)))
(*.f64 y (/.f64 x #s(literal 2 binary64)))
(.f64 (.f64 x y) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 x #s(literal -2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) y) (.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 y #s(literal -2 binary64)))
(.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (/.f64 x #s(literal 2 binary64)) y)
(*.f64 (/.f64 x #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)))
(*.f64 (/.f64 y #s(literal 2 binary64)) x)
(.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) #s(literal -1 binary64))
(*.f64 (/.f64 y #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(*.f64 (/.f64 y #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 y #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 y #s(literal -2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)))
(.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x y)))
(*.f64 #s(literal -1/2 binary64) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) y)))
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -1/2 binary64) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) y))
(.f64 (/.f64 x #s(literal -2 binary64)) (.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64)))
(*.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) y)) (/.f64 x #s(literal -2 binary64)))
(*.f64 (/.f64 y (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 y #s(literal -2 binary64)))
(*.f64 (/.f64 y #s(literal -1 binary64)) (/.f64 x #s(literal -2 binary64)))
(*.f64 (/.f64 (/.f64 y #s(literal 2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (/.f64 y #s(literal -2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64)) (/.f64 x #s(literal -2 binary64)))
(*.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64))) (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) y)
(.f64 (.f64 (/.f64 y #s(literal -2 binary64)) #s(literal -1 binary64)) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) x))
(neg.f64 (/.f64 #s(literal -2 binary64) x))
(neg.f64 (/.f64 (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) x)
(/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 x #s(literal -2 binary64)))
(/.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -1 binary64))
(/.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -2 binary64))
(*.f64 (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -1/2 binary64)))

simplify254.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

3172×	`-lowering-.f32`
3172×	`-lowering-.f64`
1540×	`fmsub-define`
1454×	`fma-lowering-fma.f32`
1454×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	1378
1	207	1378
2	646	1378
3	1652	1378
4	4033	1378
0	8121	1378

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 1/2 (* x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* -1/8 z)
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* z (- (* 1/2 (/ (* x y) z)) 1/8))
(* -1/8 z)
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z)))))
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* x (+ (* -1/8 (/ z x)) (* 1/2 y)))
(* 1/2 (* x y))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x)))))
(* -1/8 z)
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(+ (* -1/8 z) (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* y (+ (* -1/8 (/ z y)) (* 1/2 x)))
(* 1/2 (* x y))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y)))))
-1/8
(- (* 1/2 (/ (* x y) z)) 1/8)
(- (* 1/2 (/ (* x y) z)) 1/8)
(- (* 1/2 (/ (* x y) z)) 1/8)
(* 1/2 (/ (* x y) z))
(* x (- (* 1/2 (/ y z)) (* 1/8 (/ 1 x))))
(* x (- (* 1/2 (/ y z)) (* 1/8 (/ 1 x))))
(* x (- (* 1/2 (/ y z)) (* 1/8 (/ 1 x))))
(* 1/2 (/ (* x y) z))
(* -1 (* x (+ (* -1/2 (/ y z)) (* 1/8 (/ 1 x)))))
(* -1 (* x (+ (* -1/2 (/ y z)) (* 1/8 (/ 1 x)))))
(* -1 (* x (+ (* -1/2 (/ y z)) (* 1/8 (/ 1 x)))))
-1/8
(- (* 1/2 (/ (* x y) z)) 1/8)
(- (* 1/2 (/ (* x y) z)) 1/8)
(- (* 1/2 (/ (* x y) z)) 1/8)
(* 1/2 (/ (* x y) z))
(* y (- (* 1/2 (/ x z)) (* 1/8 (/ 1 y))))
(* y (- (* 1/2 (/ x z)) (* 1/8 (/ 1 y))))
(* y (- (* 1/2 (/ x z)) (* 1/8 (/ 1 y))))
(* 1/2 (/ (* x y) z))
(* -1 (* y (+ (* -1/2 (/ x z)) (* 1/8 (/ 1 y)))))
(* -1 (* y (+ (* -1/2 (/ x z)) (* 1/8 (/ 1 y)))))
(* -1 (* y (+ (* -1/2 (/ x z)) (* 1/8 (/ 1 y)))))
(* 1/2 (/ (* x y) z))
(/ (+ (* -1/8 z) (* 1/2 (* x y))) z)
(/ (+ (* -1/8 z) (* 1/2 (* x y))) z)
(/ (+ (* -1/8 z) (* 1/2 (* x y))) z)
-1/8
(- (* 1/2 (/ (* x y) z)) 1/8)
(- (* 1/2 (/ (* x y) z)) 1/8)
(- (* 1/2 (/ (* x y) z)) 1/8)
-1/8
(- (* 1/2 (/ (* x y) z)) 1/8)
(- (* 1/2 (/ (* x y) z)) 1/8)
(- (* 1/2 (/ (* x y) z)) 1/8)
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(* 1/2 (/ (* x y) z))
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(/ (* x y) z)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 (* x y))
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(/ 2 y)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)

Outputs
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(+ (* -1/8 z) (* 1/2 (* x y)))
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(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)

eval83.0ms (1.6%)

Compiler: Compiled 10481 to 1266 computations (87.9% saved)

prune69.0ms (1.3%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	738	0	738
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	738	7	745

Accuracy

100.0%

Counts

745 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(/.f64 y (/.f64 #s(literal 2 binary64) x))
✓	49.6%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) x))
✓	100.0%	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
✓	99.8%	(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
✓	92.2%	(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
✓	49.8%	(.f64 #s(literal 1/2 binary64) (.f64 x y))
✓	51.5%	(*.f64 #s(literal -1/8 binary64) z)

Compiler

Compiled 143 to 85 computations (40.6% saved)

regimes27.0ms (0.5%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal -1/8 binary64) z)
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(/.f64 y (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) x))
(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64)))))
(fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal -8 binary64)))

Outputs
(fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal -8 binary64)))

Calls

7 calls:

5.0ms	(/.f64 (*.f64 x y) #s(literal 2 binary64))
4.0ms	(/.f64 z #s(literal 8 binary64))
4.0ms	y
4.0ms	x
4.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
100.0%	1	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
100.0%	1	`(*.f64 x y)`
100.0%	1	`(/.f64 z #s(literal 8 binary64))`

Compiler

Compiled 44 to 33 computations (25% saved)

regimes44.0ms (0.8%)

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal -1/8 binary64) z)
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(/.f64 y (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) x))
(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(.f64 z (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x y) z))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal -8 binary64)))))

Outputs
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Calls

7 calls:

18.0ms	x
9.0ms	(/.f64 z #s(literal 8 binary64))
3.0ms	z
3.0ms	y
3.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))`
100.0%	1	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
100.0%	1	`(*.f64 x y)`
100.0%	1	`(/.f64 z #s(literal 8 binary64))`

Compiler

Compiled 44 to 33 computations (25% saved)

regimes14.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal -1/8 binary64) z)
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(/.f64 y (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) x))
(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))

Outputs
(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))

Calls

5 calls:

3.0ms	x
3.0ms	z
3.0ms	(/.f64 z #s(literal 8 binary64))
2.0ms	(*.f64 x y)
2.0ms	y

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`z`
99.8%	1	`(*.f64 x y)`
99.8%	1	`(/.f64 z #s(literal 8 binary64))`

Compiler

Compiled 24 to 18 computations (25% saved)

regimes9.0ms (0.2%)

Counts

4 → 3

Calls

Call 1

Inputs
(*.f64 #s(literal -1/8 binary64) z)
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(/.f64 y (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) y) x))

Outputs
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(*.f64 #s(literal -1/8 binary64) z)
(.f64 #s(literal 1/2 binary64) (.f64 x y))

Calls

4 calls:

2.0ms	x
2.0ms	z
2.0ms	y
2.0ms	(*.f64 x y)

Results

Accuracy	Segments	Branch
72.4%	3	`x`
73.4%	3	`y`
75.2%	3	`z`
80.3%	3	`(*.f64 x y)`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes5.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal -1/8 binary64) z)

Outputs
(*.f64 #s(literal -1/8 binary64) z)

Calls

3 calls:

2.0ms	x
1.0ms	y
1.0ms	z

Results

Accuracy	Segments	Branch
51.5%	1	`x`
51.5%	1	`y`
51.5%	1	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch0.0ms (0%)

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	6.133683786846046e-79	3.2409619545132523e-78
0.0ms	-2.276152981013298e+21	-95349573368314770.0

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	50
1	35	50
2	45	50
3	51	50
4	56	50
5	58	50

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal -8 binary64)))
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
(if (<=.f64 (.f64 x y) #s(literal -2000000000000000000000 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x y)) (if (<=.f64 (.f64 x y) #s(literal 8343699359066055/8343699359066055009355553539724812947666814540455674882605631280555545803830627148527195652096 binary64)) (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y))))
(*.f64 #s(literal -1/8 binary64) z)

Outputs
(fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal -8 binary64)))
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(-.f64 (/.f64 x (/.f64 #s(literal 2 binary64) y)) (/.f64 z #s(literal 8 binary64)))
(if (<=.f64 (.f64 x y) #s(literal -2000000000000000000000 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x y)) (if (<=.f64 (.f64 x y) #s(literal 8343699359066055/8343699359066055009355553539724812947666814540455674882605631280555545803830627148527195652096 binary64)) (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y))))
(if (<=.f64 (.f64 y x) #s(literal -2000000000000000000000 binary64)) (.f64 (.f64 y x) #s(literal 1/2 binary64)) (if (<=.f64 (.f64 y x) #s(literal 8343699359066055/8343699359066055009355553539724812947666814540455674882605631280555545803830627148527195652096 binary64)) (.f64 z #s(literal -1/8 binary64)) (.f64 (*.f64 y x) #s(literal 1/2 binary64))))
(*.f64 #s(literal -1/8 binary64) z)
(*.f64 z #s(literal -1/8 binary64))

soundness990.0ms (18.4%)

Rules

4654×	`-lowering-.f32`
4654×	`-lowering-.f64`
3062×	`/-lowering-/.f32`
3062×	`/-lowering-/.f64`
2038×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	481
1	132	481
2	400	481
3	1073	481
4	2981	481
5	5790	481
0	8174	481
0	9	20
1	52	19
2	513	19
0	9018	19

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 100 to 59 computations (41% saved)

preprocess38.0ms (0.7%)

Remove: (sort x y)
Compiler: Compiled 204 to 118 computations (42.2% saved)

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

analyze0.0ms (0%)

sample722.0ms (13.4%)

preprocess121.0ms (2.3%)

explain71.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify48.0ms (0.9%)

localize32.0ms (0.6%)

series7.0ms (0.1%)

rewrite327.0ms (6.1%)

simplify241.0ms (4.5%)

eval51.0ms (1%)

prune50.0ms (0.9%)

simplify70.0ms (1.3%)

localize135.0ms (2.5%)

series12.0ms (0.2%)

rewrite409.0ms (7.6%)

simplify444.0ms (8.3%)

eval233.0ms (4.3%)

prune191.0ms (3.5%)

simplify263.0ms (4.9%)

localize65.0ms (1.2%)

series42.0ms (0.8%)

rewrite297.0ms (5.5%)

simplify254.0ms (4.7%)

eval83.0ms (1.6%)

prune69.0ms (1.3%)

regimes27.0ms (0.5%)

regimes44.0ms (0.8%)

regimes14.0ms (0.3%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

simplify10.0ms (0.2%)

soundness990.0ms (18.4%)

preprocess38.0ms (0.7%)

end0.0ms (0%)

Profiling