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)

sample1.1s (42.4%)

Results

716.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 427.0ms

ival-sub: 181.0ms (42.4% of total)

ival-div: 131.0ms (30.7% of total)

ival-mult: 97.0ms (22.7% of total)

const: 16.0ms (3.7% of total)

backward-pass: 3.0ms (0.7% of total)

Bogosity

preprocess124.0ms (4.8%)

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)

explain111.0ms (4.3%)

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

78.0ms

512×

valid

Compiler

Compiled 70 to 29 computations (58.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-div: 7.0ms (38.8% of total)

ival-sub: 6.0ms (33.3% of total)

ival-mult: 5.0ms (27.7% of total)

const: 1.0ms (5.5% 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)

simplify47.0ms (1.8%)

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)

localize30.0ms (1.2%)

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 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
✓	accuracy	100.0%	(*.f64 x y)

Results

22.0ms

256×

valid

Compiler

Compiled 29 to 10 computations (65.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 3.0ms (40.1% of total)

ival-mult: 2.0ms (26.7% of total)

ival-sub: 1.0ms (13.4% of total)

const: 0.0ms (0% of total)

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

series17.0ms (0.6%)

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
8.0ms	y	@	inf	(- (/ (* x y) 2) (/ z 8))
3.0ms	y	@	-inf	(- (/ (* x y) 2) (/ z 8))
1.0ms	x	@	inf	(/ (* x y) 2)
1.0ms	x	@	0	(- (/ (* x y) 2) (/ z 8))
0.0ms	x	@	inf	(- (/ (* x y) 2) (/ z 8))

rewrite261.0ms (10.1%)

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	515	19
0	9051	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 (.f64 x y) #s(literal 8 binary64)) #s(literal 16 binary64)) (neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) z) #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 (.f64 x y) #s(literal 8 binary64)) #s(literal 16 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) z) #s(literal 16 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x y) #s(literal 8 binary64)) #s(literal 16 binary64)) (-.f64 (/.f64 (*.f64 #s(literal 2 binary64) z) #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 #s(literal 2 binary64) z) #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 #s(literal 2 binary64) z) #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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(neg.f64 (.f64 (/.f64 (.f64 x y) #s(literal -2 binary64)) #s(literal 1 binary64)))
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(/.f64 x (/.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
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(*.f64 (/.f64 y #s(literal 2 binary64)) x)
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(*.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) x))
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(/.f64 z #s(literal 8 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 8 binary64) z))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -8 binary64) z))
(/.f64 (-.f64 #s(literal 0 binary64) z) #s(literal -8 binary64))
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(*.f64 z #s(literal 1/8 binary64))
(*.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 1 binary64))
(*.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))
(*.f64 (pow.f64 (/.f64 #s(literal 8 binary64) z) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 8 binary64) z) #s(literal -1/2 binary64)))

simplify135.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

1994×	`fmsub-define`
1950×	`-lowering-.f32`
1950×	`-lowering-.f64`
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	8068	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))

eval38.0ms (1.5%)

Compiler: Compiled 5711 to 635 computations (88.9% saved)

prune31.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	313	2	315
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	313	3	316

Accuracy

100.0%

Counts

316 → 3

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)))
▶	52.8%	(.f64 #s(literal 1/2 binary64) (.f64 x y))
▶	48.9%	(*.f64 #s(literal -1/8 binary64) z)

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

28×	`-lowering-.f32`
28×	`-lowering-.f64`
12×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	13	16
2	20	16
3	22	16
0	22	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize86.0ms (3.3%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	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)

Results

79.0ms

256×

valid

Compiler

Compiled 20 to 9 computations (55% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 5.0ms (83.1% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

3 → 60

Calls

Call 1

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

Outputs
#<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)>

Calls

15 calls:

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

rewrite42.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

28×	`-lowering-.f32`
28×	`-lowering-.f64`
12×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	13	11
2	20	11
3	22	11
0	22	11

Stop Event

1×	iter limit
1×	saturated

Counts

3 → 10

Calls

Call 1

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

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

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`-lowering-.f32`
28×	`-lowering-.f64`
12×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	228
1	13	228
2	20	228
3	22	228
0	22	228

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

Inputs
(* -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)

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

eval6.0ms (0.2%)

Compiler: Compiled 325 to 18 computations (94.5% saved)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	70	3	73

Accuracy

100.0%

Counts

73 → 3

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)))
✓	52.8%	(.f64 #s(literal 1/2 binary64) (.f64 x y))
✓	48.9%	(*.f64 #s(literal -1/8 binary64) z)

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes127.0ms (4.9%)

Counts

3 → 1

Calls

Call 1

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

116.0ms	(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
2.0ms	(/.f64 z #s(literal 8 binary64))
2.0ms	z
2.0ms	(*.f64 x y)
2.0ms	y

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)

regimes7.0ms (0.3%)

Counts

2 → 3

Calls

Call 1

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

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	y
2.0ms	z
1.0ms	(*.f64 x y)

Results

Accuracy	Segments	Branch
76.7%	3	`x`
77.2%	3	`y`
72.7%	3	`z`
83.0%	3	`(*.f64 x y)`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes5.0ms (0.2%)

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:

3.0ms	z
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
48.9%	1	`z`
48.9%	1	`x`
48.9%	1	`y`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch12.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	6.979616082003686e+32	1.0476939961749533e+36
0.0ms	-3.9325738585859684e+52	-3.783100764838196e+52

Results

6.0ms

128×

valid

Compiler

Compiled 130 to 110 computations (15.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 2.0ms (79.2% of total)

ival-sub: 1.0ms (39.6% of total)

const: 0.0ms (0% of total)

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

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	33
1	27	33
2	36	33
3	42	33
4	47	33
5	49	33

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (*.f64 x y) #s(literal -37999999999999999742396049625741863105544920793874432 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x y)) (if (<=.f64 (*.f64 x y) #s(literal 94999999999999998864872209893031936 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
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64)))
(if (<=.f64 (.f64 x y) #s(literal -37999999999999999742396049625741863105544920793874432 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x y)) (if (<=.f64 (.f64 x y) #s(literal 94999999999999998864872209893031936 binary64)) (.f64 #s(literal -1/8 binary64) z) (.f64 #s(literal 1/2 binary64) (*.f64 x y))))
(if (<=.f64 (.f64 x y) #s(literal -37999999999999999742396049625741863105544920793874432 binary64)) (.f64 (.f64 x y) #s(literal 1/2 binary64)) (if (<=.f64 (.f64 x y) #s(literal 94999999999999998864872209893031936 binary64)) (.f64 z #s(literal -1/8 binary64)) (.f64 (*.f64 x y) #s(literal 1/2 binary64))))
(*.f64 #s(literal -1/8 binary64) z)
(*.f64 z #s(literal -1/8 binary64))

soundness352.0ms (13.6%)

Rules

1994×	`fmsub-define`
1950×	`-lowering-.f32`
1950×	`-lowering-.f64`
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	8068	481

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 60 to 35 computations (41.7% saved)

preprocess29.0ms (1.1%)

Remove: (sort x y)
Compiler: Compiled 176 to 110 computations (37.5% saved)

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

analyze0.0ms (0%)

sample1.1s (42.4%)

preprocess124.0ms (4.8%)

explain111.0ms (4.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify47.0ms (1.8%)

localize30.0ms (1.2%)

series17.0ms (0.6%)

rewrite261.0ms (10.1%)

simplify135.0ms (5.2%)

eval38.0ms (1.5%)

prune31.0ms (1.2%)

simplify5.0ms (0.2%)

localize86.0ms (3.3%)

series1.0ms (0%)

rewrite42.0ms (1.6%)

simplify8.0ms (0.3%)

eval6.0ms (0.2%)

prune3.0ms (0.1%)

regimes127.0ms (4.9%)

regimes7.0ms (0.3%)

regimes5.0ms (0.2%)

bsearch12.0ms (0.5%)

simplify8.0ms (0.3%)

soundness352.0ms (13.6%)

preprocess29.0ms (1.1%)

end0.0ms (0%)

Profiling