Metrics for Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

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 10 to 6 computations (40% saved)

Precisions

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

ival-add: 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)

sample1.0s (32.8%)

Results

800.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-add: 154.0ms (65.9% of total)

ival-mult: 69.0ms (29.5% of total)

const: 7.0ms (3% of total)

backward-pass: 3.0ms (1.3% of total)

Bogosity

preprocess30.0ms (1%)

Algorithm

2×	egg-herbie

Rules

124×	`sub-neg`
110×	`unsub-neg`
72×	`associate-+l-`
64×	`distribute-rgt-in`
54×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	51	43
2	152	42
3	358	42
4	531	42
5	660	42
6	686	42
0	5	7
1	9	7
2	12	7
3	13	7
0	13	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (+ (* x x) y) y)

Outputs
(+ (+ (* x x) y) y)
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))

Call 2

Inputs
(+ (+ (* x x) y) y)
(+ (+ (* (neg x) (neg x)) y) y)
(+ (+ (* x x) (neg y)) (neg y))
(neg (+ (+ (* (neg x) (neg x)) y) y))
(neg (+ (+ (* x x) (neg y)) (neg y)))
(+ (+ (* y y) x) x)

Outputs
(+ (+ (* x x) y) y)
(+ (* x x) (+ y y))
(+ (+ (* (neg x) (neg x)) y) y)
(+ (* x x) (+ y y))
(+ (+ (* x x) (neg y)) (neg y))
(- (* x x) (+ y y))
(neg (+ (+ (* (neg x) (neg x)) y) y))
(- (* y -2) (* x x))
(neg (+ (+ (* x x) (neg y)) (neg y)))
(- (+ y y) (* x x))
(+ (+ (* y y) x) x)
(+ x (+ x (* y y)))

Symmetry

(abs x)

explain55.0ms (1.8%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`y`
-	-	`(+.f64 (+.f64 (*.f64 x x) y) y)`
-	-	`(+.f64 (*.f64 x x) y)`

Results

30.0ms

512×

valid

Compiler

Compiled 49 to 17 computations (65.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-add: 7.0ms (58.5% of total)

ival-mult: 4.0ms (33.5% of total)

const: 1.0ms (8.4% of total)

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

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))

Compiler

Compiled 18 to 11 computations (38.9% saved)

localize56.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (*.f64 x x) y)
✓	cost-diff	0	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	cost-diff	0	(*.f64 y #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)
✓	accuracy	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	accuracy	100.0%	(*.f64 y #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))

Rules

14×	`+-lowering-+.f64`
14×	`+-lowering-+.f32`
8×	`accelerator-lowering-fma.f32`
8×	`accelerator-lowering-fma.f64`
6×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	14	28
2	14	28
0	14	25

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* x x) (* y 2))
(* x x)
x
(* y 2)
y
2
(+ (+ (* x x) y) y)
(+ (* x x) y)

Outputs
(+ (* x x) (* y 2))
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
(* x x)
(*.f64 x x)
x
(* y 2)
(*.f64 y #s(literal 2 binary64))
y
2
#s(literal 2 binary64)
(+ (+ (* x x) y) y)
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
(+ (* x x) y)
(+.f64 (*.f64 x x) y)

Results

30.0ms

256×

valid

Compiler

Compiled 36 to 12 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 7.0ms (58.7% of total)

ival-add: 4.0ms (33.5% of total)

const: 1.0ms (8.4% of total)

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

series8.0ms (0.2%)

Counts

5 → 96

Calls

Call 1

Inputs
#<alt (+ (* x x) (* y 2))>
#<alt (* x x)>
#<alt (* y 2)>
#<alt (+ (+ (* x x) y) y)>
#<alt (+ (* x x) y)>

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

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	y	@	inf	(* y 2)
0.0ms	x	@	0	(+ (* x x) (* y 2))
0.0ms	x	@	inf	(+ (* x x) (* y 2))
0.0ms	y	@	0	(+ (* x x) (* y 2))
0.0ms	y	@	-inf	(* y 2)

rewrite764.0ms (24.6%)

Algorithm

1×	batch-egg-rewrite

Rules

8266×	`accelerator-lowering-fma.f32`
8266×	`accelerator-lowering-fma.f64`
3972×	`-lowering-.f32`
3972×	`-lowering-.f64`
2916×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	48	25
2	449	25
3	7017	25
0	8176	22

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 635

Calls

Call 1

Inputs
(+ (* x x) (* y 2))
(* x x)
(* y 2)
(+ (+ (* x x) y) y)
(+ (* x x) y)

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

simplify403.0ms (12.9%)

Algorithm

1×	egg-herbie

Rules

4690×	`accelerator-lowering-fma.f32`
4690×	`accelerator-lowering-fma.f64`
3340×	`-lowering-.f32`
3340×	`-lowering-.f64`
1326×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	462
1	80	462
2	193	462
3	654	462
4	1927	462
5	3632	462
6	6731	462
0	8180	408

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 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)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(pow x 2)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* y (+ 2 (/ (pow x 2) y)))
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

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

eval120.0ms (3.9%)

Compiler: Compiled 18886 to 6135 computations (67.5% saved)

prune70.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	746	3	749
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	746	5	751

Accuracy

100.0%

Counts

751 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
▶	59.2%	(+.f64 (*.f64 x x) y)
▶	50.0%	(+.f64 y y)
▶	51.8%	(*.f64 x x)

Compiler

Compiled 35 to 21 computations (40% saved)

localize34.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (*.f64 x x) y)
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(*.f64 x x)

Rules

6×	`+-lowering-+.f64`
6×	`-lowering-.f32`
6×	`-lowering-.f64`
6×	`+-lowering-+.f32`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	8	13
2	9	13
0	9	12

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x x)
x
(+ y y)
y
(+ (* x x) y)

Outputs
(* x x)
(*.f64 x x)
x
(+ y y)
(*.f64 y #s(literal 2 binary64))
y
(+ (* x x) y)
(+.f64 (*.f64 x x) y)

Results

16.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-add: 2.0ms (38.5% of total)

ival-mult: 2.0ms (38.5% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Counts

3 → 48

Calls

Call 1

Inputs
#<alt (* x x)>
#<alt (+ y y)>
#<alt (+ (* x x) y)>

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

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	y	@	inf	(+ y y)
0.0ms	y	@	0	(+ y y)
0.0ms	x	@	0	(* x x)
0.0ms	y	@	-inf	(+ y y)
0.0ms	x	@	0	(+ (* x x) y)

rewrite79.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

94×	`accelerator-lowering-fma.f32`
94×	`accelerator-lowering-fma.f64`
92×	`-lowering-.f32`
92×	`-lowering-.f64`
74×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	28	11
0	219	10

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

3 → 30

Calls

Call 1

Inputs
(* x x)
(+ y y)
(+ (* x x) y)

Outputs
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(+.f64 y y)
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 y (.f64 y y))) (+.f64 (.f64 y y) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (.f64 y (.f64 y y)))) (neg.f64 (+.f64 (.f64 y y) #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 y y) #s(literal 0 binary64)) (.f64 #s(literal 2 binary64) (.f64 y (.f64 y y)))))
(*.f64 y #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) y)
(.f64 (.f64 #s(literal 2 binary64) (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))
(fma.f64 x x y)
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) y)
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 y (.f64 y y))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 y (.f64 y y))) (+.f64 (.f64 y y) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (*.f64 x x) y))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y y)) (-.f64 (*.f64 x x) y))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 y (.f64 y y)))) (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y y))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 y (.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x x) y) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (*.f64 y y))))
(/.f64 (-.f64 (.f64 y y) (.f64 (.f64 x x) (.f64 x x))) (-.f64 y (*.f64 x x)))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y (-.f64 y (*.f64 x x))))))
(.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 y y)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)))

simplify294.0ms (9.5%)

Algorithm

1×	egg-herbie

Rules

3894×	`-lowering-.f32`
3894×	`-lowering-.f64`
3312×	`accelerator-lowering-fma.f32`
3312×	`accelerator-lowering-fma.f64`
2140×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	174
1	50	174
2	112	174
3	379	174
4	1173	174
5	2511	174
6	4825	174
7	6262	174
0	8015	156

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

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

eval9.0ms (0.3%)

Compiler: Compiled 680 to 147 computations (78.4% saved)

prune7.0ms (0.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	93	6	99

Accuracy

100.0%

Counts

99 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
✓	59.2%	(+.f64 (*.f64 x x) y)
✓	50.0%	(+.f64 y y)
✓	51.8%	(*.f64 x x)
▶	10.7%	y

Compiler

Compiled 38 to 23 computations (39.5% saved)

localize12.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
y

Outputs
y

Results

5.0ms

256×

valid

Compiler

Compiled 4 to 3 computations (25% saved)

Precisions

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

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite28.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	5	5
Total	6	6

Accuracy

100.0%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
✓	59.2%	(+.f64 (*.f64 x x) y)
✓	50.0%	(+.f64 y y)
✓	51.8%	(*.f64 x x)
✓	10.7%	y

Compiler

Compiled 66 to 32 computations (51.5% saved)

regimes11.0ms (0.4%)

Counts

6 → 1

Calls

Call 1

Inputs
y
(*.f64 x x)
(+.f64 y y)
(+.f64 (*.f64 x x) y)
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
(+.f64 (+.f64 (*.f64 x x) y) y)

Outputs
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))

Calls

4 calls:

4.0ms	(*.f64 x x)
2.0ms	y
2.0ms	x
2.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 20 to 12 computations (40% saved)

regimes14.0ms (0.4%)

Counts

4 → 2

Calls

Call 1

Inputs
y
(*.f64 x x)
(+.f64 y y)
(+.f64 (*.f64 x x) y)

Outputs
(+.f64 y y)
(+.f64 (*.f64 x x) y)

Calls

3 calls:

6.0ms	y
4.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
88.1%	2	`x`
68.9%	3	`y`
88.1%	2	`(*.f64 x x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0.2%)

Counts

3 → 2

Calls

Call 1

Inputs
y
(*.f64 x x)
(+.f64 y y)

Outputs
(+.f64 y y)
(*.f64 x x)

Calls

2 calls:

3.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
87.0%	2	`x`
87.0%	2	`(*.f64 x x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes10.0ms (0.3%)

Counts

2 → 2

Calls

Call 1

Inputs
y
(*.f64 x x)

Outputs
y
(*.f64 x x)

Calls

3 calls:

6.0ms	y
2.0ms	x
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
51.8%	1	`y`
56.1%	2	`x`
56.1%	2	`(*.f64 x x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
y

Outputs
y

Calls

2 calls:

0.0ms	x
0.0ms	y

Results

Accuracy	Segments	Branch
10.7%	1	`y`
10.7%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch4.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	5.120780945060652e-72	6.619056960164376e-72

Results

2.0ms

48×

valid

Compiler

Compiled 50 to 33 computations (34% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-add: 1.0ms (173.6% of total)

const: 0.0ms (0% of total)

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

bsearch13.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	6.695494111974001e-50	3.1862929457275477e-49

Results

4.0ms

96×

valid

Compiler

Compiled 74 to 51 computations (31.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-add: 1.0ms (86.8% of total)

const: 0.0ms (0% of total)

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

bsearch10.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	2.6181044883891426e-204	1.2738688432090924e-198

Results

5.0ms

144×

valid

Compiler

Compiled 86 to 63 computations (26.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 2.0ms (116.1% of total)

const: 0.0ms (0% of total)

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

soundness1.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 46 to 17 computations (63% saved)

preprocess43.0ms (1.4%)

Remove: (abs x)
Compiler: Compiled 182 to 90 computations (50.5% saved)

Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

analyze0.0ms (0%)

sample1.0s (32.8%)

preprocess30.0ms (1%)

explain55.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize56.0ms (1.8%)

series8.0ms (0.2%)

rewrite764.0ms (24.6%)

simplify403.0ms (12.9%)

eval120.0ms (3.9%)

prune70.0ms (2.2%)

localize34.0ms (1.1%)

series3.0ms (0.1%)

rewrite79.0ms (2.5%)

simplify294.0ms (9.5%)

eval9.0ms (0.3%)

prune7.0ms (0.2%)

localize12.0ms (0.4%)

series0.0ms (0%)

rewrite28.0ms (0.9%)

simplify3.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes11.0ms (0.4%)

regimes14.0ms (0.4%)

regimes5.0ms (0.2%)

regimes10.0ms (0.3%)

regimes1.0ms (0%)

bsearch4.0ms (0.1%)

bsearch13.0ms (0.4%)

bsearch10.0ms (0.3%)

soundness1.0ms (0%)

preprocess43.0ms (1.4%)

end0.0ms (0%)

Profiling