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)

sample595.0ms (17.5%)

Results

395.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 178.0ms

ival-add: 85.0ms (47.7% of total)

ival-mult: 83.0ms (46.6% of total)

const: 7.0ms (3.9% of total)

backward-pass: 3.0ms (1.7% of total)

Bogosity

preprocess54.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

844×	`sum5-define`
752×	`fnmadd-define`
752×	`sum4-define`
716×	`fmsub-define`
690×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	59	37
2	184	36
3	637	36
4	1784	36
5	2827	36
6	3246	36
7	3320	36
0	5	6
1	11	6
2	16	6
3	19	6
4	20	6
0	20	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)
(+ y (fma x x y))
(+ (+ (* (neg x) (neg x)) y) y)
(+ y (fma x x y))
(+ (+ (* x x) (neg y)) (neg y))
(- (fmsub x x y) y)
(neg (+ (+ (* (neg x) (neg x)) y) y))
(- (fnmsub x x y) y)
(neg (+ (+ (* x x) (neg y)) (neg y)))
(fnmsub y -2 (* x x))
(+ (+ (* y y) x) x)
(+ x (fma y y x))

Symmetry

(abs x)

explain59.0ms (1.7%)

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

32.0ms

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: 6.0ms (50.9% of total)

ival-mult: 5.0ms (42.4% of total)

const: 1.0ms (8.5% 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 x x) (.f64 y #s(literal 2 binary64)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

6×	`fma-lowering-fma.f32`
6×	`fma-define`
6×	`-lowering-.f32`
6×	`-lowering-.f64`
6×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	9	15
2	11	15
0	11	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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)

localize37.0ms (1.1%)

Localize:

Found 3 expressions of interest:

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

Results

29.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

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

ival-mult: 5.0ms (74.7% of total)

ival-add: 1.0ms (14.9% 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) (* y 2))>
#<alt (* x x)>
#<alt (* y 2)>

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)>

Calls

12 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)

rewrite307.0ms (9%)

Algorithm

1×	batch-egg-rewrite

Rules

2464×	`-lowering-.f32`
2464×	`-lowering-.f64`
2180×	`/-lowering-/.f32`
2180×	`/-lowering-/.f64`
1716×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	23	12
2	203	12
3	2310	12
0	8379	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 131

Calls

Call 1

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

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

simplify188.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

2194×	`/-lowering-/.f32`
2194×	`/-lowering-/.f64`
1946×	`-lowering-.f32`
1946×	`-lowering-.f64`
1060×	`distribute-frac-neg2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	198
1	56	198
2	146	198
3	479	198
4	1527	198
5	3992	198
0	8155	198

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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)

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)

eval19.0ms (0.6%)

Compiler: Compiled 6903 to 425 computations (93.8% saved)

prune19.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	177	3	180

Accuracy

100.0%

Counts

180 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
▶	54.5%	(*.f64 x x)
▶	47.0%	(*.f64 #s(literal 2 binary64) y)

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	6	9
0	6	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize22.0ms (0.6%)

Localize:

Found 2 expressions of interest:

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

Results

16.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-mult: 6.0ms (95.6% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

2 → 24

Calls

Call 1

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

Outputs
#<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 (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)>

Calls

6 calls:

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

rewrite140.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1432×	`prod-exp`
1308×	`-lowering-.f32`
1308×	`-lowering-.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6
2	14	6
3	30	6
4	78	6
5	235	4
6	1663	4
7	1692	4
8	1822	4
9	3085	4
0	8384	4

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 4

Calls

Call 1

Inputs
(* 2 y)
(* x x)

Outputs
(*.f64 #s(literal 2 binary64) y)
(*.f64 y #s(literal 2 binary64))
#s(literal 1 binary64)
x

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	7	72
0	7	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(* 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)
(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)

Outputs
(* 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)
(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)

eval4.0ms (0.1%)

Compiler: Compiled 82 to 7 computations (91.5% saved)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	26	5	31

Accuracy

100.0%

Counts

31 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
✓	54.5%	(*.f64 x x)
✓	47.0%	(*.f64 #s(literal 2 binary64) y)
▶	5.6%	x
▶	3.8%	#s(literal 1 binary64)

Compiler

Compiled 25 to 18 computations (28% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	4	2
0	4	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
1
x

Outputs
1
#s(literal 1 binary64)
x

localize11.0ms (0.3%)

Results

8.0ms

256×

valid

Compiler

Compiled 5 to 4 computations (20% 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

rewrite10.0ms (0.3%)

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)

prune6.0ms (0.2%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	3	3
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
✓	54.5%	(*.f64 x x)
✓	47.0%	(*.f64 #s(literal 2 binary64) y)
✓	5.6%	x
✓	3.8%	#s(literal 1 binary64)

Compiler

Compiled 49 to 28 computations (42.9% saved)

regimes11.0ms (0.3%)

Counts

6 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) y)
(*.f64 x x)
(+.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:

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

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)

regimes9.0ms (0.3%)

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) y)
(*.f64 x x)

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
90.1%	2	`x`
69.2%	5	`y`
90.1%	2	`(*.f64 x x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes4.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) y)

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
47.0%	1	`y`
47.0%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x

Outputs
x

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
5.6%	1	`x`
5.6%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

3.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
3.8%	1	`x`
3.8%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	359476648159.4196	4170668077098.3257

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	16	24

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 500000000000 binary64)) (.f64 #s(literal 2 binary64) y) (*.f64 x x))
(*.f64 #s(literal 2 binary64) y)
x
#s(literal 1 binary64)

Outputs
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 500000000000 binary64)) (.f64 #s(literal 2 binary64) y) (*.f64 x x))
(if (<=.f64 (.f64 x x) #s(literal 500000000000 binary64)) (.f64 y #s(literal 2 binary64)) (*.f64 x x))
(*.f64 #s(literal 2 binary64) y)
(*.f64 y #s(literal 2 binary64))
x
#s(literal 1 binary64)

soundness1.8s (53.4%)

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
2194×	`/-lowering-/.f32`
2194×	`/-lowering-/.f64`
1946×	`-lowering-.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	11	6
2	16	6
3	19	6
4	20	6
0	20	6
0	19	198
1	56	198
2	146	198
3	479	198
4	1527	198
5	3992	198
0	8155	198
0	5	6
1	7	6
2	14	6
3	30	6
4	78	6
5	235	4
6	1663	4
7	1692	4
8	1822	4
9	3085	4
0	8384	4

Stop Event

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

Compiler

Compiled 108 to 65 computations (39.8% saved)

preprocess45.0ms (1.3%)

Remove: (abs x)
Compiler: Compiled 142 to 76 computations (46.5% saved)

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

analyze0.0ms (0%)

sample595.0ms (17.5%)

preprocess54.0ms (1.6%)

explain59.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize37.0ms (1.1%)

series3.0ms (0.1%)

rewrite307.0ms (9%)

simplify188.0ms (5.5%)

eval19.0ms (0.6%)

prune19.0ms (0.6%)

simplify4.0ms (0.1%)

localize22.0ms (0.6%)

series0.0ms (0%)

rewrite140.0ms (4.1%)

simplify6.0ms (0.2%)

eval4.0ms (0.1%)

prune3.0ms (0.1%)

simplify4.0ms (0.1%)

localize11.0ms (0.3%)

series0.0ms (0%)

rewrite10.0ms (0.3%)

simplify3.0ms (0.1%)

eval0.0ms (0%)

prune6.0ms (0.2%)

regimes11.0ms (0.3%)

regimes9.0ms (0.3%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

simplify8.0ms (0.2%)

soundness1.8s (53.4%)

preprocess45.0ms (1.3%)

end0.0ms (0%)

Profiling