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)

sample704.0ms (26.7%)

Results

526.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 215.0ms

ival-mult: 117.0ms (54.5% of total)

ival-add: 88.0ms (41% of total)

const: 7.0ms (3.3% of total)

backward-pass: 3.0ms (1.4% of total)

Bogosity

preprocess57.0ms (2.2%)

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	34
1	62	33
2	187	32
3	640	30
4	1788	30
5	2819	30
6	3238	30
7	3312	30
0	5	5
1	12	5
2	17	5
3	20	5
4	21	5
0	21	5

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)
(sum3 (square x) y y)
(+ (+ (* (neg x) (neg x)) y) y)
(sum3 (square x) y y)
(+ (+ (* x x) (neg y)) (neg y))
(fma y -2 (square x))
(neg (+ (+ (* (neg x) (neg x)) y) y))
(fnmsub y 2 (square x))
(neg (+ (+ (* x x) (neg y)) (neg y)))
(fnmsub y -2 (square x))
(+ (+ (* y y) x) x)
(sum3 x x (square y))

Symmetry

(abs x)

explain102.0ms (3.9%)

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

60.0ms

512×

valid

Compiler

Compiled 49 to 17 computations (65.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-add: 8.0ms (61.4% of total)

ival-mult: 5.0ms (38.4% of total)

const: 0.0ms (0% 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)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(+.f64 (*.f64 x x) y)
✓	cost-diff	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	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

14×	`+-lowering-+.f64`
14×	`+-lowering-+.f32`
10×	`fma-define`
8×	`fma-lowering-fma.f32`
8×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	18	26
2	22	26
3	23	26
0	23	26

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)
(* x 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)
(* x x)
(*.f64 x x)
x
y

localize46.0ms (1.7%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	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)))

Results

31.0ms

256×

valid

Compiler

Compiled 36 to 9 computations (75% saved)

Precisions

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

ival-add: 4.0ms (48% of total)

ival-mult: 4.0ms (48% of total)

const: 0.0ms (0% of total)

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

series6.0ms (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
2.0ms	x	@	inf	(+ (* x x) (* y 2))
0.0ms	y	@	inf	(* y 2)
0.0ms	x	@	0	(+ (* x x) (* y 2))
0.0ms	y	@	0	(+ (* x x) (* y 2))
0.0ms	y	@	-inf	(* y 2)

rewrite312.0ms (11.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4020×	`-lowering-.f32`
4020×	`-lowering-.f64`
2944×	`/-lowering-/.f32`
2944×	`/-lowering-/.f64`
1414×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	52	19
2	511	19
0	8388	19

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 421

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 #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 x) y) y)
(+.f64 (+.f64 (*.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(+.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 x x) (-.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.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) (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) y)) (-.f64 #s(literal 0 binary64) (.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 y #s(literal 2 binary64) (*.f64 x x))
(fma.f64 #s(literal 2 binary64) y (*.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 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y)) y)
(neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(neg.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64)))))))
(neg.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 0 binary64)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64)))))) (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64))))))
(neg.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 0 binary64)))) (+.f64 (.f64 x x) #s(literal 0 binary64))))
(/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64))))) (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64)))))
(/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (+.f64 (.f64 x x) #s(literal 0 binary64)))
(/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (neg.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (-.f64 #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 (neg.f64 (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64)))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64))))))
(/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 0 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 0 binary64))))
(/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))) (.f64 (+.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 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.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 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 x (.f64 x (.f64 x x)))))))))
(/.f64 (+.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (.f64 (.f64 (+.f64 (.f64 x x) y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) y))) (.f64 (+.f64 (.f64 x x) y) (.f64 (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) y)) (.f64 (+.f64 (.f64 x x) y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) y))))))) (.f64 (+.f64 (.f64 y y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) #s(literal 0 binary64)))) (+.f64 (.f64 (+.f64 (.f64 x x) y) (.f64 (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) y)) (.f64 (+.f64 (.f64 x x) y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (.f64 x x) y))))) (.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 (+.f64 (.f64 x x) y) (.f64 (+.f64 (.f64 x x) y) (+.f64 (*.f64 x x) y))))))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (.f64 (+.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 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))))
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(/.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) (.f64 (+.f64 (.f64 y y) (.f64 (.f64 x x) (-.f64 (.f64 x x) y))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) y)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (.f64 x x)) (-.f64 (.f64 y y) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (.f64 (-.f64 (.f64 x x) y) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y y) (+.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 y y))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (.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 (.f64 x (.f64 x x))))) (.f64 y (.f64 y y)))))
(/.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) (-.f64 y (*.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 y (.f64 y (.f64 y y)))) (.f64 (-.f64 (.f64 x x) y) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) y))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 y (.f64 y (.f64 y y)))) #s(literal 1 binary64)) (.f64 (+.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))) #s(literal 1 binary64)) (+.f64 (.f64 y y) (.f64 (.f64 x x) (-.f64 (.f64 x x) y))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)) #s(literal 1 binary64)) (-.f64 (.f64 x x) y))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (+.f64 (.f64 y y) (.f64 (.f64 x x) (-.f64 (.f64 x x) y)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y y) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))) (-.f64 (.f64 x x) y)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y))) (+.f64 (.f64 y y) (.f64 (.f64 x x) (-.f64 (*.f64 x x) y)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 y (.f64 y y))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 y y) (.f64 (.f64 x x) (-.f64 (*.f64 x x) y))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 x x) y) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) y)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) y))))
(/.f64 (neg.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x))))) (neg.f64 (-.f64 y (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y))) (+.f64 (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y))) (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))) (+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 (.f64 x x) (-.f64 (.f64 x x) y))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (/.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 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y y) (+.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 y y)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 y (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) y)) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x x) y) (.f64 (-.f64 (.f64 x x) y) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y))))
(.f64 (+.f64 (.f64 x x) y) (/.f64 (-.f64 (.f64 x x) y) (-.f64 (.f64 x x) y)))
(.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)))))
(.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))))))
(.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)))))
(.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)))
(.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))))))
(.f64 (.f64 (+.f64 (.f64 x x) y) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) y))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) y))))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) y))
(.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 x) (.f64 (.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 (.f64 y (-.f64 y (.f64 x x))) (.f64 y (-.f64 y (.f64 x x))))))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 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))))

simplify161.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

2330×	`fnmadd-define`
2012×	`fnmsub-define`
1894×	`-lowering-.f32`
1894×	`-lowering-.f64`
1878×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	426
1	85	351
2	221	351
3	736	351
4	2474	351
5	5878	351
0	8169	351

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))

eval59.0ms (2.2%)

Compiler: Compiled 15304 to 822 computations (94.6% saved)

prune40.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	532	3	535
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	532	5	537

Accuracy

100.0%

Counts

537 → 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)))
▶	57.1%	(+.f64 (*.f64 x x) y)
▶	51.7%	(+.f64 y y)
▶	49.3%	(*.f64 x x)

Compiler

Compiled 35 to 21 computations (40% saved)

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(+.f64 (*.f64 x x) y)
✓	cost-diff	(+.f64 y y)
✓	cost-diff	(*.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	15
1	10	15
2	11	15
0	11	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize32.0ms (1.2%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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)

Results

24.0ms

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: 3.0ms (59% of total)

ival-mult: 2.0ms (39.4% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

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	@	-inf	(+ y y)
0.0ms	x	@	0	(* x x)
0.0ms	y	@	0	(+ y y)
0.0ms	y	@	-inf	(+ (* x x) y)

rewrite48.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

92×	`-lowering-.f32`
92×	`-lowering-.f64`
74×	`+-lowering-+.f64`
74×	`/-lowering-/.f32`
74×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	30	9
0	244	9

Stop Event

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

Counts

3 → 29

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 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))
(fma.f64 x x y)
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 y (.f64 y y))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 y (.f64 y y))) (+.f64 (.f64 y y) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) y))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)) (-.f64 (*.f64 x x) y))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 y (.f64 y y)))) (neg.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 y (.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.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 y (*.f64 x x)))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (-.f64 y (*.f64 x x))))))
(.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)))

simplify144.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

1574×	`-lowering-.f32`
1574×	`-lowering-.f64`
1492×	`sum4-define`
1304×	`/-lowering-/.f32`
1304×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	174
1	52	141
2	124	141
3	409	141
4	1406	141
5	3811	141
6	7382	141
0	8345	141

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 (0.4%)

Compiler: Compiled 672 to 73 computations (89.1% saved)

prune5.0ms (0.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	92	6	98

Accuracy

100.0%

Counts

98 → 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)))
✓	57.1%	(+.f64 (*.f64 x x) y)
✓	51.7%	(+.f64 y y)
✓	49.3%	(*.f64 x x)
▶	11.1%	y

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify4.0ms (0.2%)

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

localize10.0ms (0.4%)

Results

7.0ms

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

rewrite9.0ms (0.4%)

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)))
✓	57.1%	(+.f64 (*.f64 x x) y)
✓	51.7%	(+.f64 y y)
✓	49.3%	(*.f64 x x)
✓	11.1%	y

Compiler

Compiled 66 to 32 computations (51.5% saved)

regimes14.0ms (0.5%)

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:

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

regimes6.0ms (0.2%)

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:

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

Results

Accuracy	Segments	Branch
88.9%	2	`x`
71.2%	3	`y`
88.9%	2	`(*.f64 x x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (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:

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

Results

Accuracy	Segments	Branch
88.0%	2	`x`
88.0%	2	`(*.f64 x x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes5.0ms (0.2%)

Counts

2 → 2

Calls

Call 1

Inputs
y
(*.f64 x x)

Outputs
y
(*.f64 x x)

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
49.3%	1	`y`
54.4%	2	`x`
54.4%	2	`(*.f64 x x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
y

Outputs
y

Calls

2 calls:

1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
11.1%	1	`y`
11.1%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch20.0ms (0.8%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	2.630901266471987e-70	6.856135510219882e-69

Results

5.0ms

112×

valid

Compiler

Compiled 98 to 65 computations (33.7% saved)

Precisions

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

ival-add: 1.0ms (75.4% of total)

const: 0.0ms (0% of total)

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

bsearch9.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	2.630901266471987e-70	6.856135510219882e-69

Results

5.0ms

112×

valid

Compiler

Compiled 84 to 58 computations (31% saved)

Precisions

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

ival-add: 1.0ms (75.1% of total)

const: 0.0ms (0% of total)

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

bsearch5.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	9.40004010615708e-213	1.6429856829202726e-212

Results

3.0ms

64×

valid

Compiler

Compiled 46 to 33 computations (28.3% saved)

Precisions

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

ival-add: 1.0ms (131.2% of total)

const: 0.0ms (0% of total)

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

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	20	44

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 2962570060644237/485667223056432267729865476705879726660601709763034880312953102434726071301302124544 binary64)) (+.f64 y y) (+.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) #s(literal 6313673899733619/971334446112864535459730953411759453321203419526069760625906204869452142602604249088 binary64)) (+.f64 y y) (.f64 x x))
(if (<=.f64 (.f64 x x) #s(literal 4737909217226285/379032737378102767370356320425415662904513187772631008578870126471203845870697482014374611530431269030880793627229265919475483409207718357286202948008100864063587640630090308972232735749901964068667724412528434753635948938919936 binary64)) y (.f64 x x))
y

Outputs
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 2962570060644237/485667223056432267729865476705879726660601709763034880312953102434726071301302124544 binary64)) (+.f64 y y) (+.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) #s(literal 6313673899733619/971334446112864535459730953411759453321203419526069760625906204869452142602604249088 binary64)) (+.f64 y y) (.f64 x x))
(if (<=.f64 (.f64 x x) #s(literal 4737909217226285/379032737378102767370356320425415662904513187772631008578870126471203845870697482014374611530431269030880793627229265919475483409207718357286202948008100864063587640630090308972232735749901964068667724412528434753635948938919936 binary64)) y (.f64 x x))
y

soundness667.0ms (25.3%)

Rules

2330×	`fnmadd-define`
2012×	`fnmsub-define`
1894×	`-lowering-.f32`
1894×	`-lowering-.f64`
1878×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	426
1	85	351
2	221	351
3	736	351
4	2474	351
5	5878	351
0	8169	351
0	5	5
1	12	5
2	17	5
3	20	5
4	21	5
0	21	5
0	18	174
1	52	141
2	124	141
3	409	141
4	1406	141
5	3811	141
6	7382	141
0	8345	141

Stop Event

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

Compiler

Compiled 120 to 63 computations (47.5% saved)

preprocess109.0ms (4.1%)

Remove: (abs x)
Compiler: Compiled 164 to 78 computations (52.4% saved)

analyze0.0ms (0%)

sample704.0ms (26.7%)

preprocess57.0ms (2.2%)

explain102.0ms (3.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.3%)

localize46.0ms (1.7%)

series6.0ms (0.2%)

rewrite312.0ms (11.8%)

simplify161.0ms (6.1%)

eval59.0ms (2.2%)

prune40.0ms (1.5%)

simplify13.0ms (0.5%)

localize32.0ms (1.2%)

series1.0ms (0%)

rewrite48.0ms (1.8%)

simplify144.0ms (5.5%)

eval9.0ms (0.4%)

prune5.0ms (0.2%)

simplify4.0ms (0.2%)

localize10.0ms (0.4%)

series0.0ms (0%)

rewrite9.0ms (0.4%)

simplify3.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes14.0ms (0.5%)

regimes6.0ms (0.2%)

regimes6.0ms (0.2%)

regimes5.0ms (0.2%)

regimes3.0ms (0.1%)

bsearch20.0ms (0.8%)

bsearch9.0ms (0.3%)

bsearch5.0ms (0.2%)

simplify14.0ms (0.5%)

soundness667.0ms (25.3%)

preprocess109.0ms (4.1%)

end0.0ms (0%)

Profiling