Metrics for Numeric.Interval.Internal:bisect from intervals-0.7.1, A

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 7 computations (30% saved)

Precisions

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

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

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

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

const: 0.0ms (0% of total)

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

sample688.0ms (24.9%)

Results

428.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 184.0ms

ival-div: 70.0ms (38% of total)

ival-sub: 59.0ms (32% of total)

ival-add: 42.0ms (22.8% of total)

const: 11.0ms (6% of total)

backward-pass: 3.0ms (1.6% of total)

Bogosity

preprocess711.0ms (25.8%)

Algorithm

2×	egg-herbie

Rules

19132×	`accelerator-lowering-fma.f32`
19132×	`accelerator-lowering-fma.f64`
4020×	`associate-+r+`
1946×	`associate-+l+`
1940×	`+-lowering-+.f64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	50	42
2	151	42
3	409	30
4	692	30
5	1116	30
6	1797	30
7	2243	30
8	2268	30
9	2286	30
10	2286	30
11	3727	30
12	4630	30
13	4856	30
14	4921	30
15	4985	30
16	4985	30
17	5008	30
18	5016	30
19	5016	30
20	5016	30
0	6	7
1	12	7
2	23	7
3	43	7
4	84	7
5	147	7
6	323	7
7	546	6
8	1296	5
9	2015	5
10	2426	5
11	2444	5
12	2458	5
13	2458	5
14	3400	5
15	3932	5
16	4088	5
17	4146	5
18	4554	5
19	6394	5
20	7058	5
21	7989	5
0	8343	5

Stop Event

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

Calls

Call 1

Inputs
(+ x (/ (- y x) 2))

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

Call 2

Inputs
(+ x (/ (- y x) 2))
(+ (neg x) (/ (- y (neg x)) 2))
(+ x (/ (- (neg y) x) 2))
(neg (+ (neg x) (/ (- y (neg x)) 2)))
(neg (+ x (/ (- (neg y) x) 2)))
(+ y (/ (- x y) 2))

Outputs
(+ x (/ (- y x) 2))
(* (+ x y) 1/2)
(+ (neg x) (/ (- y (neg x)) 2))
(* (- y x) 1/2)
(+ x (/ (- (neg y) x) 2))
(* (- y x) -1/2)
(neg (+ (neg x) (/ (- y (neg x)) 2)))
(* (- y x) -1/2)
(neg (+ x (/ (- (neg y) x) 2)))
(* (- y x) 1/2)
(+ y (/ (- x y) 2))
(* (+ x y) 1/2)

Symmetry

(sort x y)

explain62.0ms (2.2%)

FPErrors

Click to see full error table

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

Results

28.0ms

512×

valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-div: 4.0ms (38.6% of total)

ival-sub: 3.0ms (29% of total)

ival-add: 3.0ms (29% of total)

const: 1.0ms (9.7% of total)

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

eval3.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 #s(literal 1/2 binary64) (+.f64 x y))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize62.0ms (2.3%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	x
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	#s(literal 1/2 binary64)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (+.f64 x y))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (+.f64 x y))

Rules

12×	`-lowering-.f32`
12×	`-lowering-.f64`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
8×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	13	11
2	15	11
0	15	11

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

Results

45.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 2.0ms (49.1% of total)

ival-mult: 2.0ms (49.1% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Counts

4 → 60

Calls

Call 1

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

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

Calls

15 calls:

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

rewrite478.0ms (17.3%)

Algorithm

1×	batch-egg-rewrite

Rules

8694×	`accelerator-lowering-fma.f32`
8694×	`accelerator-lowering-fma.f64`
4456×	`/-lowering-/.f32`
4456×	`/-lowering-/.f64`
3962×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	26	10
2	176	10
3	1525	10
0	8364	10

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 259

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) y))
(+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (neg.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))))
(-.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x))))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) y (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 y #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (neg.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) y) (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (+.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 #s(literal 1/2 binary64) y))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 1/2 binary64) y))))) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x y))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x)) (+.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 y (-.f64 y x))) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 y (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) y) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y y) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 y (-.f64 y x))) (.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 y (*.f64 y y))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) y) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y y)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (.f64 (-.f64 (.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 y y))) (*.f64 #s(literal 1/2 binary64) (-.f64 x y)))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) (+.f64 (.f64 y y) (*.f64 x (-.f64 x y))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x y)))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) y) (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 #s(literal 1/2 binary64) y)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 y y)))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 x y))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y (-.f64 y x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) (*.f64 y y)))) (+.f64 (-.f64 #s(literal 0 binary64) x) y))
(/.f64 (+.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 x x))) (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 y (.f64 y y)))) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y (-.f64 y x))))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y y))) (+.f64 (-.f64 #s(literal 0 binary64) x) y))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y y) (*.f64 x x))) (-.f64 y x))
(/.f64 (.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) #s(literal 1/2 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y (-.f64 y x))))
(/.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y y)) #s(literal 1/2 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) x) y))
(/.f64 (.f64 (-.f64 (.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64)) (-.f64 y x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) (.f64 y y))) (-.f64 (.f64 x x) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) (.f64 (.f64 y y) #s(literal 1/4 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (-.f64 x y)) (*.f64 #s(literal 1/2 binary64) (-.f64 x y))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) y) (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 y y))))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 x y)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))))) (+.f64 (.f64 y y) (*.f64 x (-.f64 x y))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) (*.f64 y y))))) (-.f64 x y))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 x x)))) (neg.f64 (+.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))))) (+.f64 (.f64 y y) (*.f64 x (-.f64 x y))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y y)))) (-.f64 x y))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 y y) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (-.f64 y x)))
(/.f64 (neg.f64 (.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) #s(literal 1/2 binary64))) (+.f64 (.f64 y y) (*.f64 x (-.f64 x y))))
(/.f64 (neg.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y y)) #s(literal 1/2 binary64))) (-.f64 x y))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 y y) (*.f64 x x)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 y x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))) (+.f64 (.f64 (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y)))) (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 x y))) (/.f64 (.f64 (.f64 y y) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 x y)))))))
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(.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 y (.f64 y y))) (/.f64 #s(literal -1 binary64) (+.f64 (.f64 y y) (*.f64 x (-.f64 x y)))))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 y y)) (/.f64 #s(literal -1 binary64) (-.f64 x y)))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x 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 (.f64 y y) (.f64 x (-.f64 x y))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))))))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x 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 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x))))) (+.f64 (.f64 y y) (.f64 x (-.f64 x y))))))
(*.f64 #s(literal 1 binary64) (+.f64 x y))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 x (-.f64 x y)))) (+.f64 (.f64 x (.f64 x x)) (.f64 y (*.f64 y y))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) (-.f64 (.f64 x x) (*.f64 y y)))
(.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 y y) (.f64 x (-.f64 x y))) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))))
(.f64 (-.f64 (.f64 (.f64 x (.f64 x 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 y) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (+.f64 (.f64 x x) (*.f64 y y)))))))
(.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (+.f64 (.f64 y y) (.f64 x (-.f64 x y))))))
(.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (+.f64 (.f64 x x) (*.f64 y y)))) (-.f64 x y))))
(.f64 (-.f64 (.f64 y y) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 y x)))
(.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))))
(.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 x y))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x y)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))))
(.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x y)) (.f64 (-.f64 x y) (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x y) (-.f64 x y))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 y y) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 y x))))
(.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (-.f64 x y) (.f64 x x)))) (.f64 (/.f64 (.f64 y y) (-.f64 x y)) (/.f64 (/.f64 (.f64 y y) (-.f64 x y)) (/.f64 (-.f64 x y) (.f64 y y))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (-.f64 x y) (.f64 x x))) (+.f64 (/.f64 (/.f64 (.f64 y y) (-.f64 x y)) (/.f64 (-.f64 x y) (.f64 y y))) (/.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (-.f64 x y) (*.f64 y y)))))))
(.f64 (.f64 (+.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y))) (+.f64 x y)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x 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 y y) (.f64 x (-.f64 x y)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (+.f64 (.f64 y y) (.f64 x (-.f64 x y)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 x x)) (.f64 y (*.f64 y y)))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (+.f64 (.f64 x x) (.f64 y y))))))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y (.f64 y y)))) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 y y))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 (-.f64 y x) (.f64 (-.f64 y x) (-.f64 y x)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (-.f64 y x)) (-.f64 (.f64 y (-.f64 y x)) (.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (-.f64 y x) (-.f64 y x))))) (-.f64 (.f64 x x) (*.f64 y (-.f64 y x))))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) (+.f64 (.f64 x x) (*.f64 y (+.f64 x y))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 y y) (.f64 x (-.f64 x y))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x 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 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 x (*.f64 x x)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 y y) (.f64 x (-.f64 x y))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 x x)) (.f64 y (*.f64 y y)))))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (+.f64 (.f64 x x) (.f64 y y))))))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 y y))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal -1/2 binary64)))
#s(literal 1/2 binary64)
x
(exp.f64 (log.f64 x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(pow.f64 x #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))

simplify544.0ms (19.7%)

Algorithm

1×	egg-herbie

Rules

17664×	`accelerator-lowering-fma.f32`
17664×	`accelerator-lowering-fma.f64`
2856×	`+-lowering-+.f64`
2856×	`+-lowering-+.f32`
2768×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	180
1	115	180
2	264	180
3	783	180
4	1834	180
5	2668	180
6	3340	180
7	3639	180
8	3801	180
9	3837	180
10	6026	180
0	8686	180

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval35.0ms (1.3%)

Compiler: Compiled 8549 to 804 computations (90.6% saved)

prune39.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	317	2	319
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	317	3	320

Accuracy

100.0%

Counts

320 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 #s(literal 1/2 binary64) (+.f64 x y))
▶	48.5%	(*.f64 #s(literal 1/2 binary64) y)
▶	52.7%	(*.f64 #s(literal 1/2 binary64) x)

Compiler

Compiled 17 to 13 computations (23.5% saved)

localize38.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	y
✓	cost-diff	0	#s(literal 1/2 binary64)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	x
✓	cost-diff	0	#s(literal 1/2 binary64)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) y)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	7	9
0	7	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* 1/2 x)
1/2
x
(* 1/2 y)
y

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

Results

20.0ms

256×

valid

Compiler

Compiled 13 to 6 computations (53.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 11.0ms (96.3% of total)

const: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Counts

5 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite8.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	7	9
0	7	9

Stop Event

1×	iter limit
1×	saturated

Counts

5 → 7

Calls

Call 1

Inputs
(* 1/2 x)
(* 1/2 y)
1/2
x
y

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

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	96
1	7	96
0	7	96

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
x
x
x
x
x
x
x
x
x
x
x
x
y
y
y
y
y
y
y
y
y
y
y
y

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
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eval5.0ms (0.2%)

Compiler: Compiled 170 to 7 computations (95.9% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	56	3	59

Accuracy

100.0%

Counts

59 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 #s(literal 1/2 binary64) (+.f64 x y))
✓	48.5%	(*.f64 #s(literal 1/2 binary64) y)
✓	52.7%	(*.f64 #s(literal 1/2 binary64) x)

Compiler

Compiled 37 to 24 computations (35.1% saved)

regimes9.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(+.f64 x (/.f64 (-.f64 y x) #s(literal 2 binary64)))
2.0ms	y
2.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes3.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
86.2%	2	`x`
88.0%	4	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
52.7%	1	`y`
52.7%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch12.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-1.9597245963010223e-103	-5.918767842316785e-106

Results

6.0ms

128×

valid

Compiler

Compiled 110 to 90 computations (18.2% saved)

Precisions

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

ival-sub: 1.0ms (40.3% of total)

ival-div: 1.0ms (40.3% of total)

ival-add: 1.0ms (40.3% of total)

const: 0.0ms (0% of total)

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

soundness1.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 20 to 10 computations (50% saved)

preprocess37.0ms (1.3%)

Remove: (sort x y)
Compiler: Compiled 114 to 72 computations (36.8% saved)

Numeric.Interval.Internal:bisect from intervals-0.7.1, A

analyze0.0ms (0%)

sample688.0ms (24.9%)

preprocess711.0ms (25.8%)

explain62.0ms (2.2%)

eval3.0ms (0.1%)

prune1.0ms (0%)

localize62.0ms (2.3%)

series6.0ms (0.2%)

rewrite478.0ms (17.3%)

simplify544.0ms (19.7%)

eval35.0ms (1.3%)

prune39.0ms (1.4%)

localize38.0ms (1.4%)

series7.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify5.0ms (0.2%)

eval5.0ms (0.2%)

prune2.0ms (0.1%)

regimes9.0ms (0.3%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch12.0ms (0.4%)

soundness1.0ms (0%)

preprocess37.0ms (1.3%)

end0.0ms (0%)

Profiling