Metrics for Difference of squares

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-sub: 0.0ms (0% of total)

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

const: 0.0ms (0% of total)

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

sample637.0ms (11%)

Results

451.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 191.0ms

ival-mult: 140.0ms (73.1% of total)

ival-sub: 42.0ms (21.9% of total)

const: 7.0ms (3.7% of total)

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

Bogosity

preprocess1.2s (19.9%)

Algorithm

2×	egg-herbie

Rules

24584×	`accelerator-lowering-fma.f32`
24584×	`accelerator-lowering-fma.f64`
5200×	`+-lowering-+.f64`
5200×	`+-lowering-+.f32`
3904×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	45
1	54	42
2	151	42
3	383	42
4	882	42
5	1235	42
6	1761	42
7	2347	42
8	4143	42
9	4751	42
10	4864	42
11	4978	42
12	5058	42
13	5058	42
14	6439	42
15	7415	42
16	7899	42
17	7915	42
18	7915	42
0	5	7
1	13	7
2	24	7
3	50	7
4	113	7
5	316	7
6	587	7
7	1255	7
8	2543	7
9	4209	7
10	5079	7
11	5448	7
12	5678	7
13	5792	7
14	5792	7
15	6752	7
16	6912	7
17	7232	7
18	7232	7
19	7632	7
20	7792	7
21	7872	7
22	7872	7
23	7872	7
0	10335	7

Stop Event

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

Calls

Call 1

Inputs
(- (* a a) (* b b))

Outputs
(- (* a a) (* b b))
(*.f64 (+.f64 a b) (-.f64 a b))

Call 2

Inputs
(- (* a a) (* b b))
(- (* (neg a) (neg a)) (* b b))
(- (* a a) (* (neg b) (neg b)))
(neg (- (* (neg a) (neg a)) (* b b)))
(neg (- (* a a) (* (neg b) (neg b))))
(- (* b b) (* a a))

Outputs
(- (* a a) (* b b))
(* (+ a b) (- a b))
(- (* (neg a) (neg a)) (* b b))
(* (+ a b) (- a b))
(- (* a a) (* (neg b) (neg b)))
(* (+ a b) (- a b))
(neg (- (* (neg a) (neg a)) (* b b)))
(* (- b a) (+ a b))
(neg (- (* a a) (* (neg b) (neg b))))
(* (- b a) (+ a b))
(- (* b b) (* a a))
(* (- b a) (+ a b))

Symmetry

(abs a)

(abs b)

explain47.0ms (0.8%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
15	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 b b)`
0	-	-	`b`
0	-	-	`a`
0	-	-	`(*.f64 a a)`

Results

28.0ms

512×

valid

Compiler

Compiled 45 to 17 computations (62.2% saved)

Precisions

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

ival-mult: 8.0ms (74.4% of total)

ival-sub: 2.0ms (18.6% of total)

const: 0.0ms (0% of total)

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

eval0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (+.f64 a b) (-.f64 a b))

Compiler

Compiled 9 to 5 computations (44.4% saved)

localize1.7s (29.1%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

37776×	`accelerator-lowering-fma.f32`
37776×	`accelerator-lowering-fma.f64`
8740×	`+-lowering-+.f64`
8740×	`+-lowering-+.f32`
3214×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
1	9	15
2	28	15
3	70	15
4	182	15
5	346	15
6	693	15
7	1323	15
8	2261	15
9	2882	15
10	3050	15
11	3092	15
12	3130	15
13	3130	15
14	3130	15
15	3132	15
0	8264	15

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (+ a b) (- a b))
(+ a b)
a
b
(- a b)

Outputs
(* (+ a b) (- a b))
(*.f64 (+.f64 a b) (-.f64 a b))
(+ a b)
(+.f64 a b)
a
b
(- a b)
(-.f64 a b)

Results

17.0ms

256×

valid

Compiler

Compiled 18 to 6 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 5.0ms (58% of total)

ival-add: 2.0ms (23.2% of total)

ival-sub: 1.0ms (11.6% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Counts

3 → 72

Calls

Call 1

Inputs
#<alt (* (+ a b) (- a b))>
#<alt (+ a b)>
#<alt (- a b)>

Outputs
#<alt (* -1 (pow b 2))>
#<alt (+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))>
#<alt (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))>
#<alt (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))>
#<alt (pow a 2)>
#<alt (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))>
#<alt (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))>
#<alt (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))>
#<alt (pow a 2)>
#<alt (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))>
#<alt (* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))>
#<alt (* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))>
#<alt (pow a 2)>
#<alt (+ (* b (+ a (* -1 a))) (pow a 2))>
#<alt (+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))>
#<alt (+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))>
#<alt (* -1 (pow b 2))>
#<alt (* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))>
#<alt (* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))>
#<alt (* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))>
#<alt (* -1 (pow b 2))>
#<alt (* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))>
#<alt (* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))>
#<alt (* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))>
#<alt b>
#<alt (+ a b)>
#<alt (+ a b)>
#<alt (+ a b)>
#<alt a>
#<alt (* a (+ 1 (/ b a)))>
#<alt (* a (+ 1 (/ b a)))>
#<alt (* a (+ 1 (/ b a)))>
#<alt a>
#<alt (* -1 (* a (- (* -1 (/ b a)) 1)))>
#<alt (* -1 (* a (- (* -1 (/ b a)) 1)))>
#<alt (* -1 (* a (- (* -1 (/ b a)) 1)))>
#<alt a>
#<alt (+ a b)>
#<alt (+ a b)>
#<alt (+ a b)>
#<alt b>
#<alt (* b (+ 1 (/ a b)))>
#<alt (* b (+ 1 (/ a b)))>
#<alt (* b (+ 1 (/ a b)))>
#<alt b>
#<alt (* -1 (* b (- (* -1 (/ a b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ a b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ a b)) 1)))>
#<alt (* -1 b)>
#<alt (- a b)>
#<alt (- a b)>
#<alt (- a b)>
#<alt a>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt a>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt a>
#<alt (+ a (* -1 b))>
#<alt (+ a (* -1 b))>
#<alt (+ a (* -1 b))>
#<alt (* -1 b)>
#<alt (* b (- (/ a b) 1))>
#<alt (* b (- (/ a b) 1))>
#<alt (* b (- (/ a b) 1))>
#<alt (* -1 b)>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	a	@	-inf	(* (+ a b) (- a b))
0.0ms	a	@	inf	(* (+ a b) (- a b))
0.0ms	a	@	0	(* (+ a b) (- a b))
0.0ms	b	@	inf	(* (+ a b) (- a b))
0.0ms	b	@	-inf	(* (+ a b) (- a b))

rewrite732.0ms (12.6%)

Algorithm

1×	batch-egg-rewrite

Rules

5088×	`accelerator-lowering-fma.f32`
5088×	`accelerator-lowering-fma.f64`
4974×	`-lowering-.f32`
4974×	`-lowering-.f64`
3706×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	26	13
2	247	13
3	3942	13
0	9468	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 1091

Calls

Call 1

Inputs
(* (+ a b) (- a b))
(+ a b)
(- a b)

Outputs
(+.f64 (.f64 a a) (-.f64 #s(literal 0 binary64) (.f64 b b)))
(+.f64 (.f64 a a) (.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 a a))
(+.f64 (.f64 b (-.f64 a b)) (.f64 a (-.f64 a b)))
(+.f64 (.f64 a (+.f64 a b)) (neg.f64 (.f64 b (+.f64 a b))))
(+.f64 (neg.f64 (.f64 b (+.f64 a b))) (.f64 a (+.f64 a b)))
(+.f64 (.f64 a (-.f64 a b)) (.f64 b (-.f64 a b)))
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 (/.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (+.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))))) (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (+.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))))))
(-.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (+.f64 (.f64 a a) (.f64 b b))) (/.f64 (.f64 b (.f64 b (.f64 b b))) (+.f64 (.f64 a a) (.f64 b b))))
(fma.f64 a a (-.f64 #s(literal 0 binary64) (*.f64 b b)))
(fma.f64 a a (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 a (+.f64 a b) (neg.f64 (*.f64 b (+.f64 a b))))
(fma.f64 a (-.f64 a b) (*.f64 b (-.f64 a b)))
(fma.f64 b (-.f64 a b) (*.f64 a (-.f64 a b)))
(fma.f64 b (neg.f64 b) (*.f64 a a))
(fma.f64 (+.f64 a b) a (neg.f64 (*.f64 b (+.f64 a b))))
(fma.f64 (+.f64 a b) (neg.f64 b) (*.f64 a (+.f64 a b)))
(fma.f64 (-.f64 a b) a (*.f64 b (-.f64 a b)))
(fma.f64 (-.f64 a b) b (*.f64 a (-.f64 a b)))
(fma.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) (neg.f64 b)) (.f64 a (+.f64 a b)))
(fma.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) a) (.f64 b (-.f64 a b)))
(fma.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) b) (.f64 a (-.f64 a b)))
(fma.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) a) (neg.f64 (.f64 b (+.f64 a b))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(fma.f64 (neg.f64 b) (+.f64 a b) (*.f64 a (+.f64 a b)))
(fma.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b)) (neg.f64 b)) (.f64 a (+.f64 a b)))
(fma.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b)) a) (.f64 b (-.f64 a b)))
(fma.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b)) b) (.f64 a (-.f64 a b)))
(fma.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b)) a) (neg.f64 (.f64 b (+.f64 a b))))
(fma.f64 #s(literal 1 binary64) (.f64 b (-.f64 a b)) (.f64 a (-.f64 a b)))
(fma.f64 #s(literal 1 binary64) (.f64 a (+.f64 a b)) (neg.f64 (.f64 b (+.f64 a b))))
(fma.f64 #s(literal 1 binary64) (neg.f64 (.f64 b (+.f64 a b))) (.f64 a (+.f64 a b)))
(fma.f64 #s(literal 1 binary64) (.f64 a (-.f64 a b)) (.f64 b (-.f64 a b)))
(fma.f64 #s(literal -1 binary64) (.f64 b b) (.f64 a a))
(fma.f64 #s(literal -1 binary64) (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(fma.f64 (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) a) (*.f64 b (-.f64 a b)))
(fma.f64 (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) b) (*.f64 a (-.f64 a b)))
(fma.f64 (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) a) (neg.f64 (*.f64 b (+.f64 a b))))
(fma.f64 (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (neg.f64 b)) (*.f64 a (+.f64 a b)))
(fma.f64 (.f64 a (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) (neg.f64 (.f64 b (+.f64 a b))))
(fma.f64 (.f64 a (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) (.f64 b (-.f64 a b)))
(fma.f64 (.f64 b (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) (.f64 a (-.f64 a b)))
(fma.f64 (.f64 (neg.f64 b) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) (.f64 a (+.f64 a b)))
(fma.f64 (.f64 a #s(literal 1 binary64)) (+.f64 a b) (neg.f64 (.f64 b (+.f64 a b))))
(fma.f64 (.f64 a #s(literal 1 binary64)) (-.f64 a b) (.f64 b (-.f64 a b)))
(fma.f64 (.f64 b #s(literal 1 binary64)) (-.f64 a b) (.f64 a (-.f64 a b)))
(fma.f64 (.f64 (neg.f64 b) #s(literal 1 binary64)) (+.f64 a b) (.f64 a (+.f64 a b)))
(fma.f64 (.f64 a (-.f64 (.f64 a a) (.f64 b b))) (/.f64 #s(literal 1 binary64) (-.f64 a b)) (neg.f64 (.f64 b (+.f64 a b))))
(fma.f64 (.f64 a (-.f64 (.f64 a a) (.f64 b b))) (/.f64 #s(literal 1 binary64) (+.f64 a b)) (.f64 b (-.f64 a b)))
(fma.f64 (.f64 b (-.f64 (.f64 a a) (.f64 b b))) (/.f64 #s(literal 1 binary64) (+.f64 a b)) (.f64 a (-.f64 a b)))
(fma.f64 (.f64 (neg.f64 b) (-.f64 (.f64 a a) (.f64 b b))) (/.f64 #s(literal 1 binary64) (-.f64 a b)) (.f64 a (+.f64 a b)))
(fma.f64 (.f64 (+.f64 a b) #s(literal -1 binary64)) b (.f64 a (+.f64 a b)))
(fma.f64 (.f64 a (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64))) (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (*.f64 b (-.f64 a b)))
(fma.f64 (.f64 a (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64))) (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (neg.f64 (*.f64 b (+.f64 a b))))
(fma.f64 (.f64 (neg.f64 b) (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64))) (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (*.f64 a (+.f64 a b)))
(fma.f64 (.f64 b (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64))) (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (*.f64 a (-.f64 a b)))
(/.f64 (+.f64 a b) (/.f64 #s(literal 1 binary64) (-.f64 a b)))
(/.f64 (-.f64 a b) (/.f64 #s(literal 1 binary64) (+.f64 a b)))
(/.f64 (.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (-.f64 (.f64 a a) (.f64 b b))) (+.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b))))
(/.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b))) (-.f64 (.f64 a a) (*.f64 b b)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (*.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (*.f64 b b))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (-.f64 (.f64 a a) (*.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b)))) (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (*.f64 b b))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 b (.f64 b (.f64 b b))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (.f64 (-.f64 a b) (+.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 a b) (.f64 (-.f64 a b) (-.f64 (.f64 a a) (*.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (.f64 (+.f64 a b) (+.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (.f64 (+.f64 a b) (-.f64 (.f64 a a) (*.f64 b b)))))
(/.f64 (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b)))) (.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))
(/.f64 (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b)))) (+.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 b b) (+.f64 (.f64 a a) (*.f64 b b)))))
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(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a a) (.f64 b b))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b)) (-.f64 (.f64 a a) (*.f64 b b))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) (-.f64 (.f64 a a) (*.f64 b b))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64))) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a))))
(.f64 (/.f64 (-.f64 (.f64 a a) (*.f64 b b)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 a b)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64))) (pow.f64 (/.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (-.f64 (.f64 a a) (.f64 b b))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (neg.f64 (.f64 a a)) (*.f64 b b))) (-.f64 #s(literal 0 binary64) (-.f64 a b)))
(.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (.f64 b (.f64 b b)) (neg.f64 (.f64 a (.f64 a a))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a)))))
(.f64 (/.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 (+.f64 a b) (.f64 (+.f64 a b) (+.f64 a b)))))) (+.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 b (+.f64 a b)) (-.f64 (.f64 b (+.f64 a b)) (.f64 a a)))))
(.f64 (/.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (-.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 b (.f64 (+.f64 a b) (.f64 b (+.f64 a b)))))) (-.f64 (.f64 a a) (*.f64 b (+.f64 a b))))
(.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 b a))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a a) (*.f64 b b))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 a b)))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (+.f64 a b)) #s(literal -1 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a)))) (-.f64 a b)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (-.f64 a b)) #s(literal -1 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a)))) (+.f64 a b)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 b (.f64 b b)) (neg.f64 (.f64 a (.f64 a a))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (.f64 a a)) (*.f64 b b))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 a b))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))
(.f64 (pow.f64 (/.f64 (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (+.f64 a b)) #s(literal -1 binary64)) (pow.f64 (/.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (-.f64 a b)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (-.f64 a b)) #s(literal -1 binary64)) (pow.f64 (/.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (+.f64 a b)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (+.f64 (.f64 a a) (.f64 b (+.f64 a b))))))
(.f64 (pow.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))))))
(.f64 (pow.f64 (/.f64 (+.f64 a b) (.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (-.f64 (.f64 a a) (.f64 b b)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))))
(.f64 (pow.f64 (/.f64 (+.f64 a b) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a a) (.f64 b b))))
(.f64 (pow.f64 (/.f64 (+.f64 a b) (-.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 b (.f64 b (.f64 b b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b b))))
(.f64 (pow.f64 (/.f64 (+.f64 a b) (.f64 (-.f64 a b) (-.f64 (.f64 a a) (.f64 b b)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 a b)))
(.f64 (pow.f64 (/.f64 (+.f64 a b) (.f64 (-.f64 a b) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))))
(.f64 (pow.f64 (/.f64 (+.f64 a b) (.f64 (+.f64 a b) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a)))) (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 b (.f64 b b)) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (.f64 (.f64 a (.f64 a a)) (.f64 a (*.f64 a a))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b)))))

simplify596.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

14152×	`accelerator-lowering-fma.f32`
14152×	`accelerator-lowering-fma.f64`
2614×	`--lowering--.f32`
2614×	`--lowering--.f64`
2222×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	86	309
1	265	249
2	781	249
3	3257	249
0	8433	249

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* -1 (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(pow a 2)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(pow a 2)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(pow a 2)
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
b
(+ a b)
(+ a b)
(+ a b)
a
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
a
(+ a b)
(+ a b)
(+ a b)
b
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 b)
(- a b)
(- a b)
(- a b)
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
a
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
a
(+ a (* -1 b))
(+ a (* -1 b))
(+ a (* -1 b))
(* -1 b)
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* -1 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))

Outputs
(* -1 (pow b 2))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(-.f64 (.f64 a a) (.f64 b b))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(-.f64 (.f64 a a) (.f64 b b))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(-.f64 (.f64 a a) (.f64 b b))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(-.f64 (.f64 a a) (.f64 b b))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(-.f64 (.f64 a a) (.f64 b b))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(-.f64 (.f64 a a) (.f64 b b))
(pow a 2)
(*.f64 a a)
(+ (* b (+ a (* -1 a))) (pow a 2))
(*.f64 a a)
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(-.f64 (.f64 a a) (.f64 b b))
(* -1 (pow b 2))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(-.f64 (.f64 a a) (.f64 b b))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(-.f64 (.f64 a a) (.f64 b b))
(* -1 (pow b 2))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(-.f64 (.f64 a a) (.f64 b b))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(-.f64 (.f64 a a) (.f64 b b))
b
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (/ b a)))
(+.f64 b a)
(* a (+ 1 (/ b a)))
(+.f64 b a)
(* a (+ 1 (/ b a)))
(+.f64 b a)
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+.f64 b a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+.f64 b a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+.f64 b a)
a
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
b
(* b (+ 1 (/ a b)))
(+.f64 b a)
(* b (+ 1 (/ a b)))
(+.f64 b a)
(* b (+ 1 (/ a b)))
(+.f64 b a)
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(+.f64 b a)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(+.f64 b a)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(+.f64 b a)
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
a
(* a (+ 1 (* -1 (/ b a))))
(-.f64 a b)
(* a (+ 1 (* -1 (/ b a))))
(-.f64 a b)
(* a (+ 1 (* -1 (/ b a))))
(-.f64 a b)
a
(* -1 (* a (- (/ b a) 1)))
(-.f64 a b)
(* -1 (* a (- (/ b a) 1)))
(-.f64 a b)
(* -1 (* a (- (/ b a) 1)))
(-.f64 a b)
a
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(* b (- (/ a b) 1))
(-.f64 a b)
(* b (- (/ a b) 1))
(-.f64 a b)
(* b (- (/ a b) 1))
(-.f64 a b)
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 a b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 a b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 a b)

eval186.0ms (3.2%)

Compiler: Compiled 44910 to 8027 computations (82.1% saved)

prune244.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1161	2	1163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1161	3	1164

Accuracy

100.0%

Counts

1164 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.1%	(-.f64 #s(literal 0 binary64) (*.f64 b b))
✓	100.0%	(*.f64 (+.f64 a b) (-.f64 a b))
▶	56.1%	(*.f64 a a)

Compiler

Compiled 21 to 13 computations (38.1% saved)

localize41.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 b b)
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (*.f64 b b))
✓	cost-diff	0	(*.f64 a a)
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) (*.f64 b b))
✓	accuracy	100.0%	(*.f64 b b)
✓	accuracy	100.0%	(*.f64 a a)

Rules

16×	`+-lowering-+.f64`
16×	`-lowering-.f32`
16×	`-lowering-.f64`
16×	`+-lowering-+.f32`
14×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	11	13
2	18	13
3	24	13
4	33	13
5	42	13
6	45	13
7	51	13
8	52	13
0	52	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* a a)
a
(- 0 (* b b))
0
(* b b)
b

Outputs
(* a a)
(*.f64 a a)
a
(- 0 (* b b))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
0
#s(literal 0 binary64)
(* b b)
(*.f64 b b)
b

Results

15.0ms

256×

valid

Compiler

Compiled 17 to 8 computations (52.9% saved)

Precisions

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

ival-mult: 4.0ms (66.4% of total)

ival-sub: 1.0ms (16.6% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (* a a)>
#<alt (* b b)>
#<alt (- 0 (* b b))>

Outputs
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	a	@	inf	(* a a)
0.0ms	a	@	0	(* a a)
0.0ms	b	@	inf	(* b b)
0.0ms	b	@	0	(* b b)
0.0ms	b	@	inf	(- 0 (* b b))

rewrite98.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

596×	`/-lowering-/.f32`
596×	`/-lowering-/.f64`
582×	`-lowering-.f32`
582×	`-lowering-.f64`
292×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	27	10
2	193	10
0	1902	10

Stop Event

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

Counts

3 → 182

Calls

Call 1

Inputs
(* a a)
(* b b)
(- 0 (* b b))

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`+-lowering-+.f64`
16×	`-lowering-.f32`
16×	`-lowering-.f64`
16×	`+-lowering-+.f32`
14×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	120
1	11	120
2	20	120
3	22	120
4	25	120
5	32	120
6	40	120
7	48	120
8	54	120
9	55	120
0	55	120

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))

Outputs
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))

eval29.0ms (0.5%)

Compiler: Compiled 4078 to 1136 computations (72.1% saved)

prune29.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	218	3	221

Accuracy

100.0%

Counts

221 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 a b) (-.f64 a b))
✓	56.1%	(*.f64 a a)
▶	52.1%	(neg.f64 (*.f64 b b))

Compiler

Compiled 20 to 12 computations (40% saved)

localize26.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(neg.f64 (*.f64 b b))
✓	cost-diff	0	(*.f64 b b)
✓	accuracy	100.0%	(*.f64 b b)
✓	accuracy	100.0%	(neg.f64 (*.f64 b b))

Rules

16×	`+-lowering-+.f64`
16×	`+-lowering-+.f32`
14×	`-lowering-.f32`
14×	`-lowering-.f64`
14×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	8
1	10	8
2	14	8
3	20	8
4	27	8
5	35	8
6	43	8
7	49	8
8	50	8
0	50	8

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(neg (* b b))
(* b b)
b

Outputs
(neg (* b b))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(* b b)
(*.f64 b b)
b

Results

12.0ms

256×

valid

Compiler

Compiled 11 to 5 computations (54.5% saved)

Precisions

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

ival-mult: 2.0ms (54% of total)

ival-neg: 1.0ms (27% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (neg (* b b))>
#<alt (* b b)>

Outputs
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (* -1 (pow b 2))>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	b	@	0	(neg (* b b))
0.0ms	b	@	inf	(neg (* b b))
0.0ms	b	@	-inf	(neg (* b b))
0.0ms	b	@	0	(* b b)
0.0ms	b	@	inf	(* b b)

rewrite107.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

668×	`-lowering-.f32`
668×	`-lowering-.f64`
646×	`/-lowering-/.f32`
646×	`/-lowering-/.f64`
388×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	7
1	12	7
2	36	7
3	208	7
0	2127	7

Stop Event

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

Counts

2 → 186

Calls

Call 1

Inputs
(neg (* b b))
(* b b)

Outputs
(+.f64 (-.f64 #s(literal 0 binary64) (*.f64 b b)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 b b)))
(-.f64 (-.f64 #s(literal 0 binary64) (*.f64 b b)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(fma.f64 b (-.f64 #s(literal 0 binary64) b) #s(literal 0 binary64))
(fma.f64 (*.f64 b b) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 b b) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) b) b #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) (.f64 b b))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 b b) (.f64 b b)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 b b))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))) (/.f64 #s(literal 1 binary64) (.f64 b b)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 b b)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b)))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 (.f64 b b) (.f64 b b)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 b b)) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 b) (*.f64 (sqrt.f64 b) (-.f64 #s(literal 0 binary64) b)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 b b))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (*.f64 b b))) #s(literal 0 binary64))
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) b) (sqrt.f64 b)) (sqrt.f64 b) #s(literal 0 binary64))
(fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b)))) (-.f64 #s(literal 0 binary64) (*.f64 b b)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b)))) (*.f64 b b) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))) (.f64 (.f64 b b) (*.f64 b b)) #s(literal 0 binary64))
(fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (*.f64 b b))) #s(literal 0 binary64))
(fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b)))) (.f64 (.f64 b b) (*.f64 b b)) #s(literal 0 binary64))
(fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (*.f64 b b))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b)))))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (*.f64 b b))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (*.f64 b b)) #s(literal 0 binary64))
(neg.f64 (*.f64 b b))
(/.f64 (*.f64 b b) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 b b)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (.f64 (.f64 b b) (.f64 b b)))
(/.f64 (.f64 (.f64 b b) (.f64 b b)) (-.f64 #s(literal 0 binary64) (.f64 b b)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))) (.f64 b b))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 b b))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 b b))) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b)))))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))) (.f64 (.f64 b b) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 b (.f64 b b))) b)
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 b b))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) (.f64 b b))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))
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(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b)))) (.f64 b b))
(.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b)))) (-.f64 #s(literal 0 binary64) (.f64 b b)))
(.f64 (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))
(.f64 (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b)))) (.f64 (.f64 b b) (.f64 b b)))
(.f64 (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 b b))))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 b b))))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 b b) (.f64 b b))) (-.f64 #s(literal 0 binary64) (.f64 b b)))

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`+-lowering-+.f64`
16×	`+-lowering-+.f32`
14×	`-lowering-.f32`
14×	`-lowering-.f64`
14×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	84
1	8	84
2	17	84
3	19	84
4	22	84
5	29	84
6	37	84
7	45	84
8	51	84
9	52	84
0	52	84

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)

Outputs
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(*.f64 b (-.f64 #s(literal 0 binary64) b))
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)

eval25.0ms (0.4%)

Compiler: Compiled 3954 to 904 computations (77.1% saved)

prune30.0ms (0.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	210	3	213

Accuracy

100.0%

Counts

213 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 a b) (-.f64 a b))
✓	56.1%	(*.f64 a a)
✓	52.1%	(neg.f64 (*.f64 b b))

Compiler

Compiled 48 to 23 computations (52.1% saved)

regimes10.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 a a)
(neg.f64 (*.f64 b b))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(*.f64 (+.f64 a b) (-.f64 a b))
(-.f64 (.f64 a a) (.f64 b b))

Outputs
(*.f64 (+.f64 a b) (-.f64 a b))

Calls

5 calls:

3.0ms	a
2.0ms	b
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 a a)
1.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`(-.f64 (.f64 a a) (.f64 b b))`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(*.f64 b b)`

Compiler

Compiled 25 to 15 computations (40% saved)

regimes11.0ms (0.2%)

Counts

3 → 4

Calls

Call 1

Inputs
(*.f64 a a)
(neg.f64 (*.f64 b b))
(-.f64 #s(literal 0 binary64) (*.f64 b b))

Outputs
(neg.f64 (*.f64 b b))
(*.f64 a a)
(neg.f64 (*.f64 b b))
(*.f64 a a)

Calls

4 calls:

4.0ms	a
3.0ms	b
2.0ms	(*.f64 a a)
2.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
83.7%	4	`a`
81.5%	4	`b`
83.7%	4	`(*.f64 a a)`
81.5%	4	`(*.f64 b b)`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 a a)

Outputs
(*.f64 a a)

Calls

3 calls:

1.0ms	(*.f64 a a)
0.0ms	a
0.0ms	b

Results

Accuracy	Segments	Branch
56.1%	1	`b`
56.1%	1	`a`
56.1%	1	`(*.f64 a a)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch19.0ms (0.3%)

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	6.695192187552205e+166	8.926536635319521e+170
5.0ms	1.1852057458210076e+61	1.965522039255699e+61
3.0ms	5.120780945060652e-72	6.619056960164376e-72

Results

10.0ms

240×

valid

Compiler

Compiled 179 to 129 computations (27.9% saved)

Precisions

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

ival-mult: 2.0ms (56.1% of total)

ival-sub: 1.0ms (28.1% of total)

const: 0.0ms (0% of total)

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

soundness1.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 44 to 17 computations (61.4% saved)

preprocess59.0ms (1%)

Remove

(abs b)

(abs a)

Compiler

Compiled 232 to 114 computations (50.9% saved)

Difference of squares

analyze0.0ms (0%)

sample637.0ms (11%)

preprocess1.2s (19.9%)

explain47.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize1.7s (29.1%)

series5.0ms (0.1%)

rewrite732.0ms (12.6%)

simplify596.0ms (10.3%)

eval186.0ms (3.2%)

prune244.0ms (4.2%)

localize41.0ms (0.7%)

series4.0ms (0.1%)

rewrite98.0ms (1.7%)

simplify10.0ms (0.2%)

eval29.0ms (0.5%)

prune29.0ms (0.5%)

localize26.0ms (0.5%)

series2.0ms (0%)

rewrite107.0ms (1.8%)

simplify9.0ms (0.2%)

eval25.0ms (0.4%)

prune30.0ms (0.5%)

regimes10.0ms (0.2%)

regimes11.0ms (0.2%)

regimes2.0ms (0%)

bsearch19.0ms (0.3%)

soundness1.0ms (0%)

preprocess59.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	120
1	11	120
2	20	120
3	22	120
4	25	120
5	32	120
6	40	120
7	48	120
8	54	120
9	55	120
0	55	120

Iter	Nodes	Cost
0	7	120
1	11	120
2	20	120
3	22	120
4	25	120
5	32	120
6	40	120
7	48	120
8	54	120
9	55	120
0	55	120

Iter	Nodes	Cost
0	7	120
1	11	120
2	20	120
3	22	120
4	25	120
5	32	120
6	40	120
7	48	120
8	54	120
9	55	120
0	55	120