Metrics for Expression 4, p15

analyze30.0ms (0.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
0%	0%	0%	100%	0%	0%	0%	1
0%	0%	0%	100%	0%	0%	0%	2
50%	0%	0%	100%	0%	0%	0%	3
50%	0%	0%	100%	0%	0%	0%	4
75%	0%	0%	100%	0%	0%	0%	5
75%	0%	0%	100%	0%	0%	0%	6
87.5%	0%	0%	100%	0%	0%	0%	7
87.5%	0%	0%	100%	0%	0%	0%	8
93.8%	0%	0%	100%	0%	0%	0%	9
93.8%	0%	0%	100%	0%	0%	0%	10
96.9%	0%	0%	100%	0%	0%	0%	11
96.9%	0%	0%	100%	0%	0%	0%	12

Compiler

Compiled 24 to 15 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-add: 7.0ms (40% of total)

...c/correct-round.rkt:119:19: 4.0ms (22.9% of total)

ival-<=: 4.0ms (22.9% of total)

ival-mult: 2.0ms (11.4% of total)

ival-and: 1.0ms (5.7% of total)

const: 0.0ms (0% of total)

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

sample1.1s (24.5%)

Results

780.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 542.0ms

...c/correct-round.rkt:119:19: 179.0ms (33% of total)

ival-<=: 168.0ms (31% of total)

ival-mult: 77.0ms (14.2% of total)

ival-add: 72.0ms (13.3% of total)

ival-and: 28.0ms (5.2% of total)

const: 15.0ms (2.8% of total)

backward-pass: 3.0ms (0.6% of total)

Bogosity

preprocess59.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

3194×	`sum4-define`
3170×	`sum5-define`
1520×	`fnmadd-define`
1324×	`fma-define`
1178×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	61	42
2	230	42
3	789	42
4	3659	42
0	4	7
1	11	7
2	28	7
3	106	7
4	161	7
5	211	7
6	240	7
7	257	7
8	259	7
0	259	7

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

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

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

Call 2

Inputs
(* (+ a b) (+ a b))
(* (+ (neg a) b) (+ (neg a) b))
(* (+ a (neg b)) (+ a (neg b)))
(neg (* (+ (neg a) b) (+ (neg a) b)))
(neg (* (+ a (neg b)) (+ a (neg b))))
(* (+ b a) (+ b a))

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

Symmetry

(sort a b)

explain64.0ms (1.4%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`b`
-	-	`(*.f64 (+.f64 a b) (+.f64 a b))`
-	-	`a`
-	-	`(+.f64 a b)`

Results

48.0ms

512×

valid

Compiler

Compiled 39 to 14 computations (64.1% saved)

Precisions

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

ival-mult: 8.0ms (68.2% of total)

ival-add: 3.0ms (25.6% of total)

const: 0.0ms (0% of total)

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

eval0.0ms (0%)

Compiler: Compiled 9 to 4 computations (55.6% 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 4 computations (55.6% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

140×	`fma-define`
124×	`fma-lowering-fma.f32`
124×	`fma-lowering-fma.f64`
90×	`sum3-define`
86×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	12
1	11	12
2	28	12
3	106	12
4	161	12
5	211	12
6	240	12
7	257	12
8	259	12
0	259	12

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (+ 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

localize21.0ms (0.5%)

Localize:

Found 2 expressions of interest:

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

Results

16.0ms

256×

valid

Compiler

Compiled 15 to 5 computations (66.7% saved)

Precisions

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

ival-add: 2.0ms (53.2% of total)

ival-mult: 2.0ms (53.2% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Counts

2 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite385.0ms (8.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2806×	`-lowering-.f32`
2806×	`-lowering-.f64`
2352×	`fma-lowering-fma.f32`
2352×	`fma-lowering-fma.f64`
1742×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	26	8
2	235	8
3	3096	8
0	8615	8

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 271

Calls

Call 1

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

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

simplify188.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

2472×	`-lowering-.f32`
2472×	`-lowering-.f64`
1036×	`fma-lowering-fma.f32`
1036×	`fma-lowering-fma.f64`
980×	`fnmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	252
1	205	234
2	579	234
3	1926	222
4	4789	222
0	8177	222

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval74.0ms (1.6%)

Compiler: Compiled 11334 to 860 computations (92.4% saved)

prune50.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	430	4	434
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	430	5	435

Accuracy

100.0%

Counts

435 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
✓	100.0%	(*.f64 (+.f64 a b) (+.f64 a b))
▶	99.2%	(*.f64 (+.f64 a b) b)
▶	99.9%	(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
▶	99.1%	(*.f64 b b)

Compiler

Compiled 43 to 23 computations (46.5% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 a (+.f64 a b))
✓	cost-diff	0	(+.f64 a b)
✓	cost-diff	0	(*.f64 b (+.f64 a b))
✓	cost-diff	256	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
✓	cost-diff	0	(+.f64 a b)
✓	cost-diff	0	(*.f64 (+.f64 a b) b)
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) a)
✓	cost-diff	0	(+.f64 b (*.f64 #s(literal 2 binary64) a))
✓	cost-diff	0	(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
✓	cost-diff	0	(*.f64 b b)

Rules

144×	`fma-define`
124×	`fma-lowering-fma.f32`
124×	`fma-lowering-fma.f64`
86×	`+-lowering-+.f64`
86×	`+-lowering-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	32	52
2	82	52
3	137	52
4	194	52
5	243	52
6	246	52
0	246	52

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* b b)
b
(* b (+ b (* 2 a)))
b
(+ b (* 2 a))
(* 2 a)
2
a
(* (+ a b) b)
(+ a b)
a
b
(+ (* b (+ a b)) (* a (+ a b)))
(* b (+ a b))
b
(+ a b)
a
(* a (+ a b))

Outputs
(* b b)
(*.f64 b b)
b
(* b (+ b (* 2 a)))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
b
(+ b (* 2 a))
(+.f64 b (*.f64 #s(literal 2 binary64) a))
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
2
#s(literal 2 binary64)
a
(* (+ a b) b)
(*.f64 b (+.f64 b a))
(+ a b)
(+.f64 b a)
a
b
(+ (* b (+ a b)) (* a (+ a b)))
(*.f64 (+.f64 b a) (+.f64 b a))
(* b (+ a b))
(*.f64 b (+.f64 b a))
b
(+ a b)
(+.f64 b a)
a
(* a (+ a b))
(*.f64 a (+.f64 b a))

localize75.0ms (1.7%)

Localize:

Found 10 expressions of interest:

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

Results

38.0ms

256×

valid

Compiler

Compiled 61 to 13 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 16.0ms (78.8% of total)

ival-add: 4.0ms (19.7% of total)

const: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Counts

9 → 192

Calls

Call 1

Inputs
#<alt (* b b)>
#<alt (* b (+ b (* 2 a)))>
#<alt (+ b (* 2 a))>
#<alt (* 2 a)>
#<alt (* (+ a b) b)>
#<alt (+ a b)>
#<alt (+ (* b (+ a b)) (* a (+ a b)))>
#<alt (* b (+ a b))>
#<alt (* a (+ a b))>

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

Calls

48 calls:

Time	Variable		Point	Expression
1.0ms	a	@	inf	(* a (+ a b))
1.0ms	a	@	0	(* b (+ b (* 2 a)))
0.0ms	b	@	-inf	(* b (+ b (* 2 a)))
0.0ms	b	@	0	(* b (+ b (* 2 a)))
0.0ms	b	@	-inf	(* (+ a b) b)

rewrite326.0ms (7.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4670×	`-lowering-.f32`
4670×	`-lowering-.f64`
3268×	`/-lowering-/.f32`
3268×	`/-lowering-/.f64`
2054×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	64	39
2	671	39
0	8508	39

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 450

Calls

Call 1

Inputs
(* b b)
(* b (+ b (* 2 a)))
(+ b (* 2 a))
(* 2 a)
(* (+ a b) b)
(+ a b)
(+ (* b (+ a b)) (* a (+ a b)))
(* b (+ a b))
(* a (+ a b))

Outputs
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))
(pow.f64 b #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 b)) #s(literal 2 binary64))
(*.f64 b b)
(*.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)))
(+.f64 (.f64 b b) (.f64 b (*.f64 #s(literal 2 binary64) a)))
(+.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (*.f64 b b))
(-.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 b (-.f64 b (.f64 #s(literal 2 binary64) a)))) (/.f64 (.f64 (.f64 b b) (.f64 a (.f64 #s(literal 4 binary64) a))) (.f64 b (-.f64 b (*.f64 #s(literal 2 binary64) a)))))
(fma.f64 b b (.f64 b (.f64 #s(literal 2 binary64) a)))
(fma.f64 b (.f64 #s(literal 2 binary64) a) (.f64 b b))
(fma.f64 #s(literal 2 binary64) (.f64 b a) (.f64 b b))
(fma.f64 a (.f64 #s(literal 2 binary64) b) (.f64 b b))
(fma.f64 (.f64 #s(literal 2 binary64) a) b (.f64 b b))
(fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b))
(fma.f64 (.f64 b #s(literal 2 binary64)) a (.f64 b b))
(/.f64 b (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))))
(/.f64 (+.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)))) (+.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (-.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (-.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (.f64 b b)))) (+.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 b (-.f64 b (.f64 #s(literal 2 binary64) a))) (.f64 (.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a))) (.f64 b (-.f64 b (*.f64 #s(literal 2 binary64) a))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b)))) (.f64 b (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 b (.f64 #s(literal 2 binary64) a)) (.f64 b (+.f64 (.f64 b b) (.f64 (*.f64 a a) #s(literal -4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b)))) (.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) b)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 b (.f64 #s(literal 2 binary64) a)) (.f64 (+.f64 (.f64 b b) (.f64 (*.f64 a a) #s(literal -4 binary64))) b)))
(/.f64 (.f64 (.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a))) (.f64 b (-.f64 b (.f64 #s(literal 2 binary64) a)))) (.f64 b (-.f64 b (*.f64 #s(literal 2 binary64) a))))
(/.f64 (.f64 b (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)))) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b)))))
(/.f64 (.f64 b (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64)))) (-.f64 b (*.f64 #s(literal 2 binary64) a)))
(/.f64 (.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) b) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b)))))
(/.f64 (.f64 (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64))) b) (-.f64 b (*.f64 #s(literal 2 binary64) a)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (-.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (.f64 b b))))))
(/.f64 (neg.f64 (.f64 (.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a))) (.f64 b (-.f64 b (.f64 #s(literal 2 binary64) a))))) (neg.f64 (.f64 b (-.f64 b (*.f64 #s(literal 2 binary64) a)))))
(/.f64 (neg.f64 (.f64 b (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b))))))
(/.f64 (neg.f64 (.f64 b (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 b (*.f64 #s(literal 2 binary64) a))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) b)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64))) b)) (-.f64 #s(literal 0 binary64) (-.f64 b (*.f64 #s(literal 2 binary64) a))))
(/.f64 (+.f64 (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (+.f64 (.f64 (.f64 b b) (.f64 a (.f64 #s(literal 4 binary64) a))) (-.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (.f64 b b)))))
(/.f64 (-.f64 (.f64 (.f64 b b) (.f64 a (.f64 #s(literal 4 binary64) a))) (.f64 (.f64 b b) (.f64 b b))) (-.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (.f64 b b)))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(.f64 (+.f64 b (.f64 #s(literal 2 binary64) a)) b)
(.f64 (+.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (-.f64 (.f64 b (.f64 #s(literal 2 binary64) a)) (*.f64 b b))))))
(.f64 (.f64 (.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a))) (.f64 b (-.f64 b (.f64 #s(literal 2 binary64) a)))) (/.f64 #s(literal 1 binary64) (.f64 b (-.f64 b (.f64 #s(literal 2 binary64) a)))))
(.f64 (.f64 b (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (*.f64 #s(literal 2 binary64) b))))))
(.f64 (.f64 b (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 b (.f64 #s(literal 2 binary64) a))))
(.f64 (.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) b) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (*.f64 #s(literal 2 binary64) b))))))
(.f64 (.f64 (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64))) b) (/.f64 #s(literal 1 binary64) (-.f64 b (.f64 #s(literal 2 binary64) a))))
(+.f64 b (*.f64 #s(literal 2 binary64) a))
(+.f64 (*.f64 #s(literal 2 binary64) a) b)
(+.f64 (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a))) (neg.f64 (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (*.f64 #s(literal 2 binary64) a)))))
(-.f64 (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a))) (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (*.f64 #s(literal 2 binary64) a))))
(-.f64 (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 (.f64 #s(literal 2 binary64) a) b)) (/.f64 (.f64 b b) (-.f64 (*.f64 #s(literal 2 binary64) a) b)))
(fma.f64 #s(literal 2 binary64) a b)
(fma.f64 a #s(literal 2 binary64) b)
(neg.f64 (/.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (*.f64 #s(literal 2 binary64) b)))))))
(neg.f64 (/.f64 (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 b (.f64 #s(literal 2 binary64) a)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)))) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (*.f64 #s(literal 2 binary64) b))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64)))) (-.f64 b (.f64 #s(literal 2 binary64) a))))
(/.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (*.f64 #s(literal 2 binary64) b)))))
(/.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) (+.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b (-.f64 b (*.f64 #s(literal 2 binary64) a)))))
(/.f64 (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64))) (-.f64 b (.f64 #s(literal 2 binary64) a)))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (*.f64 #s(literal 2 binary64) b))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)))) (neg.f64 (+.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b (-.f64 b (*.f64 #s(literal 2 binary64) a))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 b (.f64 #s(literal 2 binary64) a))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b (-.f64 b (.f64 #s(literal 2 binary64) a)))) (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (*.f64 a a)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 2 binary64) a) b) (-.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b b))))
(/.f64 (-.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b b)) (-.f64 (.f64 #s(literal 2 binary64) a) b))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a)))))
(/.f64 (-.f64 (.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a))) (.f64 (-.f64 b (.f64 #s(literal 2 binary64) a)) (.f64 a (.f64 #s(literal 4 binary64) a)))) (.f64 (-.f64 b (.f64 #s(literal 2 binary64) a)) (-.f64 b (.f64 #s(literal 2 binary64) a))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (.f64 (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a)))) #s(literal 512 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)) (-.f64 (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)) (.f64 b (.f64 b b))))) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (*.f64 #s(literal 2 binary64) b))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) #s(literal 64 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 #s(literal -8 binary64) (.f64 a (.f64 a a)))) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) #s(literal 64 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (+.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b b)))) (-.f64 b (*.f64 #s(literal 2 binary64) a))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (.f64 a (.f64 a a)) a) #s(literal 16 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 b b) (.f64 a (.f64 #s(literal 4 binary64) a))) (-.f64 b (*.f64 #s(literal 2 binary64) a))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (*.f64 #s(literal 2 binary64) b)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 b (.f64 #s(literal 2 binary64) a)))))
(/.f64 (neg.f64 (-.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b b))) (neg.f64 (-.f64 (.f64 #s(literal 2 binary64) a) b)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (.f64 #s(literal 2 binary64) a))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a))) (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a)))) (+.f64 (.f64 (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (.f64 #s(literal 2 binary64) a))) (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (.f64 #s(literal 2 binary64) a)))) (.f64 (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a))) (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (*.f64 #s(literal 2 binary64) a)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a))) (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a)))) (.f64 (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (.f64 #s(literal 2 binary64) a))) (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (.f64 #s(literal 2 binary64) a))))) (+.f64 (/.f64 (.f64 b b) (-.f64 b (.f64 #s(literal 2 binary64) a))) (/.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (-.f64 b (*.f64 #s(literal 2 binary64) a)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b))))))
(.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b (-.f64 b (.f64 #s(literal 2 binary64) a))))))
(.f64 (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 b (*.f64 #s(literal 2 binary64) a))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b (.f64 b b)) (.f64 (.f64 a (.f64 a a)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 (.f64 #s(literal 4 binary64) a) (.f64 #s(literal 2 binary64) b)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (.f64 (.f64 a a) #s(literal -4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 b (*.f64 #s(literal 2 binary64) a)))))
(.f64 #s(literal 1 binary64) (+.f64 b (.f64 #s(literal 2 binary64) a)))
(.f64 (-.f64 (.f64 a (.f64 #s(literal 4 binary64) a)) (.f64 b b)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 2 binary64) a) b)))
(*.f64 #s(literal 2 binary64) a)
(*.f64 a #s(literal 2 binary64))
(+.f64 (.f64 b b) (.f64 b a))
(+.f64 (.f64 b a) (.f64 b b))
(-.f64 (/.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 b (-.f64 a b))) (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 b (-.f64 a b))))
(fma.f64 b b (*.f64 b a))
(fma.f64 b a (*.f64 b b))
(fma.f64 a b (*.f64 b b))
(/.f64 b (/.f64 #s(literal 1 binary64) (+.f64 b a)))
(/.f64 (+.f64 (.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (+.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 (.f64 b b) (.f64 b (-.f64 b a)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 (.f64 b b) (.f64 b (-.f64 b a)))) (+.f64 (.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 b (-.f64 a b)) (.f64 (.f64 b (+.f64 b a)) (.f64 b (-.f64 a b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (.f64 b (+.f64 (.f64 b (.f64 b b)) (.f64 a (*.f64 a a))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 a b) (.f64 (.f64 b (+.f64 b a)) (-.f64 a b))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 a (*.f64 a a))) b)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 a b) (.f64 (-.f64 (.f64 a a) (*.f64 b b)) b)))
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(/.f64 (neg.f64 (.f64 (-.f64 (.f64 a a) (*.f64 b b)) a)) (-.f64 #s(literal 0 binary64) (-.f64 a b)))
(/.f64 (+.f64 (.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a))) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a)))) (+.f64 (.f64 (.f64 b b) (.f64 a a)) (-.f64 (.f64 (.f64 a (.f64 a a)) a) (.f64 (.f64 b a) (*.f64 a a)))))
(/.f64 (-.f64 (.f64 (.f64 b b) (.f64 a a)) (.f64 (.f64 a (.f64 a a)) a)) (-.f64 (.f64 b a) (.f64 a a)))
(*.f64 a (+.f64 b a))
(*.f64 (+.f64 b a) a)
(.f64 (+.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 a (.f64 a a)) a) (.f64 (.f64 b a) (-.f64 (.f64 b a) (.f64 a a))))))
(.f64 (.f64 (.f64 a (+.f64 b a)) (.f64 a (-.f64 a b))) (/.f64 #s(literal 1 binary64) (*.f64 a (-.f64 a b))))
(.f64 (.f64 a (+.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))))
(.f64 (.f64 (*.f64 a (+.f64 b a)) (-.f64 a b)) (/.f64 #s(literal 1 binary64) (-.f64 a b)))
(.f64 (.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a))) a) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))))
(.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) a) (/.f64 #s(literal 1 binary64) (-.f64 a b)))

simplify211.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

2156×	`-lowering-.f32`
2156×	`-lowering-.f64`
1328×	`fnmadd-define`
1060×	`sum5-define`
856×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	97	891
1	337	834
2	984	834
3	2954	834
4	7480	834
0	8010	834

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

eval108.0ms (2.4%)

Compiler: Compiled 18933 to 1417 computations (92.5% saved)

prune97.0ms (2.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	761	1	762
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	761	6	767

Accuracy

100.0%

Counts

767 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 b (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))))
✓	100.0%	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
✓	100.0%	(*.f64 (+.f64 a b) (+.f64 a b))
✓	99.2%	(*.f64 (+.f64 a b) b)
✓	99.9%	(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
✓	99.1%	(*.f64 b b)

Compiler

Compiled 54 to 31 computations (42.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) a)
✓	cost-diff	0	(+.f64 b (*.f64 #s(literal 2 binary64) a))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a)))
✓	cost-diff	128	(/.f64 b (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))))

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
24×	`fma-define`
22×	`/-lowering-/.f32`
22×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	15	22
2	27	22
3	49	22
4	66	22
5	68	22
0	68	22

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize42.0ms (0.9%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a)))
✓	accuracy	100.0%	(+.f64 b (*.f64 #s(literal 2 binary64) a))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) a)
✓	accuracy	99.6%	(/.f64 b (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))))

Results

33.0ms

256×

valid

Compiler

Compiled 31 to 9 computations (71% saved)

Precisions

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

ival-div: 4.0ms (52.8% of total)

ival-mult: 2.0ms (26.4% of total)

ival-add: 1.0ms (13.2% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (/ b (/ 1 (+ b (* 2 a))))>
#<alt (/ 1 (+ b (* 2 a)))>
#<alt (+ b (* 2 a))>
#<alt (* 2 a)>

Outputs
#<alt (* 2 (* a b))>
#<alt (* b (+ b (* 2 a)))>
#<alt (* b (+ b (* 2 a)))>
#<alt (* b (+ b (* 2 a)))>
#<alt (pow b 2)>
#<alt (* (pow b 2) (+ 1 (* 2 (/ a b))))>
#<alt (* (pow b 2) (+ 1 (* 2 (/ a b))))>
#<alt (* (pow b 2) (+ 1 (* 2 (/ a b))))>
#<alt (pow b 2)>
#<alt (* (pow b 2) (+ 1 (* 2 (/ a b))))>
#<alt (* (pow b 2) (+ 1 (* 2 (/ a b))))>
#<alt (* (pow b 2) (+ 1 (* 2 (/ a b))))>
#<alt (pow b 2)>
#<alt (+ (* 2 (* a b)) (pow b 2))>
#<alt (+ (* 2 (* a b)) (pow b 2))>
#<alt (+ (* 2 (* a b)) (pow b 2))>
#<alt (* 2 (* a b))>
#<alt (* a (+ (* 2 b) (/ (pow b 2) a)))>
#<alt (* a (+ (* 2 b) (/ (pow b 2) a)))>
#<alt (* a (+ (* 2 b) (/ (pow b 2) a)))>
#<alt (* 2 (* a b))>
#<alt (* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))>
#<alt (* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))>
#<alt (* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))>
#<alt (/ 1/2 a)>
#<alt (+ (* -1/4 (/ b (pow a 2))) (* 1/2 (/ 1 a)))>
#<alt (+ (* b (- (* 1/8 (/ b (pow a 3))) (* 1/4 (/ 1 (pow a 2))))) (* 1/2 (/ 1 a)))>
#<alt (+ (* b (- (* b (+ (* -1/16 (/ b (pow a 4))) (* 1/8 (/ 1 (pow a 3))))) (* 1/4 (/ 1 (pow a 2))))) (* 1/2 (/ 1 a)))>
#<alt (/ 1 b)>
#<alt (/ (+ 1 (* -2 (/ a b))) b)>
#<alt (/ (- (+ 1 (* 4 (/ (pow a 2) (pow b 2)))) (* 2 (/ a b))) b)>
#<alt (/ (- (+ 1 (* -8 (/ (pow a 3) (pow b 3)))) (+ (* -4 (/ (pow a 2) (pow b 2))) (* 2 (/ a b)))) b)>
#<alt (/ 1 b)>
#<alt (* -1 (/ (- (* 2 (/ a b)) 1) b))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow a 2) b)) (* 2 a)) b)) 1) b))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow a 3) b)) (* 4 (pow a 2))) b)) (* 2 a)) b)) 1) b))>
#<alt (/ 1 b)>
#<alt (+ (* -2 (/ a (pow b 2))) (/ 1 b))>
#<alt (+ (* a (- (* 4 (/ a (pow b 3))) (* 2 (/ 1 (pow b 2))))) (/ 1 b))>
#<alt (+ (* a (- (* a (+ (* -8 (/ a (pow b 4))) (* 4 (/ 1 (pow b 3))))) (* 2 (/ 1 (pow b 2))))) (/ 1 b))>
#<alt (/ 1/2 a)>
#<alt (/ (+ 1/2 (* -1/4 (/ b a))) a)>
#<alt (/ (- (+ 1/2 (* 1/8 (/ (pow b 2) (pow a 2)))) (* 1/4 (/ b a))) a)>
#<alt (/ (- (+ 1/2 (* -1/16 (/ (pow b 3) (pow a 3)))) (+ (* -1/8 (/ (pow b 2) (pow a 2))) (* 1/4 (/ b a)))) a)>
#<alt (/ 1/2 a)>
#<alt (* -1 (/ (- (* 1/4 (/ b a)) 1/2) a))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow b 2) a)) (* 1/4 b)) a)) 1/2) a))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow b 3) a)) (* 1/8 (pow b 2))) a)) (* 1/4 b)) a)) 1/2) a))>
#<alt (* 2 a)>
#<alt (+ b (* 2 a))>
#<alt (+ b (* 2 a))>
#<alt (+ b (* 2 a))>
#<alt b>
#<alt (* b (+ 1 (* 2 (/ a b))))>
#<alt (* b (+ 1 (* 2 (/ a b))))>
#<alt (* b (+ 1 (* 2 (/ a b))))>
#<alt b>
#<alt (* -1 (* b (- (* -2 (/ a b)) 1)))>
#<alt (* -1 (* b (- (* -2 (/ a b)) 1)))>
#<alt (* -1 (* b (- (* -2 (/ a b)) 1)))>
#<alt b>
#<alt (+ b (* 2 a))>
#<alt (+ b (* 2 a))>
#<alt (+ b (* 2 a))>
#<alt (* 2 a)>
#<alt (* a (+ 2 (/ b a)))>
#<alt (* a (+ 2 (/ b a)))>
#<alt (* a (+ 2 (/ b a)))>
#<alt (* 2 a)>
#<alt (* -1 (* a (- (* -1 (/ b a)) 2)))>
#<alt (* -1 (* a (- (* -1 (/ b a)) 2)))>
#<alt (* -1 (* a (- (* -1 (/ b a)) 2)))>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>
#<alt (* 2 a)>

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	b	@	0	(/ 1 (+ b (* 2 a)))
0.0ms	a	@	0	(/ 1 (+ b (* 2 a)))
0.0ms	a	@	inf	(/ 1 (+ b (* 2 a)))
0.0ms	b	@	inf	(/ 1 (+ b (* 2 a)))
0.0ms	a	@	-inf	(/ 1 (+ b (* 2 a)))

rewrite318.0ms (7%)

Algorithm

1×	batch-egg-rewrite

Rules

3566×	`-lowering-.f32`
3566×	`-lowering-.f64`
1730×	`unpow-prod-down`
1688×	`pow-lowering-pow.f64`
1688×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	43	18
2	299	18
3	3164	18
0	8458	18

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 365

Calls

Call 1

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

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

simplify330.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

3152×	`-lowering-.f32`
3152×	`-lowering-.f64`
2464×	`fma-lowering-fma.f32`
2464×	`fma-lowering-fma.f64`
1978×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	708
1	565	673
2	1527	642
3	4828	638
0	8230	638

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* 2 (* a b))
(* b (+ b (* 2 a)))
(* b (+ b (* 2 a)))
(* b (+ b (* 2 a)))
(pow b 2)
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(pow b 2)
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(pow b 2)
(+ (* 2 (* a b)) (pow b 2))
(+ (* 2 (* a b)) (pow b 2))
(+ (* 2 (* a b)) (pow b 2))
(* 2 (* a b))
(* a (+ (* 2 b) (/ (pow b 2) a)))
(* a (+ (* 2 b) (/ (pow b 2) a)))
(* a (+ (* 2 b) (/ (pow b 2) a)))
(* 2 (* a b))
(* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))
(* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))
(* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))
(/ 1/2 a)
(+ (* -1/4 (/ b (pow a 2))) (* 1/2 (/ 1 a)))
(+ (* b (- (* 1/8 (/ b (pow a 3))) (* 1/4 (/ 1 (pow a 2))))) (* 1/2 (/ 1 a)))
(+ (* b (- (* b (+ (* -1/16 (/ b (pow a 4))) (* 1/8 (/ 1 (pow a 3))))) (* 1/4 (/ 1 (pow a 2))))) (* 1/2 (/ 1 a)))
(/ 1 b)
(/ (+ 1 (* -2 (/ a b))) b)
(/ (- (+ 1 (* 4 (/ (pow a 2) (pow b 2)))) (* 2 (/ a b))) b)
(/ (- (+ 1 (* -8 (/ (pow a 3) (pow b 3)))) (+ (* -4 (/ (pow a 2) (pow b 2))) (* 2 (/ a b)))) b)
(/ 1 b)
(* -1 (/ (- (* 2 (/ a b)) 1) b))
(* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow a 2) b)) (* 2 a)) b)) 1) b))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow a 3) b)) (* 4 (pow a 2))) b)) (* 2 a)) b)) 1) b))
(/ 1 b)
(+ (* -2 (/ a (pow b 2))) (/ 1 b))
(+ (* a (- (* 4 (/ a (pow b 3))) (* 2 (/ 1 (pow b 2))))) (/ 1 b))
(+ (* a (- (* a (+ (* -8 (/ a (pow b 4))) (* 4 (/ 1 (pow b 3))))) (* 2 (/ 1 (pow b 2))))) (/ 1 b))
(/ 1/2 a)
(/ (+ 1/2 (* -1/4 (/ b a))) a)
(/ (- (+ 1/2 (* 1/8 (/ (pow b 2) (pow a 2)))) (* 1/4 (/ b a))) a)
(/ (- (+ 1/2 (* -1/16 (/ (pow b 3) (pow a 3)))) (+ (* -1/8 (/ (pow b 2) (pow a 2))) (* 1/4 (/ b a)))) a)
(/ 1/2 a)
(* -1 (/ (- (* 1/4 (/ b a)) 1/2) a))
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow b 2) a)) (* 1/4 b)) a)) 1/2) a))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow b 3) a)) (* 1/8 (pow b 2))) a)) (* 1/4 b)) a)) 1/2) a))
(* 2 a)
(+ b (* 2 a))
(+ b (* 2 a))
(+ b (* 2 a))
b
(* b (+ 1 (* 2 (/ a b))))
(* b (+ 1 (* 2 (/ a b))))
(* b (+ 1 (* 2 (/ a b))))
b
(* -1 (* b (- (* -2 (/ a b)) 1)))
(* -1 (* b (- (* -2 (/ a b)) 1)))
(* -1 (* b (- (* -2 (/ a b)) 1)))
b
(+ b (* 2 a))
(+ b (* 2 a))
(+ b (* 2 a))
(* 2 a)
(* a (+ 2 (/ b a)))
(* a (+ 2 (/ b a)))
(* a (+ 2 (/ b a)))
(* 2 a)
(* -1 (* a (- (* -1 (/ b a)) 2)))
(* -1 (* a (- (* -1 (/ b a)) 2)))
(* -1 (* a (- (* -1 (/ b a)) 2)))
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)
(* 2 a)

Outputs
(* 2 (* a b))
(.f64 #s(literal 2 binary64) (.f64 a b))
(* b (+ b (* 2 a)))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(* b (+ b (* 2 a)))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(* b (+ b (* 2 a)))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(pow b 2)
(*.f64 b b)
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(.f64 (.f64 b b) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 a b))))
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(.f64 (.f64 b b) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 a b))))
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(.f64 (.f64 b b) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 a b))))
(pow b 2)
(*.f64 b b)
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(.f64 (.f64 b b) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 a b))))
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(.f64 (.f64 b b) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 a b))))
(* (pow b 2) (+ 1 (* 2 (/ a b))))
(.f64 (.f64 b b) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 a b))))
(pow b 2)
(*.f64 b b)
(+ (* 2 (* a b)) (pow b 2))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(+ (* 2 (* a b)) (pow b 2))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(+ (* 2 (* a b)) (pow b 2))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(* 2 (* a b))
(.f64 #s(literal 2 binary64) (.f64 a b))
(* a (+ (* 2 b) (/ (pow b 2) a)))
(.f64 a (.f64 b (+.f64 #s(literal 2 binary64) (/.f64 b a))))
(* a (+ (* 2 b) (/ (pow b 2) a)))
(.f64 a (.f64 b (+.f64 #s(literal 2 binary64) (/.f64 b a))))
(* a (+ (* 2 b) (/ (pow b 2) a)))
(.f64 a (.f64 b (+.f64 #s(literal 2 binary64) (/.f64 b a))))
(* 2 (* a b))
(.f64 #s(literal 2 binary64) (.f64 a b))
(* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))
(.f64 a (.f64 b (+.f64 #s(literal 2 binary64) (/.f64 b a))))
(* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))
(.f64 a (.f64 b (+.f64 #s(literal 2 binary64) (/.f64 b a))))
(* -1 (* a (+ (* -2 b) (* -1 (/ (pow b 2) a)))))
(.f64 a (.f64 b (+.f64 #s(literal 2 binary64) (/.f64 b a))))
(/ 1/2 a)
(/.f64 #s(literal 1/2 binary64) a)
(+ (* -1/4 (/ b (pow a 2))) (* 1/2 (/ 1 a)))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b #s(literal -1/4 binary64)) a)) a)
(+ (* b (- (* 1/8 (/ b (pow a 3))) (* 1/4 (/ 1 (pow a 2))))) (* 1/2 (/ 1 a)))
(+.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (+.f64 (/.f64 (.f64 b (.f64 b #s(literal 1/8 binary64))) a) (.f64 b #s(literal -1/4 binary64))) (.f64 a a)))
(+ (* b (- (* b (+ (* -1/16 (/ b (pow a 4))) (* 1/8 (/ 1 (pow a 3))))) (* 1/4 (/ 1 (pow a 2))))) (* 1/2 (/ 1 a)))
(+.f64 (.f64 (.f64 b b) (+.f64 (/.f64 (.f64 b #s(literal -1/16 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 a a)) a))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b #s(literal -1/4 binary64)) a)) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ (+ 1 (* -2 (/ a b))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 a (/.f64 #s(literal -2 binary64) b))) b)
(/ (- (+ 1 (* 4 (/ (pow a 2) (pow b 2)))) (* 2 (/ a b))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 4 binary64) (/.f64 (.f64 a a) b)) (*.f64 a #s(literal -2 binary64))) b)) b)
(/ (- (+ 1 (* -8 (/ (pow a 3) (pow b 3)))) (+ (* -4 (/ (pow a 2) (pow b 2))) (* 2 (/ a b)))) b)
(/.f64 (+.f64 (/.f64 (.f64 a (.f64 a (.f64 a #s(literal -8 binary64)))) (.f64 b (.f64 b b))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 4 binary64) (/.f64 (.f64 a a) b)) (.f64 a #s(literal -2 binary64))) b))) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(* -1 (/ (- (* 2 (/ a b)) 1) b))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 a (/.f64 #s(literal -2 binary64) b))) b)
(* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow a 2) b)) (* 2 a)) b)) 1) b))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 2 binary64) a) (.f64 #s(literal -4 binary64) (/.f64 (*.f64 a a) b))) b)) b)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow a 3) b)) (* 4 (pow a 2))) b)) (* 2 a)) b)) 1) b))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 2 binary64) a) (/.f64 (+.f64 (.f64 #s(literal 8 binary64) (.f64 a (/.f64 (.f64 a a) b))) (.f64 a (.f64 a #s(literal -4 binary64)))) b)) b)) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(+ (* -2 (/ a (pow b 2))) (/ 1 b))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 a (/.f64 #s(literal -2 binary64) b))) b)
(+ (* a (- (* 4 (/ a (pow b 3))) (* 2 (/ 1 (pow b 2))))) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 (+.f64 (.f64 #s(literal 4 binary64) (/.f64 (.f64 a a) b)) (.f64 a #s(literal -2 binary64))) (.f64 b b)))
(+ (* a (- (* a (+ (* -8 (/ a (pow b 4))) (* 4 (/ 1 (pow b 3))))) (* 2 (/ 1 (pow b 2))))) (/ 1 b))
(+.f64 (.f64 (.f64 a a) (+.f64 (/.f64 (.f64 a #s(literal -8 binary64)) (pow.f64 b #s(literal 4 binary64))) (/.f64 #s(literal 4 binary64) (.f64 b (.f64 b b))))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 a (/.f64 #s(literal -2 binary64) b))) b))
(/ 1/2 a)
(/.f64 #s(literal 1/2 binary64) a)
(/ (+ 1/2 (* -1/4 (/ b a))) a)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b #s(literal -1/4 binary64)) a)) a)
(/ (- (+ 1/2 (* 1/8 (/ (pow b 2) (pow a 2)))) (* 1/4 (/ b a))) a)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (.f64 b (.f64 b #s(literal 1/8 binary64))) a) (*.f64 b #s(literal -1/4 binary64))) a)) a)
(/ (- (+ 1/2 (* -1/16 (/ (pow b 3) (pow a 3)))) (+ (* -1/8 (/ (pow b 2) (pow a 2))) (* 1/4 (/ b a)))) a)
(/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (/.f64 (.f64 b (.f64 b b)) a)) a) a)) (/.f64 (+.f64 (/.f64 (.f64 b (.f64 b #s(literal 1/8 binary64))) a) (.f64 b #s(literal -1/4 binary64))) a)) a)
(/ 1/2 a)
(/.f64 #s(literal 1/2 binary64) a)
(* -1 (/ (- (* 1/4 (/ b a)) 1/2) a))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b #s(literal -1/4 binary64)) a)) a)
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow b 2) a)) (* 1/4 b)) a)) 1/2) a))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 b #s(literal 1/4 binary64)) (/.f64 (.f64 (*.f64 b b) #s(literal -1/8 binary64)) a)) a)) a)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow b 3) a)) (* 1/8 (pow b 2))) a)) (* 1/4 b)) a)) 1/2) a))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 b (.f64 b #s(literal 1/8 binary64))) (.f64 #s(literal -1/16 binary64) (/.f64 (.f64 b (.f64 b b)) a))) a) (.f64 b #s(literal -1/4 binary64))) a)) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(+ b (* 2 a))
(+.f64 b (*.f64 #s(literal 2 binary64) a))
(+ b (* 2 a))
(+.f64 b (*.f64 #s(literal 2 binary64) a))
(+ b (* 2 a))
(+.f64 b (*.f64 #s(literal 2 binary64) a))
b
(* b (+ 1 (* 2 (/ a b))))
(.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 a b))))
(* b (+ 1 (* 2 (/ a b))))
(.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 a b))))
(* b (+ 1 (* 2 (/ a b))))
(.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 a b))))
b
(* -1 (* b (- (* -2 (/ a b)) 1)))
(.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 a b))))
(* -1 (* b (- (* -2 (/ a b)) 1)))
(.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 a b))))
(* -1 (* b (- (* -2 (/ a b)) 1)))
(.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 a b))))
b
(+ b (* 2 a))
(+.f64 b (*.f64 #s(literal 2 binary64) a))
(+ b (* 2 a))
(+.f64 b (*.f64 #s(literal 2 binary64) a))
(+ b (* 2 a))
(+.f64 b (*.f64 #s(literal 2 binary64) a))
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* a (+ 2 (/ b a)))
(*.f64 a (+.f64 #s(literal 2 binary64) (/.f64 b a)))
(* a (+ 2 (/ b a)))
(*.f64 a (+.f64 #s(literal 2 binary64) (/.f64 b a)))
(* a (+ 2 (/ b a)))
(*.f64 a (+.f64 #s(literal 2 binary64) (/.f64 b a)))
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* -1 (* a (- (* -1 (/ b a)) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -2 binary64) (/.f64 b a))))
(* -1 (* a (- (* -1 (/ b a)) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -2 binary64) (/.f64 b a))))
(* -1 (* a (- (* -1 (/ b a)) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -2 binary64) (/.f64 b a))))
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)
(* 2 a)
(*.f64 #s(literal 2 binary64) a)

eval82.0ms (1.8%)

Compiler: Compiled 11358 to 1285 computations (88.7% saved)

prune50.0ms (1.1%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	449	0	449
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	449	6	455

Accuracy

100.0%

Counts

455 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 b (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))))
✓	100.0%	(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
✓	100.0%	(*.f64 (+.f64 a b) (+.f64 a b))
✓	99.2%	(*.f64 (+.f64 a b) b)
✓	99.9%	(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
✓	99.1%	(*.f64 b b)

Compiler

Compiled 98 to 47 computations (52% saved)

regimes12.0ms (0.3%)

Counts

6 → 1

Calls

Call 1

Inputs
(*.f64 b b)
(*.f64 (+.f64 a b) b)
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(*.f64 (+.f64 a b) (+.f64 a b))
(/.f64 b (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))))
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 20 to 11 computations (45% saved)

regimes10.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 b b)
(*.f64 (+.f64 a b) b)
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(*.f64 (+.f64 a b) (+.f64 a b))
(/.f64 b (/.f64 #s(literal 1 binary64) (+.f64 b (*.f64 #s(literal 2 binary64) a))))

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 20 to 11 computations (45% saved)

regimes4.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 b b)
(*.f64 (+.f64 a b) b)
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))

Outputs
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))

Calls

2 calls:

2.0ms	b
2.0ms	a

Results

Accuracy	Segments	Branch
99.9%	1	`a`
99.9%	1	`b`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 b b)
(*.f64 (+.f64 a b) b)

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

Calls

2 calls:

1.0ms	b
1.0ms	a

Results

Accuracy	Segments	Branch
99.2%	1	`a`
99.2%	1	`b`

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 b b)

Outputs
(*.f64 b b)

Calls

2 calls:

2.0ms	b
1.0ms	a

Results

Accuracy	Segments	Branch
99.1%	1	`a`
99.1%	1	`b`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	19	33

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(*.f64 (+.f64 a b) (+.f64 a b))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(*.f64 (+.f64 a b) b)
(*.f64 b b)

Outputs
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(+.f64 (.f64 b (+.f64 b a)) (.f64 a (+.f64 b a)))
(*.f64 (+.f64 a b) (+.f64 a b))
(*.f64 (+.f64 b a) (+.f64 b a))
(.f64 b (+.f64 b (.f64 #s(literal 2 binary64) a)))
(.f64 b (+.f64 b (.f64 a #s(literal 2 binary64))))
(*.f64 (+.f64 a b) b)
(*.f64 b (+.f64 b a))
(*.f64 b b)

soundness736.0ms (16.3%)

Rules

2806×	`-lowering-.f32`
2806×	`-lowering-.f64`
2472×	`-lowering-.f32`
2472×	`-lowering-.f64`
2352×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	252
1	205	234
2	579	234
3	1926	222
4	4789	222
0	8177	222
0	4	8
1	26	8
2	235	8
3	3096	8
0	8615	8

Stop Event

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

Compiler

Compiled 69 to 31 computations (55.1% saved)

preprocess71.0ms (1.6%)

Remove: (sort a b)
Compiler: Compiled 252 to 108 computations (57.1% saved)

Expression 4, p15

analyze30.0ms (0.7%)

sample1.1s (24.5%)

preprocess59.0ms (1.3%)

explain64.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify14.0ms (0.3%)

localize21.0ms (0.5%)

series2.0ms (0.1%)

rewrite385.0ms (8.5%)

simplify188.0ms (4.2%)

eval74.0ms (1.6%)

prune50.0ms (1.1%)

simplify12.0ms (0.3%)

localize75.0ms (1.7%)

series9.0ms (0.2%)

rewrite326.0ms (7.2%)

simplify211.0ms (4.7%)

eval108.0ms (2.4%)

prune97.0ms (2.2%)

simplify6.0ms (0.1%)

localize42.0ms (0.9%)

series3.0ms (0.1%)

rewrite318.0ms (7%)

simplify330.0ms (7.3%)

eval82.0ms (1.8%)

prune50.0ms (1.1%)

regimes12.0ms (0.3%)

regimes10.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

simplify8.0ms (0.2%)

soundness736.0ms (16.3%)

preprocess71.0ms (1.6%)

end0.0ms (0%)

Profiling