Metrics for bug366, discussion (missed optimization)

analyze48.0ms (0.6%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
30.8%	25%	56.2%	0.1%	0%	18.7%	0%	5
32%	25%	53.1%	0.1%	0%	21.9%	0%	6
55.8%	37.5%	29.7%	0.1%	0%	32.8%	0%	7
57.8%	37.5%	27.3%	0.1%	0%	35.1%	0%	8
74.2%	43.7%	15.2%	0.1%	0%	41%	0%	9
75.9%	43.7%	13.9%	0.1%	0%	42.3%	0%	10
85.9%	46.8%	7.7%	0.1%	0%	45.4%	0%	11
87%	46.8%	7%	0.1%	0%	46.1%	0%	12

Compiler

Compiled 11 to 7 computations (36.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 8.0ms (51.8% of total)

ival-sqrt: 4.0ms (25.9% of total)

ival-sub: 3.0ms (19.4% of total)

const: 0.0ms (0% of total)

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

sample894.0ms (10.4%)

Results

652.0ms	8256×	0	valid
39.0ms	595×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 352.0ms

ival-mult: 176.0ms (50% of total)

ival-sqrt: 118.0ms (33.5% of total)

ival-sub: 45.0ms (12.8% of total)

const: 8.0ms (2.3% of total)

backward-pass: 3.0ms (0.9% of total)

Bogosity

preprocess199.0ms (2.3%)

Algorithm

2×	egg-herbie

Rules

2632×	`sum4-define`
2236×	`sum3-define`
1930×	`fnmadd-define`
1482×	`fma-define`
1446×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	71	38
2	172	38
3	466	38
4	1361	38
5	3199	38
6	6508	38
7	7820	38
0	6	6
1	18	6
2	30	6
3	60	6
4	141	6
5	567	6
6	2334	6
7	4137	6
8	7874	6
0	8060	6

Stop Event

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

Calls

Call 1

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

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

Call 2

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

Outputs
(sqrt (- (* a a) (* b b)))
(sqrt (fmsub a a (square b)))
(sqrt (- (* (neg a) (neg a)) (* b b)))
(sqrt (fmsub a a (square b)))
(sqrt (- (* a a) (* (neg b) (neg b))))
(sqrt (fmsub a a (square b)))
(neg (sqrt (- (* (neg a) (neg a)) (* b b))))
(neg (sqrt (fmsub a a (square b))))
(neg (sqrt (- (* a a) (* (neg b) (neg b)))))
(neg (sqrt (fmsub a a (square b))))
(sqrt (- (* b b) (* a a)))
(sqrt (fnmadd a a (square b)))

Symmetry

(abs a)

(abs b)

explain173.0ms (2%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
118	-	-	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
17	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 b b)`
0	-	-	`b`
0	-	-	`a`
0	-	-	`(*.f64 a a)`

Results

150.0ms

512×

valid

Compiler

Compiled 62 to 20 computations (67.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 121.0ms

ival-sqrt: 110.0ms (90.8% of total)

ival-mult: 8.0ms (6.6% of total)

ival-sub: 3.0ms (2.5% of total)

const: 1.0ms (0.8% of total)

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

eval25.0ms (0.3%)

Compiler: Compiled 10 to 6 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.5%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify127.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 b b)
✓	cost-diff	(*.f64 a a)
✓	cost-diff	(-.f64 (.f64 a a) (.f64 b b))
✓	cost-diff	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Rules

2632×	`sum4-define`
1446×	`sum3-define`
1442×	`fmsub-define`
1396×	`fma-define`
1298×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	18	17
2	30	17
3	60	17
4	141	17
5	567	17
6	2334	17
7	4137	17
8	7874	17
0	8060	17

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize41.0ms (0.5%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 b b)
✓	accuracy	100.0%	(*.f64 a a)
✓	accuracy	94.7%	(-.f64 (.f64 a a) (.f64 b b))
✓	accuracy	57.1%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Results

33.0ms

256×

valid

Compiler

Compiled 26 to 7 computations (73.1% saved)

Precisions

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

ival-mult: 4.0ms (50.8% of total)

ival-sqrt: 2.0ms (25.4% of total)

ival-sub: 1.0ms (12.7% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Counts

4 → 72

Calls

Call 1

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

Outputs
#<alt (* b (sqrt -1))>
#<alt (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))>
#<alt (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))>
#<alt (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))>
#<alt a>
#<alt (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))>
#<alt (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))>
#<alt (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))>
#<alt (* -1 a)>
#<alt (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))>
#<alt (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))>
#<alt (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))>
#<alt a>
#<alt (+ a (* -1/2 (/ (pow b 2) a)))>
#<alt (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))>
#<alt (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))>
#<alt (* b (sqrt -1))>
#<alt (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))>
#<alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))>
#<alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))>
#<alt (* -1 (* b (sqrt -1)))>
#<alt (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))>
#<alt (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))>
#<alt (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))>
#<alt (* -1 (pow b 2))>
#<alt (- (pow a 2) (pow b 2))>
#<alt (- (pow a 2) (pow b 2))>
#<alt (- (pow a 2) (pow b 2))>
#<alt (pow a 2)>
#<alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))>
#<alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))>
#<alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))>
#<alt (pow a 2)>
#<alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))>
#<alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))>
#<alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))>
#<alt (pow a 2)>
#<alt (+ (* -1 (pow b 2)) (pow a 2))>
#<alt (+ (* -1 (pow b 2)) (pow a 2))>
#<alt (+ (* -1 (pow b 2)) (pow a 2))>
#<alt (* -1 (pow b 2))>
#<alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))>
#<alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))>
#<alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))>
#<alt (* -1 (pow b 2))>
#<alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))>
#<alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))>
#<alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow a 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>
#<alt (pow b 2)>

Calls

18 calls:

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

rewrite3.8s (44.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1884×	`-lowering-.f32`
1884×	`-lowering-.f64`
1848×	`sum3-define`
1652×	`fma-lowering-fma.f32`
1652×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	39	15
2	278	15
3	3449	15
0	8005	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 239

Calls

Call 1

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

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (.f64 a a) (*.f64 b b)))))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (*.f64 b b))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (*.f64 a a))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b)))) (hypot.f64 a b))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a a) (.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))))) (sqrt.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (*.f64 b b)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 a b) (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (*.f64 b b)))))))
(/.f64 (sqrt.f64 (+.f64 (neg.f64 (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 b b)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a a) (.f64 b b)))))
(/.f64 (sqrt.f64 (+.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b)))) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b)))))) (sqrt.f64 (+.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))))) (sqrt.f64 (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (*.f64 b b)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))))) (neg.f64 (sqrt.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (*.f64 b b)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b))))) (neg.f64 (hypot.f64 a b)))
(pow.f64 (-.f64 (.f64 a a) (.f64 b b)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (*.f64 b b))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (-.f64 (.f64 a a) (.f64 b b)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a a) (.f64 b b)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))))) (sqrt.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (*.f64 b b)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (hypot.f64 a b) (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b))))) #s(literal -1 binary64))
(*.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (sqrt.f64 (/.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 (sqrt.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b)))))))
(.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b b))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b b)))))
(.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (*.f64 b b)))) (/.f64 #s(literal 1 binary64) (hypot.f64 a b)))
(.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (.f64 a a) (*.f64 b b)) #s(literal 1/4 binary64)))
(+.f64 (.f64 a a) (-.f64 #s(literal 0 binary64) (.f64 b b)))
(+.f64 (.f64 a a) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))))
(+.f64 (.f64 a a) (neg.f64 (-.f64 (.f64 b b) (.f64 #s(literal 0 binary64) (.f64 b b)))))
(+.f64 (.f64 a a) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 #s(literal 0 binary64) (.f64 b b))))
(+.f64 (.f64 a a) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (*.f64 b b)))))
(+.f64 (.f64 a a) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (*.f64 b b)))))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b)))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (*.f64 b b))))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 #s(literal 0 binary64) (*.f64 b b))))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (*.f64 b b)))))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 b b)))))
(+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 a a))
(+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (+.f64 (.f64 a a) (.f64 #s(literal 0 binary64) (.f64 b b))))
(+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (+.f64 (.f64 a a) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (*.f64 b b)))))
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(/.f64 (neg.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))))) (neg.f64 (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (*.f64 b b)))))
(/.f64 (+.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (pow.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))) #s(literal 3 binary64))) (+.f64 (.f64 a (.f64 a (.f64 a a))) (-.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b)))) (.f64 (.f64 a a) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (*.f64 b b)))))))
(/.f64 (+.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 b b))) #s(literal 3 binary64))) (+.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b))) (-.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 b b)))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (*.f64 b b)))))))
(/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (pow.f64 (-.f64 (.f64 b b) (.f64 #s(literal 0 binary64) (.f64 b b))) #s(literal 3 binary64))) (+.f64 (.f64 a (.f64 a (.f64 a a))) (+.f64 (.f64 (-.f64 (.f64 b b) (.f64 #s(literal 0 binary64) (.f64 b b))) (-.f64 (.f64 b b) (.f64 #s(literal 0 binary64) (.f64 b b)))) (.f64 (.f64 a a) (-.f64 (.f64 b b) (.f64 #s(literal 0 binary64) (*.f64 b b)))))))
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(/.f64 (.f64 (-.f64 (.f64 a a) (*.f64 b b)) (+.f64 a b)) (+.f64 a b))
(/.f64 (.f64 (-.f64 (.f64 a a) (*.f64 b b)) (-.f64 a b)) (-.f64 a b))
(/.f64 (.f64 (-.f64 a b) (-.f64 (.f64 a a) (*.f64 b b))) (-.f64 a b))
(/.f64 (.f64 (+.f64 a b) (-.f64 (.f64 a a) (*.f64 b b))) (+.f64 a b))
(/.f64 (.f64 (+.f64 a b) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))
(/.f64 (.f64 (-.f64 a b) (+.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a)))) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))))) (.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (.f64 b b) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))))) (/.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 (.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (+.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 a a) (.f64 a (.f64 a (*.f64 a a)))))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (/.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 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (*.f64 b b)))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b b)))) (+.f64 (.f64 (.f64 a a) (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a))))) (.f64 (.f64 (.f64 b b) (.f64 b b)) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (*.f64 b b))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 a a) (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a))))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b b)))) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (*.f64 b b))))
(/.f64 (.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a))) (-.f64 a b)) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a))))
(/.f64 (.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (+.f64 a b)) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a a) (.f64 b b))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 a a)))) (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (*.f64 b b))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b))))) (+.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b)))) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 a a) (.f64 b b))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (*.f64 b b))))) #s(literal -1 binary64))
(.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (/.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 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 a a))))))
(.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b)))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (/.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 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b)))) (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (*.f64 b b))))))
(.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b b))))
(.f64 (+.f64 (.f64 a a) (.f64 b b)) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b b)))))
(.f64 (+.f64 (.f64 a a) (.f64 b b)) (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (.f64 a a) (*.f64 b b))))
(*.f64 (+.f64 a b) (-.f64 a b))
(*.f64 (-.f64 a b) (+.f64 a b))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b)))))))
(.f64 (+.f64 (neg.f64 (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 b b))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a a) (*.f64 b b)))))
(.f64 (+.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b)))) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (.f64 #s(literal 0 binary64) (.f64 b b)) (-.f64 (.f64 a a) (*.f64 b b)))))))
(.f64 #s(literal 1 binary64) (-.f64 (.f64 a a) (*.f64 b b)))
(.f64 (/.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 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b b))) (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (*.f64 b b))))
(.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b)))) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 #s(literal 0 binary64) (.f64 b b)))))
(.f64 (/.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b))) (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b)))) (-.f64 (.f64 a a) (*.f64 b b)))
(.f64 (/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (+.f64 (.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a))))) (.f64 (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))))))) (+.f64 (.f64 (.f64 a a) (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a))))) (.f64 (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))) (-.f64 (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))) (.f64 a (.f64 a (*.f64 a a)))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b)))) (-.f64 (.f64 (.f64 a a) (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a))))) (.f64 (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b)))))) (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b)))))
(.f64 (/.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (.f64 b b))) (+.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (-.f64 (.f64 b b) (.f64 a a)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 a)))
(pow.f64 a #s(literal 2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 a)) #s(literal 2 binary64))
(*.f64 a a)
(*.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 b)))
(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)))

simplify265.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

3920×	`-lowering-.f32`
3920×	`-lowering-.f64`
1966×	`fnmadd-define`
1424×	`/-lowering-/.f32`
1424×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	776
1	356	649
2	1295	607
3	5518	604
0	8050	604

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)

Outputs
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+.f64 (.f64 b (sqrt.f64 #s(literal -1 binary64))) (.f64 a (.f64 a (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+.f64 (.f64 b (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 a a) (+.f64 (.f64 (/.f64 (/.f64 (.f64 a a) b) (.f64 b b)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+.f64 (.f64 b (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 a a) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 a a) (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 a (/.f64 a (pow.f64 b #s(literal 5 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 b (.f64 b b))))))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(.f64 a (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 b b)) (.f64 a a))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(.f64 a (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 b b)) (.f64 a a))) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (.f64 a (.f64 a (.f64 a a))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(.f64 a (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 b b)) (.f64 a a)) (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (.f64 a (.f64 a (.f64 a a)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 b #s(literal 6 binary64))) (pow.f64 a #s(literal 6 binary64)))))))
(* -1 a)
(-.f64 #s(literal 0 binary64) a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(.f64 a (-.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 b b)) (.f64 a a))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(.f64 a (-.f64 #s(literal -1 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 b b)) (.f64 a a)) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (.f64 a (.f64 a (.f64 a a)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
(.f64 a (-.f64 #s(literal -1 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 b b)) (.f64 a a)) (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (.f64 a (.f64 a (.f64 a a)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 b #s(literal 6 binary64))) (pow.f64 a #s(literal 6 binary64)))))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+.f64 a (.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a))))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+.f64 a (.f64 (.f64 b b) (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (.f64 a (.f64 a a))) (/.f64 #s(literal -1/2 binary64) a))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
(+.f64 a (.f64 (.f64 b b) (+.f64 (.f64 (.f64 b b) (+.f64 (/.f64 (.f64 (.f64 b b) #s(literal -1/16 binary64)) (pow.f64 a #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 a (.f64 a a))))) (/.f64 #s(literal -1/2 binary64) a))))
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(.f64 b (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 a (.f64 a (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))) b)))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(.f64 b (+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 a (.f64 a (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))) b)) (/.f64 (.f64 (.f64 a (.f64 a (.f64 a a))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 b #s(literal 4 binary64)))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(.f64 b (+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 a (.f64 a (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))) b)) (+.f64 (/.f64 (.f64 (.f64 a (.f64 a (.f64 a a))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 b #s(literal 4 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 b #s(literal 6 binary64))) (pow.f64 a #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))
(* -1 (* b (sqrt -1)))
(-.f64 #s(literal 0 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(.f64 b (-.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 a (.f64 a (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))) b)))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(-.f64 #s(literal 0 binary64) (.f64 b (+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 a (.f64 a (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))) b)) (/.f64 (.f64 (.f64 a (.f64 a (.f64 a a))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 b #s(literal 4 binary64))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 a (.f64 a (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))) b)) (+.f64 (/.f64 (.f64 (.f64 a (.f64 a (.f64 a a))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 b #s(literal 4 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 b #s(literal 6 binary64))) (pow.f64 a #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (-.f64 #s(literal 0 binary64) b))
(* -1 (pow b 2))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(- (pow a 2) (pow b 2))
(-.f64 (.f64 a a) (.f64 b b))
(- (pow a 2) (pow b 2))
(-.f64 (.f64 a a) (.f64 b b))
(- (pow a 2) (pow b 2))
(-.f64 (.f64 a a) (.f64 b b))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 a (.f64 a (-.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 a a)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 a (.f64 a (-.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 a a)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 a (.f64 a (-.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 a a)))))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 a (.f64 a (-.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 a a)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 a (.f64 a (-.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 a a)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 a (.f64 a (-.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 a a)))))
(pow a 2)
(*.f64 a a)
(+ (* -1 (pow b 2)) (pow a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+ (* -1 (pow b 2)) (pow a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+ (* -1 (pow b 2)) (pow a 2))
(-.f64 (.f64 a a) (.f64 b b))
(* -1 (pow b 2))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (.f64 b b) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 a a) (.f64 b b))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (.f64 b b) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 a a) (.f64 b b))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (.f64 b b) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 a a) (.f64 b b))))
(* -1 (pow b 2))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (.f64 b b) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 a a) (.f64 b b))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (.f64 b b) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 a a) (.f64 b b))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (.f64 b b) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 a a) (.f64 b b))))
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)

eval104.0ms (1.2%)

Compiler: Compiled 11066 to 863 computations (92.2% saved)

prune48.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	308	3	311
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	309	3	312

Accuracy

100.0%

Counts

312 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(+.f64 a (.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a))))
▶	99.3%	(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
▶	99.1%	a

Compiler

Compiled 27 to 17 computations (37% saved)

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) a)
✓	cost-diff	0	(*.f64 b (/.f64 #s(literal -1/2 binary64) a))
✓	cost-diff	0	(.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a)))
✓	cost-diff	0	(+.f64 a (.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a))))
✓	cost-diff	0	(-.f64 a b)
✓	cost-diff	64	(pow.f64 (+.f64 a b) #s(literal 1/2 binary64))
✓	cost-diff	64	(pow.f64 (-.f64 a b) #s(literal 1/2 binary64))
✓	cost-diff	128	(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))

Rules

920×	`fnmadd-define`
732×	`fmsub-define`
714×	`fnmsub-define`
700×	`fma-lowering-fma.f32`
700×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	26	51
2	44	51
3	56	51
4	76	51
5	130	51
6	229	51
7	428	51
8	1040	51
9	1911	51
10	2647	51
11	3505	51
12	3567	51
13	3597	51
14	3717	51
15	3733	51
0	3733	51

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize78.0ms (0.9%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) a)
✓	accuracy	100.0%	(+.f64 a (.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a))))
✓	accuracy	99.8%	(.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a)))
✓	accuracy	99.7%	(*.f64 b (/.f64 #s(literal -1/2 binary64) a))
✓	accuracy	100.0%	(-.f64 a b)
✓	accuracy	100.0%	(+.f64 a b)
✓	accuracy	100.0%	(pow.f64 (-.f64 a b) #s(literal 1/2 binary64))
✓	accuracy	99.2%	(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))

Results

57.0ms

256×

valid

Compiler

Compiled 61 to 14 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-pow: 13.0ms (51.6% of total)

ival-mult: 5.0ms (19.8% of total)

ival-add: 3.0ms (11.9% of total)

ival-sub: 2.0ms (7.9% of total)

ival-div: 2.0ms (7.9% of total)

const: 1.0ms (4% of total)

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

series39.0ms (0.5%)

Counts

9 → 204

Calls

Call 1

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

Outputs
#<alt (* b (sqrt -1))>
#<alt (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))>
#<alt a>
#<alt (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))>
#<alt (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))>
#<alt (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))>
#<alt (* -1 (* a (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))>
#<alt a>
#<alt (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))>
#<alt (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))>
#<alt (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))>
#<alt (* b (sqrt -1))>
#<alt (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))>
#<alt (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))>
#<alt (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))>
#<alt (* -1 (* b (sqrt -1)))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))>
#<alt (* (sqrt b) (sqrt -1))>
#<alt (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))>
#<alt (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt a)>
#<alt (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))>
#<alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))>
#<alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))>
#<alt (* (sqrt b) (sqrt -1))>
#<alt (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))>
#<alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))>
#<alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt b) (sqrt -1)))>
#<alt (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))>
#<alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))>
#<alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))>
#<alt (sqrt b)>
#<alt (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))>
#<alt (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))>
#<alt (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt a)>
#<alt (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))>
#<alt (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))>
#<alt (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))>
#<alt (sqrt b)>
#<alt (* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))>
#<alt (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))>
#<alt (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))>
#<alt (* -1 (* (sqrt b) (pow (sqrt -1) 2)))>
#<alt (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 b)>
#<alt (- a b)>
#<alt (- a b)>
#<alt (- a b)>
#<alt a>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt a>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt a>
#<alt (+ a (* -1 b))>
#<alt (+ a (* -1 b))>
#<alt (+ a (* -1 b))>
#<alt (* -1 b)>
#<alt (* b (- (/ a b) 1))>
#<alt (* b (- (/ a b) 1))>
#<alt (* b (- (/ a b) 1))>
#<alt (* -1 b)>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)>
#<alt (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)>
#<alt (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)>
#<alt a>
#<alt (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))>
#<alt (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))>
#<alt (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))>
#<alt a>
#<alt (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))>
#<alt (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))>
#<alt (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))>
#<alt a>
#<alt (+ a (* -1/2 (/ (pow b 2) a)))>
#<alt (+ a (* -1/2 (/ (pow b 2) a)))>
#<alt (+ a (* -1/2 (/ (pow b 2) a)))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))>
#<alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))>
#<alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))>
#<alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))>
#<alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ (pow b 2) a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (* -1/2 (/ b a))>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<alt (/ -1/2 a)>
#<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

51 calls:

Time	Variable		Point	Expression
17.0ms	b	@	0	(* b (/ -1/2 a))
2.0ms	a	@	-inf	(/ -1/2 a)
1.0ms	b	@	inf	(pow (- a b) 1/2)
1.0ms	a	@	0	(* (pow (- a b) 1/2) (pow (+ a b) 1/2))
1.0ms	b	@	-inf	(* b (/ -1/2 a))

rewrite313.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4246×	`-lowering-.f32`
4246×	`-lowering-.f64`
2984×	`/-lowering-/.f32`
2984×	`/-lowering-/.f64`
1764×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	75	41
2	567	41
3	7039	41
0	8483	41

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 482

Calls

Call 1

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

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (.f64 a a) (*.f64 b b)))))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))))) (sqrt.f64 (.f64 (+.f64 (.f64 b b) (.f64 a (-.f64 a b))) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (*.f64 b b))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (-.f64 (.f64 a a) (.f64 b b)))) (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (-.f64 (.f64 a a) (.f64 b b)))) (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b)))) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))))
(/.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 b (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))))
(/.f64 (sqrt.f64 (.f64 (-.f64 a b) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 b b) (*.f64 a (-.f64 a b)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 a b) (-.f64 (.f64 a a) (*.f64 b b)))) (sqrt.f64 (-.f64 a b)))
(/.f64 (sqrt.f64 (.f64 (+.f64 a b) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 a b) (-.f64 (.f64 a a) (*.f64 b b)))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
(/.f64 (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b)))) (sqrt.f64 (-.f64 a b)))
(/.f64 (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 b b) (*.f64 a (-.f64 a b)))))
(/.f64 (.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))
(/.f64 (.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b)))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))) (sqrt.f64 (-.f64 a b))) (sqrt.f64 (-.f64 a b)))
(/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (sqrt.f64 (-.f64 a b))) (sqrt.f64 (+.f64 (.f64 b b) (*.f64 a (-.f64 a b)))))
(pow.f64 (-.f64 (.f64 a a) (.f64 b b)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 (.f64 a a) (*.f64 b b))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (-.f64 (.f64 a a) (.f64 b b)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (-.f64 a b)) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 a b)))
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(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 b a))
(/.f64 (.f64 (+.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))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 a b))))) (+.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 (.f64 (-.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (-.f64 a b))) (.f64 (+.f64 (.f64 b b) (.f64 a (-.f64 a b))) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (-.f64 a b))) (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b)))))
(/.f64 (.f64 (.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 a b))) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))
(/.f64 (.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 b (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (-.f64 a b))) (+.f64 (.f64 a a) (*.f64 b b)))
(/.f64 (.f64 (.f64 (-.f64 a b) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (-.f64 a b))) (+.f64 (.f64 b b) (.f64 a (-.f64 a b))))
(/.f64 (.f64 (.f64 (+.f64 a b) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (-.f64 a b))) (+.f64 (.f64 a a) (.f64 b (+.f64 a b))))
(/.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) #s(literal 1 binary64)) (-.f64 a b))
(/.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 b b) (.f64 a (-.f64 a b)))) #s(literal 1 binary64))) (+.f64 (.f64 b b) (*.f64 a (-.f64 a b))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b)) #s(literal -1 binary64))
(*.f64 (-.f64 a b) (/.f64 (+.f64 a b) (-.f64 a b)))
(.f64 (-.f64 a b) (.f64 (+.f64 a b) (/.f64 #s(literal 1 binary64) (-.f64 a b))))
(*.f64 (+.f64 a b) #s(literal 1 binary64))
(.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 b b) (*.f64 a (-.f64 a b)))))
(.f64 (+.f64 (.f64 b b) (.f64 a (-.f64 a b))) (/.f64 (+.f64 a b) (+.f64 (.f64 b b) (*.f64 a (-.f64 a b)))))
(.f64 (+.f64 (.f64 b b) (.f64 a (-.f64 a b))) (.f64 (+.f64 a b) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 a b))))))
(.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 a b))
(.f64 (-.f64 (.f64 a a) (*.f64 b b)) (/.f64 #s(literal 1 binary64) (-.f64 a b)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 b b) (*.f64 a (-.f64 a b))))))
(.f64 (+.f64 (neg.f64 (.f64 a a)) (*.f64 b b)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 a b))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 b b) (.f64 a (-.f64 a b)))) (+.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b)) (-.f64 (.f64 a a) (*.f64 b b)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b)) (.f64 (+.f64 a b) (+.f64 a b)))
(.f64 (-.f64 (.f64 b b) (*.f64 a a)) (/.f64 #s(literal 1 binary64) (-.f64 b a)))
(.f64 (.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (+.f64 (.f64 a a) (.f64 b (+.f64 a b))))
(.f64 (.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (+.f64 (.f64 a a) (.f64 (-.f64 #s(literal 0 binary64) b) (-.f64 (-.f64 #s(literal 0 binary64) b) a))))
(.f64 (/.f64 (-.f64 a b) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 (+.f64 a b) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))))
(*.f64 (/.f64 (-.f64 a b) #s(literal 1 binary64)) (/.f64 (+.f64 a b) (-.f64 a b)))
(.f64 (/.f64 (-.f64 a b) (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 b b) (.f64 a (-.f64 a b)))) #s(literal 1 binary64))) (/.f64 (+.f64 a b) (+.f64 (.f64 b b) (.f64 a (-.f64 a b)))))
(.f64 (/.f64 (+.f64 a b) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 (-.f64 a b) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))))
(*.f64 (/.f64 (+.f64 a b) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (/.f64 (+.f64 a b) (.f64 (/.f64 (-.f64 a b) (+.f64 (.f64 b b) (.f64 a (-.f64 a b)))) #s(literal 1 binary64))) (/.f64 (-.f64 a b) (+.f64 (.f64 b b) (.f64 a (-.f64 a b)))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) #s(literal 1 binary64))) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))
(.f64 (/.f64 (-.f64 (.f64 a a) (*.f64 b b)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 a b)))
(.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 b (.f64 (-.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 (/.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (.f64 (+.f64 (.f64 b b) (.f64 a (-.f64 a b))) (-.f64 (.f64 a a) (.f64 b (-.f64 b a))))) (-.f64 (.f64 a a) (.f64 b (-.f64 b a))))
(.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (neg.f64 (.f64 a a)) (*.f64 b b))) (-.f64 #s(literal 0 binary64) (+.f64 a b)))
(.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))

simplify229.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

4156×	`-lowering-.f32`
4156×	`-lowering-.f64`
2126×	`+-lowering-+.f64`
2126×	`+-lowering-+.f32`
1366×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	449	2592
1	1568	2086
2	6805	2063
0	8008	2063

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* (sqrt b) (sqrt -1))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(* (sqrt b) (sqrt -1))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* (sqrt b) (sqrt -1)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(sqrt b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(sqrt b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(* -1 b)
(- a b)
(- a b)
(- a b)
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
a
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
a
(+ a (* -1 b))
(+ a (* -1 b))
(+ a (* -1 b))
(* -1 b)
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* -1 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1/2 (/ (pow b 2) a))
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
a
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* -1/2 (/ (pow b 2) a)))
(* -1/2 (/ (pow b 2) a))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* -1/2 (/ (pow b 2) a))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ (pow b 2) a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
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
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+.f64 (.f64 a (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (.f64 b b))))) (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(+.f64 (.f64 b (sqrt.f64 #s(literal -1 binary64))) (.f64 a (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b) (/.f64 (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (.f64 b (.f64 b b)))))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (.f64 b b))))) (*.f64 b (sqrt.f64 #s(literal -1 binary64)))))))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(+.f64 a (/.f64 #s(literal 0 binary64) a))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(.f64 a (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) a)) (.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (neg.f64 (+.f64 (*.f64 b b) #s(literal 0 binary64))) a))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(.f64 a (+.f64 (+.f64 (.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (neg.f64 (+.f64 (.f64 b b) #s(literal 0 binary64))) a)) (/.f64 #s(literal 0 binary64) a)) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (+.f64 (.f64 b b) #s(literal 0 binary64))) #s(literal 0 binary64)) (.f64 a (*.f64 a a))))))
(* -1 (* a (pow (sqrt -1) 2)))
a
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(+.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) a)) a)
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 b (*.f64 b #s(literal -1/2 binary64))) #s(literal 0 binary64)) a) #s(literal 0 binary64)) a)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 b b)) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) a)) a)) a)) (-.f64 #s(literal 0 binary64) a))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+.f64 a (/.f64 #s(literal 0 binary64) a))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+.f64 a (.f64 b (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 b (/.f64 (/.f64 #s(literal 0 binary64) a) a))) a) (/.f64 #s(literal 0 binary64) a))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(+.f64 (+.f64 a (/.f64 #s(literal 0 binary64) a)) (+.f64 (/.f64 (.f64 b (.f64 #s(literal -1/2 binary64) (+.f64 b (/.f64 (/.f64 #s(literal 0 binary64) a) a)))) a) (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (/.f64 #s(literal 0 binary64) a) a) #s(literal 0 binary64))) (.f64 a (*.f64 a a)))))
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(.f64 b (+.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 a a) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1 binary64))) (.f64 b b)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(.f64 b (+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 b (.f64 b b))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 a a) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1 binary64))) (.f64 b b))))
(* -1 (* b (sqrt -1)))
(-.f64 #s(literal 0 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(-.f64 #s(literal 0 binary64) (+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(-.f64 #s(literal 0 binary64) (.f64 b (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 a a) #s(literal 0 binary64))) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) b))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(.f64 (-.f64 #s(literal 0 binary64) b) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 a a) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)) b)) b)))
(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (*.f64 #s(literal 1/2 binary64) a)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)) (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (/.f64 (.f64 a #s(literal -1/8 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)) (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 a (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 a #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal -1/2 binary64)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal -1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (*.f64 b b) #s(literal -1/8 binary64))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal -1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (*.f64 b b)) #s(literal -1/16 binary64))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 a))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal -1/2 binary64))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal -1/2 binary64))) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) #s(literal -1 binary64)))))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal -1/2 binary64))) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (/.f64 (.f64 b (.f64 b b)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64)))))))
(sqrt a)
(sqrt.f64 a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+.f64 (sqrt.f64 a) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 b #s(literal -1/2 binary64))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (*.f64 b #s(literal -1/8 binary64))))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 b (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (*.f64 b #s(literal -1/16 binary64))))))))
(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(.f64 b (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(.f64 b (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 a (/.f64 a (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1 binary64)))))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 b (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 a (/.f64 a (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (/.f64 (.f64 (.f64 a (*.f64 a a)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))
(* -1 (* (sqrt b) (sqrt -1)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 b)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) a)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 a (*.f64 (sqrt.f64 #s(literal -1 binary64)) a)))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 a (.f64 (sqrt.f64 #s(literal -1 binary64)) a)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a))) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (.f64 (.f64 (.f64 a (.f64 a a)) #s(literal 1/16 binary64)) (sqrt.f64 #s(literal -1 binary64))))))))
(sqrt b)
(sqrt.f64 b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+.f64 (sqrt.f64 b) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 #s(literal 1/2 binary64) a)))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+.f64 (sqrt.f64 b) (.f64 a (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 a #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(+.f64 (sqrt.f64 b) (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 a (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 a #s(literal 1/16 binary64))))))))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal 1/2 binary64)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (*.f64 b #s(literal 1/2 binary64))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (*.f64 b b)) #s(literal 1/16 binary64))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 a))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (*.f64 b #s(literal 1/2 binary64)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) #s(literal -1 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal 1/2 binary64))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) #s(literal -1 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal 1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (/.f64 (.f64 b (.f64 b b)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64)))))))
(sqrt a)
(sqrt.f64 a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+.f64 (sqrt.f64 a) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 b #s(literal 1/2 binary64))))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a)) (.f64 b #s(literal -1/8 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 b (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (*.f64 b #s(literal 1/16 binary64))))))))
(sqrt b)
(sqrt.f64 b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(.f64 b (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (*.f64 #s(literal 1/2 binary64) a))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(.f64 b (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (.f64 a a) #s(literal -1/8 binary64))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(.f64 b (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) a)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (.f64 a a) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (.f64 (.f64 a (.f64 a a)) #s(literal 1/16 binary64)))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 b))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) a)) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) a)) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 (*.f64 a a) #s(literal -1/8 binary64)) #s(literal -1 binary64)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) a)) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (/.f64 (.f64 (.f64 a (*.f64 a a)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))))
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
a
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(.f64 b (.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(.f64 b (.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(.f64 b (.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/.f64 (+.f64 (.f64 a a) (.f64 b (*.f64 b #s(literal -1/2 binary64)))) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/.f64 (+.f64 (.f64 a a) (.f64 b (*.f64 b #s(literal -1/2 binary64)))) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/.f64 (+.f64 (.f64 a a) (.f64 b (*.f64 b #s(literal -1/2 binary64)))) a)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(.f64 a (+.f64 #s(literal 1 binary64) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (.f64 a a))))
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(.f64 a (+.f64 #s(literal 1 binary64) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (.f64 a a))))
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(.f64 a (+.f64 #s(literal 1 binary64) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (.f64 a a))))
a
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b)) (.f64 a a))))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b)) (.f64 a a))))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b)) (.f64 a a))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+.f64 a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(+ a (* -1/2 (/ (pow b 2) a)))
(+.f64 a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(+ a (* -1/2 (/ (pow b 2) a)))
(+.f64 a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ (pow b 2) a))
(/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
b
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(.f64 a (.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 b (-.f64 #s(literal 0 binary64) a)))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(.f64 a (.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 b (-.f64 #s(literal 0 binary64) a)))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(.f64 a (.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 b (-.f64 #s(literal 0 binary64) a)))))
a
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
b
(* b (+ 1 (/ a b)))
(*.f64 b (+.f64 #s(literal 1 binary64) (/.f64 a b)))
(* b (+ 1 (/ a b)))
(*.f64 b (+.f64 #s(literal 1 binary64) (/.f64 a b)))
(* b (+ 1 (/ a b)))
(*.f64 b (+.f64 #s(literal 1 binary64) (/.f64 a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 #s(literal -1 binary64) (/.f64 a (-.f64 #s(literal 0 binary64) b))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 #s(literal -1 binary64) (/.f64 a (-.f64 #s(literal 0 binary64) b))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 #s(literal -1 binary64) (/.f64 a (-.f64 #s(literal 0 binary64) b))))

eval107.0ms (1.2%)

Compiler: Compiled 17262 to 2087 computations (87.9% saved)

prune79.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	685	1	686
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	686	3	689

Accuracy

100.0%

Counts

689 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(+.f64 a (.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a))))
▶	99.3%	(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 a b)))
✓	99.1%	a

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

168×	`fnmadd-define`
160×	`sum3-define`
128×	`fma-lowering-fma.f32`
128×	`fnmsub-define`
128×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	13	26
2	18	26
3	25	26
4	36	26
5	76	26
6	149	26
7	254	26
8	355	26
9	520	26
10	653	26
11	681	26
12	689	26
0	689	26

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize48.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 a b)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 a b))
✓	accuracy	100.0%	(pow.f64 (-.f64 a b) #s(literal 1/2 binary64))
✓	accuracy	99.2%	(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 a b)))

Results

38.0ms

256×

valid

Compiler

Compiled 31 to 9 computations (71% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow: 7.0ms (46.4% of total)

ival-sub: 2.0ms (13.3% of total)

ival-add: 2.0ms (13.3% of total)

ival-mult: 2.0ms (13.3% of total)

ival-sqrt: 2.0ms (13.3% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0%)

Counts

5 → 120

Calls

Call 1

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

Outputs
#<alt (* b (sqrt -1))>
#<alt (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))>
#<alt a>
#<alt (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))>
#<alt (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))>
#<alt (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))>
#<alt (* -1 (* a (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))>
#<alt a>
#<alt (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))>
#<alt (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))>
#<alt (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))>
#<alt (* b (sqrt -1))>
#<alt (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))>
#<alt (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))>
#<alt (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))>
#<alt (* -1 (* b (sqrt -1)))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))>
#<alt (* (sqrt b) (sqrt -1))>
#<alt (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))>
#<alt (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt a)>
#<alt (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))>
#<alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))>
#<alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))>
#<alt (* (sqrt b) (sqrt -1))>
#<alt (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))>
#<alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))>
#<alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt b) (sqrt -1)))>
#<alt (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))>
#<alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))>
#<alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))>
#<alt (* -1 b)>
#<alt (- a b)>
#<alt (- a b)>
#<alt (- a b)>
#<alt a>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt a>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt a>
#<alt (+ a (* -1 b))>
#<alt (+ a (* -1 b))>
#<alt (+ a (* -1 b))>
#<alt (* -1 b)>
#<alt (* b (- (/ a b) 1))>
#<alt (* b (- (/ a b) 1))>
#<alt (* b (- (/ a b) 1))>
#<alt (* -1 b)>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (sqrt b)>
#<alt (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))>
#<alt (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))>
#<alt (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt a)>
#<alt (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))>
#<alt (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))>
#<alt (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))>
#<alt (sqrt b)>
#<alt (* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))>
#<alt (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))>
#<alt (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))>
#<alt (* -1 (* (sqrt b) (pow (sqrt -1) 2)))>
#<alt (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))>
#<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

30 calls:

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

rewrite299.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2380×	`fma-lowering-fma.f32`
2380×	`fma-lowering-fma.f64`
2138×	`-lowering-.f32`
2138×	`-lowering-.f64`
1754×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	39	20
2	271	20
3	3794	20
0	8043	20

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 370

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 a a) (*.f64 b b))) #s(literal 1/2 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 a b))) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 a b)))))
(exp.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 a b))) (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 a b)))))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(/.f64 (sqrt.f64 (.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (.f64 b b) (+.f64 (.f64 a a) (.f64 b b))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 b (.f64 b (.f64 b b))))) (hypot.f64 a b))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))) (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) (sqrt.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) (sqrt.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))) (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b)))))
(/.f64 (.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b)))) (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)))
(/.f64 (.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b (-.f64 b a)))))
(/.f64 (.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))
(/.f64 (.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b)))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64))) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))) (pow.f64 (-.f64 a b) #s(literal 1/2 binary64))) (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)))
(/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (pow.f64 (-.f64 a b) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b (-.f64 b a)))))
(pow.f64 (-.f64 (.f64 a a) (.f64 b b)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)) (.f64 (pow.f64 (+.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64))))
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(pow.f64 (/.f64 (-.f64 b a) (-.f64 (.f64 b b) (.f64 a a))) #s(literal -1 binary64))
(*.f64 (+.f64 a b) #s(literal 1 binary64))
(.f64 (+.f64 a b) (.f64 (-.f64 a b) (/.f64 #s(literal 1 binary64) (-.f64 a b))))
(.f64 (+.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 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a)))))
(.f64 (+.f64 (.f64 a a) (.f64 b (-.f64 b a))) (.f64 (+.f64 a b) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a))))))
(.f64 (+.f64 (.f64 a a) (.f64 b (+.f64 a b))) (.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) #s(literal 1 binary64)))
(.f64 (-.f64 (.f64 a a) (*.f64 b b)) (/.f64 #s(literal 1 binary64) (-.f64 a b)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a))))))
(.f64 (+.f64 (neg.f64 (.f64 a a)) (*.f64 b b)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 a b))))
(*.f64 #s(literal 1 binary64) (+.f64 a b))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b)) (-.f64 (.f64 a a) (*.f64 b b)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))) (+.f64 (.f64 a (.f64 a a)) (.f64 b (*.f64 b b))))
(.f64 (-.f64 (.f64 b b) (*.f64 a a)) (/.f64 #s(literal 1 binary64) (-.f64 b a)))
(.f64 (.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (+.f64 (.f64 a a) (.f64 b (+.f64 a b))))
(.f64 (.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (+.f64 (.f64 a a) (.f64 (-.f64 #s(literal 0 binary64) b) (-.f64 #s(literal 0 binary64) (+.f64 a b)))))
(.f64 (.f64 #s(literal 1 binary64) (+.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 (/.f64 (+.f64 a b) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b)))) (/.f64 (-.f64 a b) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))))
(*.f64 (/.f64 (+.f64 a b) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (/.f64 (+.f64 a b) (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (/.f64 (-.f64 a b) (+.f64 (.f64 a a) (*.f64 b (-.f64 b a)))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 a b) (+.f64 (.f64 a a) (.f64 b (+.f64 a b)))) #s(literal 1 binary64))) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b))))
(.f64 (/.f64 (-.f64 (.f64 a a) (*.f64 b b)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 a b)))
(.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 b (.f64 (-.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 (/.f64 (+.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 a a) (.f64 b (-.f64 b a))))
(.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (neg.f64 (.f64 a a)) (*.f64 b b))) (-.f64 #s(literal 0 binary64) (+.f64 a b)))
(.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 a (.f64 a a)) (.f64 b (.f64 b b))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 a a) (*.f64 b (+.f64 a b)))))

simplify266.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

4014×	`-lowering-.f32`
4014×	`-lowering-.f64`
2182×	`+-lowering-+.f64`
2182×	`+-lowering-+.f32`
1368×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	429	2031
1	1513	1591
2	6650	1563
0	8082	1563

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* (sqrt b) (sqrt -1))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(* (sqrt b) (sqrt -1))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* (sqrt b) (sqrt -1)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(* -1 b)
(- a b)
(- a b)
(- a b)
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
a
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
a
(+ a (* -1 b))
(+ a (* -1 b))
(+ a (* -1 b))
(* -1 b)
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* -1 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(sqrt b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(sqrt b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
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
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+.f64 (.f64 a (/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (/.f64 (/.f64 #s(literal 0 binary64) b) b)) b)) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(+.f64 (+.f64 (.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)) (+.f64 (/.f64 (/.f64 #s(literal 0 binary64) (.f64 b (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (.f64 b (.f64 b b))) (.f64 a (/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (/.f64 (/.f64 #s(literal 0 binary64) b) b)) b)) (sqrt.f64 #s(literal -1 binary64))))))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(+.f64 a (/.f64 #s(literal 0 binary64) a))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(.f64 a (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 0 binary64) a) (/.f64 (.f64 b b) (.f64 a a))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(.f64 a (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 0 binary64) a) (/.f64 (.f64 b b) (.f64 a a)))) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) #s(literal 0 binary64)) (.f64 a (.f64 a a))))))
(* -1 (* a (pow (sqrt -1) 2)))
a
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 0 binary64) a)) a)
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (*.f64 b b)) #s(literal 0 binary64)) a) #s(literal 0 binary64)) a)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 b b) #s(literal 0 binary64))) (/.f64 #s(literal 0 binary64) a)) (-.f64 #s(literal 0 binary64) a)) a)) (-.f64 #s(literal 0 binary64) a))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+.f64 a (/.f64 #s(literal 0 binary64) a))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 (+.f64 b (/.f64 (/.f64 #s(literal 0 binary64) a) a)) a) b)) (+.f64 a (/.f64 #s(literal 0 binary64) a)))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(+.f64 (+.f64 a (/.f64 #s(literal 0 binary64) a)) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 (+.f64 b (/.f64 (/.f64 #s(literal 0 binary64) a) a)) a) b)) (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (/.f64 #s(literal 0 binary64) a) a) #s(literal 0 binary64))) (.f64 a (*.f64 a a)))))
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
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(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
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(* -1 (* b (sqrt -1)))
(-.f64 #s(literal 0 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
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(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(-.f64 #s(literal 0 binary64) (.f64 b (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 a a) #s(literal 0 binary64))) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) b))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
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(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
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(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
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(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
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(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 b #s(literal -1/2 binary64)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
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(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
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(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 a))
(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
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(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
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(* -1 (* a (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
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(sqrt a)
(sqrt.f64 a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+.f64 (sqrt.f64 a) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 b #s(literal -1/2 binary64))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/8 binary64))))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 b (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 b #s(literal -1/16 binary64))))))))
(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(.f64 b (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
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(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
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(* -1 (* (sqrt b) (sqrt -1)))
(.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 b))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(.f64 b (.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (.f64 (.f64 (.f64 a (.f64 a a)) #s(literal 1/16 binary64)) (sqrt.f64 #s(literal -1 binary64)))))) #s(literal -1 binary64)))
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
a
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 #s(literal 0 binary64) (*.f64 b (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 #s(literal 0 binary64) (*.f64 b (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 #s(literal 0 binary64) (*.f64 b (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(sqrt b)
(sqrt.f64 b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+.f64 (sqrt.f64 b) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 #s(literal 1/2 binary64) a)))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+.f64 (sqrt.f64 b) (.f64 a (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 a #s(literal -1/8 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(+.f64 (sqrt.f64 b) (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 a (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (*.f64 a #s(literal 1/16 binary64))))))))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 b #s(literal 1/2 binary64)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(.f64 a (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (.f64 b b)) #s(literal 1/16 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 a))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(.f64 a (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 b #s(literal 1/2 binary64))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64)))) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) #s(literal -1 binary64)) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (*.f64 b b)) #s(literal 1/16 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))
(sqrt a)
(sqrt.f64 a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+.f64 (sqrt.f64 a) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 b #s(literal 1/2 binary64))))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 b (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 b #s(literal 1/16 binary64))))))))
(sqrt b)
(sqrt.f64 b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(.f64 b (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) a))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(.f64 b (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) a)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (*.f64 a a) #s(literal -1/8 binary64))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(.f64 b (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (.f64 (.f64 a (.f64 a a)) #s(literal 1/16 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (*.f64 a a) #s(literal -1/8 binary64))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 b))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) a)) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) a)) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) #s(literal -1 binary64))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (.f64 b b))) (.f64 #s(literal 1/2 binary64) a)) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (/.f64 (.f64 (.f64 a (.f64 a a)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))))
b
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -1 binary64) (/.f64 b a))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -1 binary64) (/.f64 b a))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -1 binary64) (/.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 (+.f64 #s(literal 1 binary64) (/.f64 a b)))
(* b (+ 1 (/ a b)))
(*.f64 b (+.f64 #s(literal 1 binary64) (/.f64 a b)))
(* b (+ 1 (/ a b)))
(*.f64 b (+.f64 #s(literal 1 binary64) (/.f64 a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (-.f64 #s(literal -1 binary64) (/.f64 a b)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (-.f64 #s(literal -1 binary64) (/.f64 a b)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (-.f64 #s(literal -1 binary64) (/.f64 a b)))

eval66.0ms (0.8%)

Compiler: Compiled 14020 to 1741 computations (87.6% saved)

prune64.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	489	1	490
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	490	3	493

Accuracy

100.0%

Counts

493 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(+.f64 a (.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a))))
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b)))
✓	99.1%	a

Compiler

Compiled 25 to 16 computations (36% saved)

simplify38.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

168×	`fnmadd-define`
160×	`sum3-define`
128×	`fma-lowering-fma.f32`
128×	`fnmsub-define`
128×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	25
1	11	25
2	16	25
3	23	25
4	34	25
5	74	25
6	147	25
7	251	25
8	353	25
9	518	25
10	651	25
11	679	25
12	687	25
0	687	25

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize47.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 a b)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 a b))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 a b))
✓	accuracy	99.2%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b)))

Results

39.0ms

256×

valid

Compiler

Compiled 28 to 8 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sqrt: 19.0ms (79.1% of total)

ival-sub: 2.0ms (8.3% of total)

ival-mult: 2.0ms (8.3% of total)

ival-add: 1.0ms (4.2% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0%)

Counts

5 → 120

Calls

Call 1

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

Outputs
#<alt (* b (sqrt -1))>
#<alt (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))>
#<alt a>
#<alt (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))>
#<alt (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))>
#<alt (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))>
#<alt (* -1 (* a (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))>
#<alt a>
#<alt (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))>
#<alt (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))>
#<alt (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))>
#<alt (* b (sqrt -1))>
#<alt (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))>
#<alt (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))>
#<alt (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))>
#<alt (* -1 (* b (sqrt -1)))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))>
#<alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))>
#<alt (* (sqrt b) (sqrt -1))>
#<alt (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))>
#<alt (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))>
#<alt (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt a)>
#<alt (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))>
#<alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))>
#<alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))>
#<alt (* (sqrt b) (sqrt -1))>
#<alt (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))>
#<alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))>
#<alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt b) (sqrt -1)))>
#<alt (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))>
#<alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))>
#<alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))>
#<alt (* -1 b)>
#<alt (- a b)>
#<alt (- a b)>
#<alt (- a b)>
#<alt a>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt (* a (+ 1 (* -1 (/ b a))))>
#<alt a>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt (* -1 (* a (- (/ b a) 1)))>
#<alt a>
#<alt (+ a (* -1 b))>
#<alt (+ a (* -1 b))>
#<alt (+ a (* -1 b))>
#<alt (* -1 b)>
#<alt (* b (- (/ a b) 1))>
#<alt (* b (- (/ a b) 1))>
#<alt (* b (- (/ a b) 1))>
#<alt (* -1 b)>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (* -1 (* b (+ 1 (* -1 (/ a b)))))>
#<alt (sqrt b)>
#<alt (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))>
#<alt (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))>
#<alt (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt a)>
#<alt (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))>
#<alt (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))>
#<alt (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))>
#<alt (sqrt b)>
#<alt (* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))>
#<alt (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))>
#<alt (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))>
#<alt (* -1 (* (sqrt b) (pow (sqrt -1) 2)))>
#<alt (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))>
#<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

30 calls:

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

rewrite312.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3062×	`-lowering-.f32`
3062×	`-lowering-.f64`
2774×	`/-lowering-/.f32`
2774×	`/-lowering-/.f64`
1316×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	33	20
2	275	20
3	5353	20
0	8285	20

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 366

Calls

Call 1

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

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

simplify230.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

4190×	`-lowering-.f32`
4190×	`-lowering-.f64`
2094×	`+-lowering-+.f64`
2094×	`+-lowering-+.f32`
1400×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	434	2046
1	1530	1584
2	6849	1567
0	8057	1567

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* (sqrt b) (sqrt -1))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(* (sqrt b) (sqrt -1))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* (sqrt b) (sqrt -1)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(* -1 b)
(- a b)
(- a b)
(- a b)
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
a
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
a
(+ a (* -1 b))
(+ a (* -1 b))
(+ a (* -1 b))
(* -1 b)
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* -1 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(sqrt b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(sqrt b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
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
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 b (sqrt.f64 #s(literal -1 binary64))))) a)) (+.f64 (.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(+.f64 (.f64 b (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b) (+.f64 (/.f64 (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 (.f64 b b) (-.f64 #s(literal 0 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 a (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (.f64 b b))) (.f64 b (sqrt.f64 #s(literal -1 binary64))))) a)))))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(+.f64 a (/.f64 #s(literal 0 binary64) a))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(.f64 a (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) a)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) #s(literal 0 binary64)) (.f64 a a)))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(.f64 a (+.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) #s(literal 0 binary64)) (.f64 a a))) (/.f64 #s(literal 0 binary64) a)) (/.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 a (.f64 a a))))))
(* -1 (* a (pow (sqrt -1) 2)))
a
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(+.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) a)) a)
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (*.f64 b b)) #s(literal 0 binary64)) a) #s(literal 0 binary64)) a)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 b b)) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) a)) (-.f64 #s(literal 0 binary64) a)) a)) (-.f64 #s(literal 0 binary64) a))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+.f64 a (/.f64 #s(literal 0 binary64) a))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 b (/.f64 (/.f64 #s(literal 0 binary64) a) a))) b) a) (+.f64 a (/.f64 #s(literal 0 binary64) a)))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(+.f64 (+.f64 a (/.f64 #s(literal 0 binary64) a)) (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 b (/.f64 (/.f64 #s(literal 0 binary64) a) a))) b) a) (/.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (/.f64 #s(literal 0 binary64) a) a) #s(literal 0 binary64))) (.f64 a (*.f64 a a)))))
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(.f64 b (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 a a) #s(literal 0 binary64))) (.f64 b (*.f64 b (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(.f64 b (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 b (.f64 b b))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 a a) #s(literal 0 binary64))) (.f64 b (*.f64 b (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* b (sqrt -1)))
(-.f64 #s(literal 0 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(-.f64 #s(literal 0 binary64) (+.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(-.f64 #s(literal 0 binary64) (.f64 b (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 a a)) #s(literal 0 binary64)) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) b))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(.f64 (-.f64 #s(literal 0 binary64) b) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 a a) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) b)) b)) b)))
(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (*.f64 #s(literal 1/2 binary64) a)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)) (.f64 a (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 a #s(literal -1/8 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)) (.f64 a (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (sqrt.f64 #s(literal -1 binary64))) (.f64 a (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal 1/16 binary64) (/.f64 a (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 b #s(literal -1/2 binary64)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(.f64 a (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (.f64 b b)) #s(literal -1/16 binary64)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 a))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/2 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/2 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (.f64 (.f64 (*.f64 b b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))) #s(literal 1/8 binary64))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(-.f64 #s(literal 0 binary64) (.f64 a (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/2 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (+.f64 (.f64 (.f64 (.f64 b b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))) #s(literal 1/8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (*.f64 b b)) #s(literal -1/16 binary64)))))))
(sqrt a)
(sqrt.f64 a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+.f64 (sqrt.f64 a) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 b #s(literal -1/2 binary64))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 #s(literal -1/8 binary64) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 b (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 b #s(literal -1/16 binary64))))))))
(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(.f64 b (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(.f64 b (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 b (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (/.f64 (.f64 (.f64 a (.f64 a a)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))
(* -1 (* (sqrt b) (sqrt -1)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 b)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (.f64 b (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) a))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 a (*.f64 (sqrt.f64 #s(literal -1 binary64)) a)))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 a (.f64 (sqrt.f64 #s(literal -1 binary64)) a)))) (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 a (.f64 a a))))))))
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
a
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (* -1 (/ b a))))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
(* -1 (* a (- (/ b a) 1)))
(*.f64 a (-.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* b (- (/ a b) 1))
(*.f64 b (+.f64 #s(literal -1 binary64) (/.f64 a b)))
(* -1 b)
(-.f64 #s(literal 0 binary64) b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(.f64 b (.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(.f64 b (.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(.f64 b (.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 a b))))
(sqrt b)
(sqrt.f64 b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+.f64 (sqrt.f64 b) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 #s(literal 1/2 binary64) a)))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+.f64 (sqrt.f64 b) (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 a #s(literal -1/8 binary64))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(+.f64 (sqrt.f64 b) (.f64 a (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 a (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 a #s(literal 1/16 binary64))))))))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 b #s(literal 1/2 binary64)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(.f64 a (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (.f64 b b)) #s(literal 1/16 binary64)))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 a))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64)))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (*.f64 b b) #s(literal -1/8 binary64))) #s(literal -1 binary64))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 (+.f64 (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64)))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64))) #s(literal -1 binary64))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (*.f64 b b)) #s(literal 1/16 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))
(sqrt a)
(sqrt.f64 a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+.f64 (sqrt.f64 a) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 b #s(literal 1/2 binary64))))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 #s(literal -1/8 binary64) b)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(+.f64 (sqrt.f64 a) (.f64 b (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (.f64 b (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 b #s(literal 1/16 binary64))))))))
(sqrt b)
(sqrt.f64 b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(.f64 b (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 #s(literal 1/2 binary64) (.f64 a (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (*.f64 b b))))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(.f64 b (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 #s(literal 1/2 binary64) (.f64 a (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (.f64 a a) #s(literal -1/8 binary64)))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(.f64 b (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (.f64 a a) #s(literal -1/8 binary64))) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 a (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (.f64 (.f64 a (.f64 a a)) #s(literal 1/16 binary64)))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 b))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 a (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 a (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))))) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 (*.f64 a a) #s(literal -1/8 binary64)) #s(literal -1 binary64))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 a (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))))) (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (/.f64 (.f64 (.f64 a (*.f64 a a)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))))
b
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 b a))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 b a))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) a) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.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 (+.f64 #s(literal 1 binary64) (/.f64 a b)))
(* b (+ 1 (/ a b)))
(*.f64 b (+.f64 #s(literal 1 binary64) (/.f64 a b)))
(* b (+ 1 (/ a b)))
(*.f64 b (+.f64 #s(literal 1 binary64) (/.f64 a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 #s(literal -1 binary64) (/.f64 a (-.f64 #s(literal 0 binary64) b))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 #s(literal -1 binary64) (/.f64 a (-.f64 #s(literal 0 binary64) b))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal 0 binary64) b) (+.f64 #s(literal -1 binary64) (/.f64 a (-.f64 #s(literal 0 binary64) b))))

eval72.0ms (0.8%)

Compiler: Compiled 13969 to 1761 computations (87.4% saved)

prune119.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	486	0	486
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	486	3	489

Accuracy

100.0%

Counts

489 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(+.f64 a (.f64 b (.f64 b (/.f64 #s(literal -1/2 binary64) a))))
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b)))
✓	99.1%	a

Compiler

Compiled 75 to 37 computations (50.7% saved)

regimes14.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

6 calls:

2.0ms	b
2.0ms	a
2.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
2.0ms	(-.f64 (.f64 a a) (.f64 b b))
2.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
99.8%	1	`a`
99.8%	1	`b`
99.8%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.8%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.8%	1	`(*.f64 a a)`
99.8%	1	`(*.f64 b b)`

Compiler

Compiled 35 to 21 computations (40% saved)

regimes15.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
a

Outputs
a

Calls

2 calls:

13.0ms	a
1.0ms	b

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness291.0ms (3.4%)

Rules

3920×	`-lowering-.f32`
3920×	`-lowering-.f64`
1966×	`fnmadd-define`
1424×	`/-lowering-/.f32`
1424×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	776
1	356	649
2	1295	607
3	5518	604
0	8050	604

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 26 to 16 computations (38.5% saved)

preprocess32.0ms (0.4%)

Remove: (abs b)
Compiler: Compiled 140 to 86 computations (38.6% saved)

Iter	Nodes	Cost
0	8	26
1	13	26
2	18	26
3	25	26
4	36	26
5	76	26
6	149	26
7	254	26
8	355	26
9	520	26
10	653	26
11	681	26
12	689	26
0	689	26

Iter	Nodes	Cost
0	7	25
1	11	25
2	16	25
3	23	25
4	34	25
5	74	25
6	147	25
7	251	25
8	353	25
9	518	25
10	651	25
11	679	25
12	687	25
0	687	25

Iter	Nodes	Cost
0	8	26
1	13	26
2	18	26
3	25	26
4	36	26
5	76	26
6	149	26
7	254	26
8	355	26
9	520	26
10	653	26
11	681	26
12	689	26
0	689	26

Iter	Nodes	Cost
0	7	25
1	11	25
2	16	25
3	23	25
4	34	25
5	74	25
6	147	25
7	251	25
8	353	25
9	518	25
10	651	25
11	679	25
12	687	25
0	687	25

analyze48.0ms (0.6%)

sample894.0ms (10.4%)

preprocess199.0ms (2.3%)

explain173.0ms (2%)

eval25.0ms (0.3%)

prune1.0ms (0%)

simplify127.0ms (1.5%)

localize41.0ms (0.5%)

series5.0ms (0.1%)

rewrite3.8s (44.1%)

simplify265.0ms (3.1%)

eval104.0ms (1.2%)

prune48.0ms (0.6%)

simplify90.0ms (1.1%)

localize78.0ms (0.9%)

series39.0ms (0.5%)

rewrite313.0ms (3.6%)

simplify229.0ms (2.7%)

eval107.0ms (1.2%)

prune79.0ms (0.9%)

simplify19.0ms (0.2%)

localize48.0ms (0.6%)

series3.0ms (0%)

rewrite299.0ms (3.5%)

simplify266.0ms (3.1%)

eval66.0ms (0.8%)

prune64.0ms (0.7%)

simplify38.0ms (0.4%)

localize47.0ms (0.6%)

series4.0ms (0%)

rewrite312.0ms (3.6%)

simplify230.0ms (2.7%)

eval72.0ms (0.8%)

prune119.0ms (1.4%)

regimes14.0ms (0.2%)

regimes15.0ms (0.2%)

simplify7.0ms (0.1%)

soundness291.0ms (3.4%)

preprocess32.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	26
1	13	26
2	18	26
3	25	26
4	36	26
5	76	26
6	149	26
7	254	26
8	355	26
9	520	26
10	653	26
11	681	26
12	689	26
0	689	26

Iter	Nodes	Cost
0	7	25
1	11	25
2	16	25
3	23	25
4	34	25
5	74	25
6	147	25
7	251	25
8	353	25
9	518	25
10	651	25
11	679	25
12	687	25
0	687	25