Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze55.0ms (1.5%)

Memory

-17.6MiB live, 21.8MiB allocated

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 10 to 8 computations (20% saved)

sample1.0s (28.3%)

Memory

4.1MiB live, 909.3MiB allocated

Samples

610.0ms	8 256×	0	valid
51.0ms	618×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 363.0ms

ival-mult: 220.0ms (60.6% of total)

ival-sqrt: 94.0ms (25.9% of total)

ival-sub: 39.0ms (10.7% of total)

ival-true: 6.0ms (1.7% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain98.0ms (2.7%)

Memory

33.9MiB live, 71.6MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	oflow-rescue	116	0
↳	`(*.f64 b b)`	overflow	17
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	116
↳	`(*.f64 a a)`	overflow	116
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	18	0
↳	`(*.f64 b b)`	underflow	99
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	18
↳	`(*.f64 a a)`	underflow	18
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	17	0
↳	`(*.f64 a a)`	overflow	116
↳	`(*.f64 b b)`	overflow	17

Confusion

	Predicted +	Predicted -
+	134	0
-	0	122

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	134	0	0
-	0	0	122

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	122
1	117
2	17

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 81 to 28 computations (65.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 7.0ms (51.2% of total)

ival-sqrt: 4.0ms (29.3% of total)

ival-sub: 2.0ms (14.6% of total)

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

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

preprocess242.0ms (6.8%)

Memory

-9.0MiB live, 186.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	69	42
2	209	42
3	726	42
4	2333	42
5	3303	42
6	4300	42
7	6458	42
8	7352	42
0	6	8
0	10	8
1	27	8
2	97	8
3	352	8
4	1283	8
5	2976	8
6	4595	8
7	7642	8
0	8151	8

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

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

Symmetry

(abs b)

(abs a)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.7%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify138.0ms (3.9%)

Memory

-20.5MiB live, 142.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	27	23
2	97	23
3	352	23
4	1283	23
5	2976	23
6	4595	23
7	7642	23
0	8151	23

Stop Event

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

Calls

Call 1

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

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

localize18.0ms (0.5%)

Memory

30.4MiB live, 30.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 b b)
accuracy	0.0	(*.f64 a a)
accuracy	3.3906250000000004	(-.f64 (.f64 a a) (.f64 b b))
accuracy	31.21315179931217	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Samples

13.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

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

ival-mult: 3.0ms (46.4% of total)

ival-sqrt: 2.0ms (30.9% of total)

ival-sub: 1.0ms (15.5% of total)

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

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

series21.0ms (0.6%)

Memory

-29.3MiB live, 8.6MiB allocated

Counts

4 → 29

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms	a	@	0	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms	b	@	0	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))

simplify21.0ms (0.6%)

Memory

23.9MiB live, 23.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	542
0	367	518

Stop Event

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

Counts

29 → 28

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

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

rewrite128.0ms (3.6%)

Memory

-3.7MiB live, 151.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	45	21
2	385	21
3	4959	18
0	8582	14

Stop Event

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

Counts

4 → 238

Calls

Call 1

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

Outputs
(*.f64 (neg.f64 (sqrt.f64 (-.f64 a b))) (neg.f64 (sqrt.f64 (-.f64 a b))))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 a b))) (fabs.f64 (sqrt.f64 (-.f64 a b))))
(.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (pow.f64 (hypot.f64 (.f64 b (-.f64 a b)) (*.f64 a a)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (-.f64 a b)))
(*.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (pow.f64 (hypot.f64 b a) #s(literal -1 binary64)))
(pow.f64 (/.f64 (hypot.f64 (.f64 b (-.f64 a b)) (.f64 a a)) (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 a b))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (sqrt.f64 (-.f64 a b))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (hypot.f64 b a) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 a b)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (neg.f64 (hypot.f64 (.f64 b (-.f64 a b)) (.f64 a a))))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (.f64 b (-.f64 a b)) (.f64 a a)) (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 b a) #s(literal -1 binary64)))
(/.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (hypot.f64 (.f64 b (-.f64 a b)) (.f64 a a)))
(/.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (neg.f64 (hypot.f64 b a)))
(/.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (hypot.f64 b a))
(sqrt.f64 (exp.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))))
(sqrt.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(fabs.f64 (hypot.f64 b a))
(hypot.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 b)))
(hypot.f64 (exp.f64 (log.f64 a)) b)
(hypot.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 a)))
(hypot.f64 (exp.f64 (log.f64 b)) a)
(hypot.f64 b (exp.f64 (log.f64 a)))
(hypot.f64 b a)
(hypot.f64 a (exp.f64 (log.f64 b)))
(hypot.f64 a b)
(exp.f64 (fma.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 1/4 binary64) (*.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64) (*.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 a b))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (hypot.f64 b a)))
(+.f64 (cosh.f64 (log.f64 (hypot.f64 b a))) (sinh.f64 (log.f64 (hypot.f64 b a))))
(*.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64))))) (-.f64 (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (+.f64 (pow.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))))
(*.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(.f64 (/.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (/.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (pow.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(.f64 (pow.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(*.f64 (-.f64 a b) (-.f64 a b))
(*.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (pow.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (pow.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (hypot.f64 b a) (hypot.f64 b a))
(pow.f64 (*.f64 (exp.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))) (exp.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (exp.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (exp.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (-.f64 a b)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (hypot.f64 b a) #s(literal 2 binary64))
(/.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 a b)) (-.f64 a b))
(/.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))
(/.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (pow.f64 (-.f64 (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 a b)) (fma.f64 b (-.f64 a b) (.f64 a a)))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 18 binary64)) (pow.f64 b #s(literal 18 binary64))) (pow.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64))) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64))))
(/.f64 (.f64 (-.f64 a b) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 b (-.f64 a b) (.f64 a a)))
(/.f64 (*.f64 (-.f64 a b) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) (-.f64 a b))
(/.f64 (*.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (-.f64 a b)) (-.f64 a b))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 2 binary64))) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64))) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))))))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))
(/.f64 (.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 (-.f64 a b) (fma.f64 b (-.f64 a b) (*.f64 a a))))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (*.f64 b a) #s(literal 4 binary64)))) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 18 binary64)) (pow.f64 b #s(literal 18 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (.f64 b a) #s(literal 6 binary64))) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(/.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) (.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64)))) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (.f64 (-.f64 (pow.f64 (.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 b #s(literal 6 binary64)))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (*.f64 b a) #s(literal 4 binary64)))))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (hypot.f64 (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(/.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))
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(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 b)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 b) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 b) #s(literal 2 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 b b))

eval39.0ms (1.1%)

Memory: 0.6MiB live, 83.2MiB allocated
Compiler: Compiled 4 728 to 848 computations (82.1% saved)

prune8.0ms (0.2%)

Memory

-15.5MiB live, 23.6MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	258	7	265
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	258	8	266

Accuracy

99.0%

Counts

266 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(hypot.f64 b a)
	96.6%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (-.f64 a b)))
▶	50.7%	(sqrt.f64 (fma.f64 b b (*.f64 a a)))
✓	50.7%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
▶	1.3%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
	89.7%	(exp.f64 (log.f64 (hypot.f64 b a)))
▶	92.7%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
▶	1.2%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))

Compiler

Compiled 138 to 98 computations (29% saved)

simplify132.0ms (3.7%)

Memory

6.4MiB live, 118.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 b b)
cost-diff	0	(/.f64 (*.f64 b b) a)
cost-diff	0	(fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a)
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
cost-diff	0	(*.f64 a a)
cost-diff	0	(fma.f64 b b (*.f64 a a))
cost-diff	4	(sqrt.f64 (fma.f64 b b (*.f64 a a)))
cost-diff	0	(*.f64 b b)
cost-diff	0	(neg.f64 (*.f64 b b))
cost-diff	0	#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
cost-diff	0	(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
cost-diff	0	(neg.f64 a)
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
cost-diff	0	(hypot.f64 b a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	102
0	30	102
1	61	102
2	182	102
3	610	102
4	2422	102
5	4581	102
6	5657	102
0	8079	102

Stop Event

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

Calls

Call 1

Inputs
(hypot.f64 b a)
b
a
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
a
(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
(neg.f64 (*.f64 b b))
(*.f64 b b)
b
(sqrt.f64 (fma.f64 b b (*.f64 a a)))
(fma.f64 b b (*.f64 a a))
b
(*.f64 a a)
a
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
(fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a)
(/.f64 (*.f64 b b) a)
(*.f64 b b)
b
a
#s(literal -1/2 binary64)

Outputs
(hypot.f64 b a)
(hypot.f64 a b)
b
a
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
a
(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(neg.f64 (*.f64 b b))
(*.f64 (neg.f64 b) b)
(*.f64 b b)
b
(sqrt.f64 (fma.f64 b b (*.f64 a a)))
(hypot.f64 a b)
(fma.f64 b b (*.f64 a a))
(fma.f64 a a (*.f64 b b))
b
(*.f64 a a)
a
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 b b) a) a))
(fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a)
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 b b) a) a)
(/.f64 (*.f64 b b) a)
(*.f64 b b)
b
a
#s(literal -1/2 binary64)

localize44.0ms (1.2%)

Memory

26.4MiB live, 102.8MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a)
accuracy	0.0	(*.f64 b b)
accuracy	0.2964769237575724	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
accuracy	7.462917617404587	(/.f64 (*.f64 b b) a)
accuracy	0.0	(*.f64 a a)
accuracy	0.00390625	(fma.f64 b b (*.f64 a a))
accuracy	31.21315196666799	(sqrt.f64 (fma.f64 b b (*.f64 a a)))
accuracy	0.0	(*.f64 b b)
accuracy	0.0	(neg.f64 (*.f64 b b))
accuracy	31.21315179931217	(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
accuracy	58.304835051820305	#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
accuracy	0.0	(neg.f64 a)
accuracy	63.23939388584669	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
accuracy	0.0	(hypot.f64 b a)

Samples

32.0ms

256×

valid

Compiler

Compiled 200 to 36 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-hypot: 6.0ms (28.2% of total)

ival-mult: 5.0ms (23.5% of total)

ival-sub: 3.0ms (14.1% of total)

ival-div: 2.0ms (9.4% of total)

ival-add: 2.0ms (9.4% of total)

ival-sqrt: 2.0ms (9.4% of total)

ival-neg: 2.0ms (9.4% of total)

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

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

exact: 0.0ms (0% of total)

series26.0ms (0.7%)

Memory

-13.7MiB live, 37.5MiB allocated

Counts

13 → 57

Calls

Call 1

Inputs
(hypot.f64 b a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
(neg.f64 (*.f64 b b))
(*.f64 b b)
(sqrt.f64 (fma.f64 b b (*.f64 a a)))
(fma.f64 b b (*.f64 a a))
(*.f64 a a)
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
(fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a)
(/.f64 (*.f64 b b) a)

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	b	@	0	((sqrt (+ (* b b) (* a a))) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a))
9.0ms	a	@	-inf	((sqrt (+ (* b b) (* a a))) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a))
2.0ms	a	@	0	((sqrt (+ (* b b) (* a a))) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a))
2.0ms	b	@	inf	((sqrt (+ (* b b) (* a a))) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a))
2.0ms	a	@	inf	((sqrt (+ (* b b) (* a a))) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a))

simplify38.0ms (1.1%)

Memory

-9.2MiB live, 29.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	195	1024
0	623	971

Stop Event

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

Counts

57 → 55

Calls

Call 1

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

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

rewrite110.0ms (3.1%)

Memory

1.1MiB live, 156.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	90
0	30	89
1	106	89
2	881	73
0	9784	73

Stop Event

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

Counts

13 → 604

Calls

Call 1

Inputs
(hypot.f64 b a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
(neg.f64 (*.f64 b b))
(*.f64 b b)
(sqrt.f64 (fma.f64 b b (*.f64 a a)))
(fma.f64 b b (*.f64 a a))
(*.f64 a a)
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
(fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a)
(/.f64 (*.f64 b b) a)

Outputs
(*.f64 (neg.f64 (sqrt.f64 (-.f64 a b))) (neg.f64 (sqrt.f64 (-.f64 a b))))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 a b))) (fabs.f64 (sqrt.f64 (-.f64 a b))))
(*.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) b a)) (sqrt.f64 (fma.f64 #s(literal -1 binary64) b a)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))) (hypot.f64 a b))
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))) (hypot.f64 (fma.f64 b b (.f64 a b)) (*.f64 a a)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 a b))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (fma.f64 b b (.f64 a b)) (*.f64 a a)))
(.f64 (.f64 (hypot.f64 a b) (hypot.f64 a b)) (/.f64 #s(literal 1 binary64) (hypot.f64 a b)))
(.f64 (.f64 (hypot.f64 a b) (hypot.f64 a b)) (sqrt.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal -1 binary64))))
(.f64 (.f64 (hypot.f64 a b) (hypot.f64 a b)) (pow.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (hypot.f64 (fma.f64 b b (.f64 a b)) (*.f64 a a))))
(.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (.f64 a a) (fma.f64 a a (*.f64 b b)) (pow.f64 b #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (pow.f64 (pow.f64 (fma.f64 (.f64 a a) (fma.f64 a a (*.f64 b b)) (pow.f64 b #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (-.f64 a b)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 a a (*.f64 b b)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 a b)) #s(literal 2 binary64))
(pow.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) #s(literal 1/4 binary64))
(pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (*.f64 (hypot.f64 a b) (hypot.f64 a b))) (neg.f64 (hypot.f64 a b)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (neg.f64 (hypot.f64 (fma.f64 b b (.f64 a b)) (.f64 a a))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 a a (*.f64 b b)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 a a) (fma.f64 a a (.f64 b b)) (pow.f64 b #s(literal 4 binary64))))))
(/.f64 (*.f64 (hypot.f64 a b) (hypot.f64 a b)) (hypot.f64 a b))
(/.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (hypot.f64 (fma.f64 b b (.f64 a b)) (.f64 a a)))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 a b) (*.f64 (hypot.f64 a b) (hypot.f64 a b))))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (fma.f64 b b (.f64 a b)) (.f64 a a)) (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal -1 binary64))))
(sqrt.f64 (fma.f64 a a (*.f64 b b)))
(fabs.f64 (hypot.f64 a b))
(hypot.f64 (/.f64 (.f64 a a) (fma.f64 #s(literal -1 binary64) b a)) (/.f64 (.f64 b b) (fma.f64 #s(literal -1 binary64) b a)))
(hypot.f64 (/.f64 (.f64 a a) (fma.f64 #s(literal -1 binary64) b a)) (/.f64 (.f64 b b) (-.f64 a b)))
(hypot.f64 (/.f64 (.f64 b b) (fma.f64 #s(literal -1 binary64) b a)) (/.f64 (.f64 a a) (fma.f64 #s(literal -1 binary64) b a)))
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(fma.f64 (.f64 a a) (pow.f64 a #s(literal -1 binary64)) (.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) b)) (/.f64 b a)))
(fma.f64 (.f64 a a) (pow.f64 a #s(literal -1 binary64)) (.f64 (neg.f64 b) (*.f64 (/.f64 b a) #s(literal -1/2 binary64))))
(fma.f64 (.f64 a a) (pow.f64 a #s(literal -1 binary64)) (neg.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b b) a))))
(fma.f64 (.f64 a a) (pow.f64 a #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b b) a)))
(fma.f64 (*.f64 b b) (/.f64 #s(literal 1/2 binary64) a) a)
(fma.f64 (.f64 b b) (.f64 (pow.f64 a #s(literal -1 binary64)) #s(literal -1/2 binary64)) a)
(fma.f64 a #s(literal -1 binary64) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) b)) (/.f64 b a)))
(fma.f64 a #s(literal -1 binary64) (.f64 (neg.f64 b) (.f64 (/.f64 b a) #s(literal -1/2 binary64))))
(fma.f64 a #s(literal -1 binary64) (neg.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a))))
(fma.f64 a #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)))
(fma.f64 a #s(literal 1 binary64) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) b)) (/.f64 b a)))
(fma.f64 a #s(literal 1 binary64) (.f64 (neg.f64 b) (.f64 (/.f64 b a) #s(literal -1/2 binary64))))
(fma.f64 a #s(literal 1 binary64) (neg.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a))))
(fma.f64 a #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)))
(fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)))))
(-.f64 (/.f64 (.f64 a a) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b b) a) a)))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)) (/.f64 (.f64 a a) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b b) a) a)))
(-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) a)
(-.f64 a (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) b)) (/.f64 b a)))
(-.f64 a (.f64 (neg.f64 b) (.f64 (/.f64 b a) #s(literal -1/2 binary64))))
(-.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)))
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a a (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 b b) a) a))))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 3 binary64)) (fma.f64 a a (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 b b) a) a))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 3 binary64)) (fma.f64 a a (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 b b) a) a))))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a a (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 b b) a) a))))))
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)))) (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)) (neg.f64 (/.f64 (.f64 a a) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b b) a) a))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)) (/.f64 (.f64 a a) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b b) a) a)))
(+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)) a)
(+.f64 a (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) b)) (/.f64 b a)))
(+.f64 a (.f64 (neg.f64 b) (.f64 (/.f64 b a) #s(literal -1/2 binary64))))
(+.f64 a (neg.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a))))
(+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)))
(.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 a (*.f64 b b)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 b #s(literal 1 binary64)) (/.f64 b a))
(.f64 (.f64 b #s(literal -1 binary64)) (/.f64 b a))
(*.f64 (/.f64 b a) (/.f64 b #s(literal 1 binary64)))
(.f64 (/.f64 b a) (.f64 b #s(literal -1 binary64)))
(*.f64 (/.f64 b a) b)
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 a (.f64 b b)))))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 b b) a))
(*.f64 (pow.f64 a #s(literal -1 binary64)) (pow.f64 (pow.f64 b #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 a #s(literal -1 binary64)) (.f64 b b))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) a))
(*.f64 (neg.f64 b) (/.f64 b a))
(.f64 (/.f64 (.f64 b b) a) #s(literal 1 binary64))
(.f64 (.f64 b b) (pow.f64 a #s(literal -1 binary64)))
(*.f64 b (/.f64 b a))
(pow.f64 (/.f64 a (*.f64 b b)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64))) (/.f64 (.f64 b b) a))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 a (.f64 b b)) #s(literal -3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (/.f64 a (.f64 b b)) #s(literal -2 binary64)) (.f64 #s(literal 0 binary64) (/.f64 (.f64 b b) a)))))
(/.f64 (.f64 (neg.f64 b) #s(literal 1 binary64)) (.f64 #s(literal -1 binary64) (/.f64 a b)))
(/.f64 (.f64 (neg.f64 (pow.f64 b #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (*.f64 b b) a))
(/.f64 (.f64 (pow.f64 b #s(literal 6 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) #s(literal 0 binary64)) a))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 a (.f64 b b))) (*.f64 a a))
(/.f64 (/.f64 b #s(literal 1 binary64)) (/.f64 a b))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 a (*.f64 b b))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 a (*.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 a (*.f64 b b)))
(/.f64 (neg.f64 b) (/.f64 a b))
(/.f64 (/.f64 (*.f64 b b) a) #s(literal 1 binary64))
(/.f64 (*.f64 b b) a)
(/.f64 b (/.f64 a b))
(neg.f64 (/.f64 (*.f64 b b) a))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 b b) a))
(exp.f64 (.f64 (log.f64 (/.f64 a (.f64 b b))) #s(literal -1 binary64)))
(+.f64 #s(literal 0 binary64) (/.f64 (*.f64 b b) a))

eval74.0ms (2.1%)

Memory: 30.2MiB live, 102.2MiB allocated
Compiler: Compiled 14 263 to 1 709 computations (88% saved)

prune15.0ms (0.4%)

Memory

-10.5MiB live, 29.8MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	563	2	565
Fresh	2	0	2
Picked	5	0	5
Done	0	1	1
Total	570	3	573

Accuracy

99.8%

Counts

573 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.7%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
▶	99.5%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a))
▶	98.5%	#s(approx (sqrt (- (* a a) (* b b))) a)

Compiler

Compiled 35 to 24 computations (31.4% saved)

simplify117.0ms (3.3%)

Memory

9.3MiB live, 120.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 b a)
cost-diff	0	(*.f64 (/.f64 b a) b)
cost-diff	0	(fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a)
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a))
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	47
0	16	47
1	39	47
2	136	47
3	486	47
4	1862	47
5	4658	47
6	6572	47
0	8829	47

Stop Event

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

Calls

Call 1

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

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

localize44.0ms (1.2%)

Memory

-21.9MiB live, 64.6MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a)
accuracy	0.0	(/.f64 b a)
accuracy	0.1171875	(*.f64 (/.f64 b a) b)
accuracy	0.2964769237575724	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a))
accuracy	0.9699269366743634	#s(approx (sqrt (- (* a a) (* b b))) a)

Samples

36.0ms

256×

valid

Compiler

Compiled 86 to 25 computations (70.9% saved)

Precisions

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

ival-mult: 6.0ms (46.4% of total)

ival-div: 2.0ms (15.5% of total)

ival-sqrt: 2.0ms (15.5% of total)

ival-sub: 1.0ms (7.7% of total)

ival-add: 1.0ms (7.7% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

5 → 28

Calls

Call 1

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

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

Calls

6 calls:

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

simplify25.0ms (0.7%)

Memory

-7.9MiB live, 29.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	544
0	365	518

Stop Event

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

Counts

28 → 27

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

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

rewrite229.0ms (6.4%)

Memory

24.1MiB live, 110.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
0	16	43
1	74	43
2	626	43
0	8412	33

Stop Event

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

Counts

5 → 192

Calls

Call 1

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

Outputs
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b) a))
(.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a) #s(literal 2 binary64)))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64)) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a)))
(.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a) (-.f64 (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b)) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 a) a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64))) (fma.f64 (neg.f64 a) a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a))
(.f64 (/.f64 (fma.f64 (neg.f64 a) a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (fma.f64 a (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a) (pow.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b)) #s(literal 2 binary64))))
(.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 a (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b)))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)) (fma.f64 (neg.f64 a) a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64))))
(.f64 (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a)) #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))
(.f64 (neg.f64 (fma.f64 (neg.f64 a) a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)))
(.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a)))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))))
(.f64 (fma.f64 (neg.f64 a) a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a) (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a))))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b))) a)) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a)) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) a) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b) a)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) (fma.f64 a a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) (fma.f64 (.f64 a a) (fma.f64 a a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b)) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a)) #s(literal -1 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 a #s(literal 9 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 9 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a)) #s(literal -1 binary64))) (-.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) a) #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 (neg.f64 a) a (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64))) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a)))
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(fma.f64 (*.f64 b b) (/.f64 #s(literal -1/2 binary64) a) a)
(fma.f64 (.f64 b b) (.f64 (pow.f64 a #s(literal -1 binary64)) #s(literal -1/2 binary64)) a)
(fma.f64 b (*.f64 #s(literal -1/2 binary64) (/.f64 b a)) a)
(fma.f64 (.f64 a a) (/.f64 a (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b))) a))))
(fma.f64 a (/.f64 (.f64 a a) (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b))) a))))
(fma.f64 a #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)))
(-.f64 (/.f64 (.f64 a a) (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 2 binary64)) (-.f64 a (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b)))))
(-.f64 (.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a)))) (.f64 a (/.f64 a (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b) (neg.f64 a)))))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) (neg.f64 a))
(-.f64 a (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b)))
(+.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 0 binary64)) a)
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))) a))))
(+.f64 (.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a)))) (neg.f64 (.f64 a (/.f64 a (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b) (neg.f64 a))))))
(+.f64 (.f64 (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b) (neg.f64 a)))) (/.f64 (.f64 (neg.f64 a) a) (fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b) (neg.f64 a))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)) a)
(+.f64 a (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)))
(*.f64 (/.f64 b #s(literal 1 binary64)) (/.f64 b a))
(*.f64 (/.f64 b #s(literal -1 binary64)) (/.f64 (neg.f64 b) a))
(*.f64 (/.f64 (neg.f64 b) #s(literal -1 binary64)) (/.f64 b a))
(.f64 (.f64 (*.f64 b b) #s(literal 1 binary64)) (pow.f64 a #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 b) a) (neg.f64 b))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 (neg.f64 b) b) a))
(.f64 (.f64 (neg.f64 b) b) (/.f64 #s(literal -1 binary64) a))
(*.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 b (pow.f64 b #s(literal -1 binary64))))
(.f64 (pow.f64 a #s(literal -1 binary64)) (.f64 b b))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 b a) b))
(*.f64 (neg.f64 b) (/.f64 (neg.f64 b) a))
(*.f64 (/.f64 b a) (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal -1 binary64))))
(*.f64 (/.f64 b a) b)
(.f64 (.f64 b b) (pow.f64 a #s(literal -1 binary64)))
(*.f64 b (/.f64 b a))
(pow.f64 (/.f64 (/.f64 a b) b) #s(literal -1 binary64))
(/.f64 (/.f64 (*.f64 (neg.f64 b) b) #s(literal -1 binary64)) a)
(/.f64 (.f64 (.f64 b b) #s(literal 1 binary64)) a)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 a b) b)))
(/.f64 (*.f64 (neg.f64 b) b) (neg.f64 a))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 a b) b) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 a b) b))
(/.f64 (neg.f64 b) (/.f64 (neg.f64 a) b))
(/.f64 (/.f64 b a) (pow.f64 b #s(literal -1 binary64)))
(/.f64 (*.f64 b b) a)
(/.f64 b (/.f64 a b))
(neg.f64 (/.f64 (*.f64 (neg.f64 b) b) a))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 a)) (/.f64 (*.f64 (neg.f64 b) b) a))
(*.f64 (pow.f64 (/.f64 a b) #s(literal -1/2 binary64)) (pow.f64 (/.f64 a b) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 b)) (/.f64 #s(literal -1 binary64) a))
(*.f64 (/.f64 #s(literal -1 binary64) a) (neg.f64 b))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 b) a))
(*.f64 (pow.f64 a #s(literal -1 binary64)) (pow.f64 (pow.f64 b #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 a #s(literal -1 binary64)) b)
(*.f64 #s(literal 1 binary64) (/.f64 b a))
(*.f64 (neg.f64 b) (/.f64 #s(literal -1 binary64) a))
(*.f64 (/.f64 b a) #s(literal 1 binary64))
(*.f64 b (pow.f64 a #s(literal -1 binary64)))
(pow.f64 (/.f64 a b) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.f64 b) #s(literal -1 binary64)) a)
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 b)) (neg.f64 a))
(/.f64 (*.f64 (neg.f64 b) #s(literal 1 binary64)) (neg.f64 a))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 a) b))
(/.f64 (pow.f64 a #s(literal -1 binary64)) (pow.f64 b #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 a b))
(/.f64 (neg.f64 b) (neg.f64 a))
(/.f64 (/.f64 b a) #s(literal 1 binary64))
(/.f64 b a)
(neg.f64 (/.f64 (neg.f64 b) a))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 a)) (/.f64 (neg.f64 b) a))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 b) a))
(exp.f64 (*.f64 (log.f64 (/.f64 a b)) #s(literal -1 binary64)))

eval29.0ms (0.8%)

Memory: -20.6MiB live, 53.4MiB allocated
Compiler: Compiled 8 335 to 803 computations (90.4% saved)

prune4.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	218	4	222

Accuracy

99.8%

Counts

222 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.7%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
✓	99.5%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a))
▶	98.8%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
✓	98.5%	#s(approx (sqrt (- (* a a) (* b b))) a)

Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify191.0ms (5.4%)

Memory

-14.8MiB live, 64.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))
cost-diff	0	(sqrt.f64 a)
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
cost-diff	4	(fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
0	19	47
1	52	47
2	187	47
3	875	47
4	3772	47
5	5601	47
6	7059	47
0	8006	45

Stop Event

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

Calls

Call 1

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

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

localize54.0ms (1.5%)

Memory

0.3MiB live, 38.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))
accuracy	0.1171875	(*.f64 (/.f64 b a) b)
accuracy	0.2964769237575724	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
accuracy	0.47494125976844204	(fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b)))

Samples

23.0ms

256×

valid

Compiler

Compiled 96 to 28 computations (70.8% saved)

Precisions

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

ival-mult: 8.0ms (51.9% of total)

ival-sqrt: 3.0ms (19.5% of total)

ival-div: 2.0ms (13% of total)

ival-sub: 1.0ms (6.5% of total)

ival-add: 1.0ms (6.5% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

11.8MiB live, 11.8MiB allocated

Counts

5 → 30

Calls

Call 1

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

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

Calls

6 calls:

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

simplify27.0ms (0.8%)

Memory

-2.6MiB live, 33.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	126	561
0	383	535

Stop Event

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

Counts

30 → 29

Calls

Call 1

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

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

rewrite158.0ms (4.4%)

Memory

-3.8MiB live, 115.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	47
0	19	41
1	89	41
2	715	39
0	8648	34

Stop Event

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

Counts

5 → 283

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 b a)) (.f64 b (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))))
(.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 b a)) (.f64 b (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) #s(literal 3 binary64)) (pow.f64 a #s(literal 6 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 b a)) (.f64 b (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))) (pow.f64 a #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a))) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))
(.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))))
(.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) (pow.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))) #s(literal -1 binary64))))
(.f64 (pow.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) #s(literal -1 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))
(.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) #s(literal -1 binary64)) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)))
(.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))
(.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)))))
(.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) (pow.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a) #s(literal -1 binary64)))
(/.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (pow.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) #s(literal -1 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) #s(literal -1 binary64))) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 6 binary64))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a) #s(literal -1 binary64))) (+.f64 (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 b a)) (.f64 b (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 6 binary64))) (pow.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) #s(literal -1 binary64))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b)) #s(literal 9 binary64)) (pow.f64 a #s(literal 9 binary64))) (pow.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (pow.f64 a #s(literal 6 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64)) (.f64 a a)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))
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(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 b a)) b)
(.f64 (pow.f64 a #s(literal -1 binary64)) (.f64 (*.f64 b #s(literal -1/2 binary64)) b))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b)))
(.f64 (neg.f64 b) (.f64 #s(literal 1/2 binary64) (/.f64 b a)))
(.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b))
(.f64 (.f64 b b) (/.f64 #s(literal -1/2 binary64) a))
(.f64 (.f64 b b) (*.f64 (pow.f64 a #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 b b) (*.f64 (pow.f64 a #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 b a) b) #s(literal 1/2 binary64))
(.f64 (.f64 (/.f64 b a) b) #s(literal -1/2 binary64))
(.f64 (/.f64 b a) (fabs.f64 (.f64 b #s(literal -1/2 binary64))))
(.f64 (/.f64 b a) (.f64 #s(literal 1/2 binary64) b))
(.f64 (/.f64 b a) (.f64 b #s(literal -1/2 binary64)))
(.f64 b (fabs.f64 (.f64 #s(literal 1/2 binary64) (/.f64 b a))))
(.f64 b (.f64 #s(literal 1/2 binary64) (/.f64 b a)))
(.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))
(/.f64 (/.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) b) (sqrt.f64 a)) (sqrt.f64 a))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b)) (sqrt.f64 a)) (sqrt.f64 a))
(/.f64 (.f64 (.f64 b (/.f64 b (sqrt.f64 a))) #s(literal -1/2 binary64)) (sqrt.f64 a))
(/.f64 (.f64 (/.f64 b (sqrt.f64 a)) (.f64 b #s(literal -1/2 binary64))) (sqrt.f64 a))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 b #s(literal -1/2 binary64))) (/.f64 a b))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 b #s(literal -1/2 binary64))) (/.f64 a b))
(/.f64 (.f64 (neg.f64 b) (.f64 b #s(literal -1/2 binary64))) a)
(/.f64 (.f64 (.f64 b (/.f64 b (sqrt.f64 a))) #s(literal 1/2 binary64)) (sqrt.f64 a))
(/.f64 (.f64 (.f64 (neg.f64 b) b) #s(literal 1/2 binary64)) a)
(/.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) (/.f64 b (sqrt.f64 a))) (sqrt.f64 a))
(/.f64 (.f64 b (.f64 #s(literal 1/2 binary64) b)) a)
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 b (/.f64 b (sqrt.f64 a)))) (sqrt.f64 a))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) b) (/.f64 b (sqrt.f64 a))) (sqrt.f64 a))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) b) #s(literal -1 binary64)) (/.f64 a b))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) b) #s(literal 1 binary64)) (/.f64 a b))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b (/.f64 b (sqrt.f64 a)))) (sqrt.f64 a))
(/.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 a b))
(/.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) (neg.f64 b)) a)
(/.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 a b))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (neg.f64 b) b)) a)
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 b) b)) a)
(/.f64 (.f64 (.f64 (neg.f64 b) b) #s(literal -1/2 binary64)) a)
(/.f64 (neg.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) b)) a)
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b))) a)
(/.f64 (fabs.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) b)) a)
(/.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) b) a)
(/.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 a b))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b)) a)
(/.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 a b))
(/.f64 #s(literal 1 binary64) (/.f64 a (.f64 (.f64 b #s(literal -1/2 binary64)) b)))
(/.f64 #s(literal 1 binary64) (/.f64 a (.f64 #s(literal 1/2 binary64) (.f64 b b))))
(/.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 a b) b))
(/.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 a b) b))
(neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b)))
(sqrt.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b)))
(fabs.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b)))
(*.f64 (/.f64 b #s(literal 1 binary64)) (/.f64 b a))
(*.f64 (/.f64 (neg.f64 b) #s(literal -1 binary64)) (/.f64 b a))
(*.f64 (/.f64 b #s(literal -1 binary64)) (/.f64 b a))
(.f64 (.f64 (*.f64 b b) #s(literal 1 binary64)) (pow.f64 a #s(literal -1 binary64)))
(*.f64 (pow.f64 a #s(literal -1/2 binary64)) (/.f64 b (/.f64 (sqrt.f64 a) b)))
(.f64 (pow.f64 a #s(literal -1/2 binary64)) (.f64 b (/.f64 b (sqrt.f64 a))))
(.f64 (.f64 b (/.f64 b (sqrt.f64 a))) (pow.f64 a #s(literal -1/2 binary64)))
(*.f64 (/.f64 b (sqrt.f64 a)) (/.f64 b (sqrt.f64 a)))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 b a) b))
(.f64 (.f64 (neg.f64 b) b) (pow.f64 a #s(literal -1 binary64)))
(*.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 b (pow.f64 b #s(literal -1 binary64))))
(.f64 (pow.f64 a #s(literal -1 binary64)) (.f64 b b))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 b a) b))
(*.f64 (neg.f64 b) (/.f64 b a))
(.f64 (.f64 b b) (fabs.f64 (pow.f64 a #s(literal -1 binary64))))
(.f64 (.f64 b b) (pow.f64 a #s(literal -1 binary64)))
(*.f64 (/.f64 b a) (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal -1 binary64))))
(*.f64 (/.f64 b a) (neg.f64 b))
(*.f64 (/.f64 b a) b)
(*.f64 b (/.f64 b a))
(pow.f64 (/.f64 (/.f64 a b) b) #s(literal -1 binary64))
(pow.f64 (/.f64 b (sqrt.f64 a)) #s(literal 2 binary64))
(/.f64 (/.f64 (*.f64 b (/.f64 b (sqrt.f64 a))) #s(literal -1 binary64)) (sqrt.f64 a))
(/.f64 (/.f64 (*.f64 b (/.f64 b (sqrt.f64 a))) (pow.f64 a #s(literal 1/4 binary64))) (pow.f64 a #s(literal 1/4 binary64)))
(/.f64 (/.f64 (*.f64 (neg.f64 b) b) #s(literal -1 binary64)) a)
(/.f64 (*.f64 (/.f64 b (sqrt.f64 a)) (neg.f64 b)) (sqrt.f64 a))
(/.f64 (*.f64 (/.f64 b (sqrt.f64 a)) b) (sqrt.f64 a))
(/.f64 (.f64 (.f64 b b) #s(literal 1 binary64)) a)
(/.f64 (*.f64 b (/.f64 b (sqrt.f64 a))) (sqrt.f64 a))
(/.f64 (/.f64 b (sqrt.f64 a)) (/.f64 (sqrt.f64 a) b))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 a b) b))
(/.f64 (*.f64 (neg.f64 b) b) a)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 a) (*.f64 b (/.f64 b (sqrt.f64 a)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 a b) b) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 a b) b))
(/.f64 (neg.f64 b) (/.f64 a b))
(/.f64 (*.f64 b b) a)
(/.f64 (/.f64 b a) (pow.f64 b #s(literal -1 binary64)))
(/.f64 b (fabs.f64 (/.f64 a b)))
(/.f64 b (/.f64 a b))
(neg.f64 (*.f64 (/.f64 b a) b))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) a) (*.f64 (/.f64 b a) b))
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 b a) b))
(fabs.f64 (*.f64 (/.f64 b a) b))
(exp.f64 (-.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)) (log.f64 a)))

eval54.0ms (1.5%)

Memory: 5.8MiB live, 77.1MiB allocated
Compiler: Compiled 10 759 to 1 182 computations (89% saved)

prune8.0ms (0.2%)

Memory

21.5MiB live, 21.5MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	342	2	344
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	342	6	348

Accuracy

99.8%

Counts

348 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.7%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
	99.4%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 a (sqrt.f64 a)) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
✓	99.5%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a))
✓	98.8%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
	92.0%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (sqrt.f64 a) (exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
✓	98.5%	#s(approx (sqrt (- (* a a) (* b b))) a)

Compiler

Compiled 275 to 117 computations (57.5% saved)

regimes30.0ms (0.8%)

Memory

-18.1MiB live, 31.8MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
(sqrt.f64 (fma.f64 b b (*.f64 a a)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #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)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 a (sqrt.f64 a)) (sqrt.f64 a) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
(hypot.f64 b a)
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (sqrt.f64 a) (exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 b a) b))))
(exp.f64 (log.f64 (hypot.f64 b a)))

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

Calls

6 calls:

11.0ms	(-.f64 (.f64 a a) (.f64 b b))
4.0ms	b
4.0ms	a
4.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
4.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
99.5%	1	`a`
99.5%	1	`b`
99.5%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.5%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.5%	1	`(*.f64 a a)`
99.5%	1	`(*.f64 b b)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes11.0ms (0.3%)

Memory

21.5MiB live, 21.5MiB allocated

Accuracy

Total -62.6b remaining (-6449.5%)

Threshold costs -62.6b (-6449.5%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
(sqrt.f64 (fma.f64 b b (*.f64 a a)))

Outputs
#s(approx (sqrt (- (* a a) (* b b))) a)

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
98.5%	1	`a`
98.5%	1	`b`
98.5%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
98.5%	1	`(-.f64 (.f64 a a) (.f64 b b))`
98.5%	1	`(*.f64 a a)`
98.5%	1	`(*.f64 b b)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify82.0ms (2.3%)

Memory

-3.8MiB live, 69.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	29	27
2	99	27
3	357	27
4	1437	27
5	2803	27
6	5345	27

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness221.0ms (6.2%)

Memory

-33.1MiB live, 176.7MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	542
0	367	518
0	20	90
0	30	89
1	106	89
2	881	73
0	9784	73

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Compiler

Compiled 65 to 40 computations (38.5% saved)

preprocess52.0ms (1.4%)

Memory: 11.5MiB live, 94.2MiB allocated
Remove: (abs b)
Compiler: Compiled 198 to 120 computations (39.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze55.0ms (1.5%)

sample1.0s (28.3%)

explain98.0ms (2.7%)

preprocess242.0ms (6.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify138.0ms (3.9%)

localize18.0ms (0.5%)

series21.0ms (0.6%)

simplify21.0ms (0.6%)

rewrite128.0ms (3.6%)

eval39.0ms (1.1%)

prune8.0ms (0.2%)

simplify132.0ms (3.7%)

localize44.0ms (1.2%)

series26.0ms (0.7%)

simplify38.0ms (1.1%)

rewrite110.0ms (3.1%)

eval74.0ms (2.1%)

prune15.0ms (0.4%)

simplify117.0ms (3.3%)

localize44.0ms (1.2%)

series7.0ms (0.2%)

simplify25.0ms (0.7%)

rewrite229.0ms (6.4%)

eval29.0ms (0.8%)

prune4.0ms (0.1%)

simplify191.0ms (5.4%)

localize54.0ms (1.5%)

series6.0ms (0.2%)

simplify27.0ms (0.8%)

rewrite158.0ms (4.4%)

eval54.0ms (1.5%)

prune8.0ms (0.2%)

regimes30.0ms (0.8%)

regimes11.0ms (0.3%)

simplify82.0ms (2.3%)

soundness221.0ms (6.2%)

preprocess52.0ms (1.4%)

end0.0ms (0%)

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