Metrics for NMSE Section 6.1 mentioned, B

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze90.0ms (1%)

Memory

-6.4MiB live, 195.5MiB 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
12.5%	12.5%	87.4%	0.1%	0%	0%	0%	5
25%	25%	74.9%	0.1%	0%	0%	0%	6
46.9%	46.8%	53.1%	0.1%	0%	0%	0%	7
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	8
71.1%	71%	28.9%	0.1%	0%	0%	0%	9
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	10
85%	84.9%	15%	0.1%	0%	0%	0%	11
87.9%	87.8%	12.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 23 to 17 computations (26.1% saved)

sample1.4s (16%)

Memory

55.8MiB live, 1 774.5MiB allocated

Samples

1.0s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 690.0ms

ival-div: 293.0ms (42.5% of total)

ival-mult: 211.0ms (30.6% of total)

ival-pi: 92.0ms (13.3% of total)

ival-sub: 78.0ms (11.3% of total)

exact: 8.0ms (1.2% of total)

ival-true: 5.0ms (0.7% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain164.0ms (1.9%)

Memory

-2.1MiB live, 270.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
27	1	(3.138083908017419e+269 -1.572678449830746e-216)	3	(-2.344350915712001e+161 1.5171828992289433e-205)	`(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))`
16	0	-	0	-	`(-.f64 (.f64 b b) (.f64 a a))`
4	1	(-2.344350915712001e+161 1.5171828992289433e-205)	0	-	`(/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))`
0	0	-	0	-	`(.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (*.f64 a a))))`
0	0	-	0	-	`(*.f64 a a)`
0	0	-	0	-	`a`
0	0	-	0	-	`(/.f64 (PI.f64) #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(*.f64 b b)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) b)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) a)`
0	0	-	0	-	`b`
0	0	-	0	-	`(-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))`
0	0	-	0	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))`	*nu**	25	0
`-.f64`	`(-.f64 (.f64 b b) (.f64 a a))`	nan-rescue	16	0
↳	`(*.f64 b b)`	overflow	51
↳	`(*.f64 a a)`	overflow	66
`/.f64`	`(/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))`	n/o	5	0
↳	`(*.f64 b b)`	overflow	51
↳	`(*.f64 a a)`	overflow	66
↳	`(-.f64 (.f64 b b) (.f64 a a))`	overflow	101

Confusion

	Predicted +	Predicted -
+	43	5
-	3	205

Precision

0.9347826086956522

Recall

0.8958333333333334

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	43	0	5
-	3	0	205

Precision?

0.9347826086956522

Recall?

0.8958333333333334

Freqs

test

number	freq
0	210
1	46

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

51.0ms

512×

valid

Compiler

Compiled 179 to 49 computations (72.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-div: 13.0ms (39.1% of total)

ival-mult: 12.0ms (36.1% of total)

ival-sub: 4.0ms (12% of total)

ival-pi: 2.0ms (6% of total)

exact: 1.0ms (3% of total)

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

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

preprocess156.0ms (1.8%)

Memory

17.5MiB live, 166.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 062×	`lower-fma.f64`
8 062×	`lower-fma.f32`
4 668×	`lower-*.f32`
4 660×	`lower-*.f64`
2 098×	`lower-neg.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	109
1	115	95
2	418	95
3	2087	95
4	6060	95
0	15	21
0	26	21
1	46	19
2	108	19
3	393	18
4	1569	17
5	4280	17
0	8405	17

Stop Event

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

Calls

Call 1

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

Outputs

(*.f64 (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))

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

Symmetry

(sort a b)

Compiler

Compiled 21 to 15 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	80.1%	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify163.0ms (1.9%)

Memory

-33.7MiB live, 123.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	128	(-.f64 (.f64 b b) (.f64 a a))
cost-diff	320	(.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (*.f64 a a))))
cost-diff	320	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))
cost-diff	384	(/.f64 (PI.f64) #s(literal 2 binary64))

Rules

8 062×	`lower-fma.f64`
8 062×	`lower-fma.f32`
4 668×	`lower-*.f32`
4 660×	`lower-*.f64`
2 098×	`lower-neg.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	77
0	26	77
1	46	73
2	108	73
3	393	72
4	1569	71
5	4280	71
0	8405	71

Stop Event

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

Calls

Call 1

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

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

localize61.0ms (0.7%)

Memory

20.6MiB live, 56.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1875	(.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (*.f64 a a))))
accuracy	0.6365177071907723	(/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))
accuracy	3.296870871660412	(-.f64 (.f64 b b) (.f64 a a))
accuracy	5.859665247932151	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))

Samples

51.0ms

256×

valid

Compiler

Compiled 79 to 17 computations (78.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-sub: 29.0ms (67.9% of total)

ival-div: 7.0ms (16.4% of total)

ival-mult: 6.0ms (14% of total)

ival-pi: 1.0ms (2.3% of total)

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

exact: 0.0ms (0% of total)

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

series31.0ms (0.4%)

Memory

-37.3MiB live, 43.0MiB allocated

Counts

5 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 (PI.f64) #s(literal 2 binary64)) (patch (/.f64 (PI.f64) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b) (taylor 0 b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b) (taylor 0 b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b) (taylor 0 b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ (PI) (pow a 2))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (PI) (pow a 2))) (* -1/2 (/ (* (pow b 2) (PI)) (pow a 4)))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (PI) (pow a 2))) (* (pow b 2) (+ (* -1/2 (/ (PI) (pow a 4))) (* -1/2 (/ (* (pow b 2) (PI)) (pow a 6)))))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (PI) (pow a 2))) (* (pow b 2) (+ (* -1/2 (/ (PI) (pow a 4))) (* (pow b 2) (+ (* -1/2 (/ (PI) (pow a 6))) (* -1/2 (/ (* (pow b 2) (PI)) (pow a 8)))))))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow a 2)) (taylor 0 b) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (- (pow b 2) (pow a 2)) (taylor 0 b) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (- (pow b 2) (pow a 2)) (taylor 0 b) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (- (pow b 2) (pow a 2)) (taylor 0 b) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (pow a 2)) (taylor 0 b) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (pow b 2) (pow a 4))) (/ 1 (pow a 2))) (taylor 0 b) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow b 2) (- (* -1 (/ (pow b 2) (pow a 6))) (/ 1 (pow a 4)))) (/ 1 (pow a 2))) (taylor 0 b) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow b 2) (- (* (pow b 2) (- (* -1 (/ (pow b 2) (pow a 8))) (/ 1 (pow a 6)))) (/ 1 (pow a 4)))) (/ 1 (pow a 2))) (taylor 0 b) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* a (pow b 2)))) (taylor inf b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2)) (taylor inf b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2)) (taylor inf b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (* -1/2 (PI)) (* -1/2 (/ (* (pow b 2) (PI)) (pow a 2)))) (pow a 2)) (taylor inf a) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (PI)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 2))) (* -1/2 (/ (* (pow b 4) (PI)) (pow a 4))))) (pow a 2)) (taylor inf a) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (PI)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 2))) (+ (* -1/2 (/ (* (pow b 4) (PI)) (pow a 4))) (* -1/2 (/ (* (pow b 6) (PI)) (pow a 6)))))) (pow a 2)) (taylor inf a) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow a 2)) (taylor inf a) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (/ (pow b 2) (pow a 2)) 1)) (taylor inf a) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (/ (pow b 2) (pow a 2)) 1)) (taylor inf a) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (/ (pow b 2) (pow a 2)) 1)) (taylor inf a) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (pow a 2)) (taylor inf a) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (pow b 2) (pow a 2))) 1) (pow a 2)) (taylor inf a) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (pow b 4) (pow a 4))) (+ 1 (/ (pow b 2) (pow a 2)))) (pow a 2)) (taylor inf a) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (pow b 6) (pow a 6))) (+ 1 (+ (/ (pow b 2) (pow a 2)) (/ (pow b 4) (pow a 4))))) (pow a 2)) (taylor inf a) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) (patch (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ (PI) (pow a 2))) (taylor -inf a) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (PI)) (* -1/2 (/ (* (pow b 2) (PI)) (pow a 2)))) (pow a 2)) (taylor -inf a) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (PI)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 2))) (* -1/2 (/ (* (pow b 4) (PI)) (pow a 4))))) (pow a 2)) (taylor -inf a) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (PI)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 2))) (+ (* -1/2 (/ (* (pow b 4) (PI)) (pow a 4))) (* -1/2 (/ (* (pow b 6) (PI)) (pow a 6)))))) (pow a 2)) (taylor -inf a) (#s(alt (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (patch (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow a 2)) (taylor -inf a) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (/ (pow b 2) (pow a 2)) 1)) (taylor -inf a) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (/ (pow b 2) (pow a 2)) 1)) (taylor -inf a) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (/ (pow b 2) (pow a 2)) 1)) (taylor -inf a) (#s(alt (-.f64 (.f64 b b) (.f64 a a)) (patch (-.f64 (.f64 b b) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (pow b 2) (pow a 2))) 1) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (pow b 4) (pow a 4))) (+ 1 (/ (pow b 2) (pow a 2)))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 (/ (pow b 6) (pow a 6))) (+ 1 (+ (/ (pow b 2) (pow a 2)) (/ (pow b 4) (pow a 4))))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) (patch (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	b	@	0	((/ (PI) 2) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (* b b) (* a a)) (/ 1 (- (* b b) (* a a))))
2.0ms	b	@	inf	((/ (PI) 2) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (* b b) (* a a)) (/ 1 (- (* b b) (* a a))))
2.0ms	a	@	inf	((/ (PI) 2) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (* b b) (* a a)) (/ 1 (- (* b b) (* a a))))
1.0ms	a	@	0	((/ (PI) 2) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (* b b) (* a a)) (/ 1 (- (* b b) (* a a))))
1.0ms	b	@	-inf	((/ (PI) 2) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (* b b) (* a a)) (/ 1 (- (* b b) (* a a))))

simplify204.0ms (2.3%)

Memory

25.9MiB live, 216.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 618×	`lower-fma.f64`
12 618×	`lower-fma.f32`
5 734×	`lower-*.f64`
5 734×	`lower-*.f32`
2 064×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	291	1696
1	768	1666
2	2293	1612
3	6395	1612
0	8352	1525

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

rewrite204.0ms (2.3%)

Memory

-1.0MiB live, 265.7MiB allocated

Rules

6 700×	`lower-*.f32`
6 692×	`lower-*.f64`
4 958×	`lower-fma.f64`
4 958×	`lower-fma.f32`
2 990×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	53
0	26	49
1	124	49
2	1123	49
0	9193	49

Stop Event

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

Counts

5 → 583

Calls

Call 1

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

Outputs
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eval93.0ms (1.1%)

Memory: 45.1MiB live, 267.8MiB allocated
Compiler: Compiled 19 185 to 2 101 computations (89% saved)

prune29.0ms (0.3%)

Memory

6.1MiB live, 86.9MiB allocated

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	662	17	679
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	663	17	680

Accuracy

100.0%

Counts

680 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	90.2%	(fma.f64 (/.f64 (PI.f64) (+.f64 a b)) (.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (pow.f64 a #s(literal -1 binary64))) (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 a b)) (/.f64 (PI.f64) (-.f64 b a))) (neg.f64 b)))
▶	89.0%	(fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))))
▶	90.2%	(/.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
	84.7%	(/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (.f64 (.f64 a b) #s(literal 2 binary64)) (*.f64 (+.f64 a b) (-.f64 b a))))
	86.3%	(/.f64 (.f64 (.f64 (-.f64 b a) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))) (.f64 a b))
	78.6%	(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) (-.f64 b a)))) (.f64 (.f64 (fma.f64 (neg.f64 b) b (*.f64 a a)) a) b))
	46.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 a b) (.f64 a b)) (.f64 (/.f64 (PI.f64) (+.f64 a b)) (*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal -2 binary64)) (pow.f64 b #s(literal -2 binary64)))))))
	83.4%	(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (-.f64 b a) a) b)))
	88.6%	(.f64 (.f64 (/.f64 (/.f64 (-.f64 b a) a) b) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)))
▶	90.2%	(.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 a b))))
	84.5%	(.f64 (.f64 (-.f64 b a) (PI.f64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 a b) #s(literal 2 binary64)) (.f64 (+.f64 a b) (-.f64 b a)))))
	80.0%	(.f64 (.f64 (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))
	52.0%	(.f64 #s(approx ( (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (*.f64 (/.f64 (/.f64 (PI.f64) b) b) #s(literal 1/2 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))
▶	50.1%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)))
	51.6%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 #s(literal -1/2 binary64) b))) (.f64 b b)))
	59.6%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64)))
▶	59.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))

Compiler

Compiled 678 to 468 computations (31% saved)

simplify133.0ms (1.5%)

Memory

-23.0MiB live, 168.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	192	(*.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64))
cost-diff	256	(.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a))))
cost-diff	2688	(fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))))
cost-diff	6080	(*.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b)))
cost-diff	0	(*.f64 (+.f64 a b) (-.f64 b a))
cost-diff	0	(PI.f64)
cost-diff	0	(.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 a b))))
cost-diff	1408	(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))
cost-diff	0	(+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))
cost-diff	0	(PI.f64)
cost-diff	0	(*.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)))
cost-diff	0	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) (.f64 b (.f64 a a)))
cost-diff	0	(.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))
cost-diff	0	(+.f64 a b)
cost-diff	0	(*.f64 (+.f64 a b) (-.f64 b a))
cost-diff	0	(PI.f64)
cost-diff	1408	(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))

Rules

4 972×	`lower-*.f32`
4 948×	`lower-*.f64`
3 048×	`lower-/.f32`
3 026×	`lower-/.f64`
2 410×	`lower-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	387
0	84	380
1	175	374
2	485	323
3	1995	307
4	5217	307
0	8979	307

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))
(/.f64 (PI.f64) (*.f64 (+.f64 a b) (-.f64 b a)))
(PI.f64)
(*.f64 (+.f64 a b) (-.f64 b a))
(+.f64 a b)
a
b
(-.f64 b a)
(.f64 #s(literal 2 binary64) (.f64 a b))
#s(literal 2 binary64)
(*.f64 a b)
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))
(.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))
(/.f64 (PI.f64) (.f64 b (.f64 a a)))
(PI.f64)
(.f64 b (.f64 a a))
b
(*.f64 a a)
a
#s(literal 1/2 binary64)
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)))
(/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))
(*.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)))
(PI.f64)
(+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))
(/.f64 #s(literal 1/2 binary64) b)
#s(literal 1/2 binary64)
b
(/.f64 #s(literal -1/2 binary64) a)
#s(literal -1/2 binary64)
a
(*.f64 a a)
(.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 a b))))
(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))
(/.f64 (PI.f64) (*.f64 (+.f64 a b) (-.f64 b a)))
(PI.f64)
(*.f64 (+.f64 a b) (-.f64 b a))
(+.f64 a b)
a
b
(-.f64 b a)
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))
#s(literal 1 binary64)
(.f64 #s(literal 2 binary64) (.f64 a b))
#s(literal 2 binary64)
(*.f64 a b)
(fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))))
(*.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b)))
(pow.f64 a #s(literal -1 binary64))
a
#s(literal -1 binary64)
(/.f64 (PI.f64) (+.f64 a b))
(PI.f64)
(+.f64 a b)
b
(/.f64 #s(literal 1/2 binary64) (-.f64 b a))
#s(literal 1/2 binary64)
(-.f64 b a)
(.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a))))
(*.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64))
(/.f64 #s(literal -1 binary64) b)
(/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a)))
#s(literal -1/2 binary64)
(fma.f64 (neg.f64 b) b (*.f64 a a))
(neg.f64 b)
(*.f64 a a)

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

localize142.0ms (1.6%)

Memory

17.5MiB live, 235.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.6180139393282923	(/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a)))
accuracy	2.619872088562818	(.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a))))
accuracy	3.351542546022561	(fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))))
accuracy	3.5038677164778425	(fma.f64 (neg.f64 b) b (*.f64 a a))
accuracy	0.1875	(.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 a b))))
accuracy	0.21875	(/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))
accuracy	0.7028633914162529	(/.f64 (PI.f64) (*.f64 (+.f64 a b) (-.f64 b a)))
accuracy	26.77482828530513	(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))
accuracy	0.015625	(+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))
accuracy	0.37890625	(*.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)))
accuracy	2.6324797807986466	(/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))
accuracy	29.317064440931205	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)))
accuracy	0.1993315017619471	(.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))
accuracy	0.3903425112112845	(/.f64 (PI.f64) (.f64 b (.f64 a a)))
accuracy	5.400889743003612	(.f64 b (.f64 a a))
accuracy	23.430333761737135	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))
accuracy	0	(PI.f64)
accuracy	0.1484375	(/.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
accuracy	0.7028633914162529	(/.f64 (PI.f64) (*.f64 (+.f64 a b) (-.f64 b a)))
accuracy	26.77482828530513	(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))

Samples

100.0ms

256×

valid

Compiler

Compiled 370 to 51 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 29.0ms (41.9% of total)

ival-div: 24.0ms (34.7% of total)

ival-add: 5.0ms (7.2% of total)

ival-pow: 5.0ms (7.2% of total)

ival-sub: 3.0ms (4.3% of total)

ival-pi: 1.0ms (1.4% of total)

exact: 1.0ms (1.4% of total)

ival-neg: 1.0ms (1.4% of total)

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

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

series71.0ms (0.8%)

Memory

-22.7MiB live, 103.1MiB allocated

Counts

22 → 492

Calls

Call 1

Inputs
#s(alt (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (patch (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 a b) (-.f64 b a)) (patch (.f64 (+.f64 a b) (-.f64 b a)) #<representation binary64>) () ())
#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (PI.f64) (.f64 b (.f64 a a))) (patch (/.f64 (PI.f64) (.f64 b (.f64 a a))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) (patch #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (patch (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) #<representation binary64>) () ())
#s(alt (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) (patch (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) (patch (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (patch (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))))) (patch (fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))) (patch (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (patch (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) #<representation binary64>) () ())
#s(alt (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (patch (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())
#s(alt (.f64 b (.f64 a a)) (patch (.f64 b (.f64 a a)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)) (patch (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())
#s(alt (fma.f64 (neg.f64 b) b (.f64 a a)) (patch (fma.f64 (neg.f64 b) b (.f64 a a)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) (patch (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) #<representation binary64>) () ())

Outputs
#s(alt (/ (PI) a) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (patch (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* b (PI)) (pow a 2))) (/ (PI) a)) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (patch (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* b (- (/ (* b (PI)) (pow a 3)) (/ (PI) (pow a 2)))) (/ (PI) a)) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (patch (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 4))) (* -1 (/ (PI) (pow a 3))))) (/ (PI) (pow a 2)))) (/ (PI) a)) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (patch (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow a 2)) (taylor 0 b) (#s(alt (.f64 (+.f64 a b) (-.f64 b a)) (patch (.f64 (+.f64 a b) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow a 2)) (* b (+ a (* -1 a)))) (taylor 0 b) (#s(alt (.f64 (+.f64 a b) (-.f64 b a)) (patch (.f64 (+.f64 a b) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow a 2)) (* b (+ a (+ b (* -1 a))))) (taylor 0 b) (#s(alt (.f64 (+.f64 a b) (-.f64 b a)) (patch (.f64 (+.f64 a b) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow a 2)) (* b (+ a (+ b (* -1 a))))) (taylor 0 b) (#s(alt (.f64 (+.f64 a b) (-.f64 b a)) (patch (.f64 (+.f64 a b) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 b (.f64 a a))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (* (pow a 2) b)) (taylor 0 b) (#s(alt (/.f64 (PI.f64) (.f64 b (.f64 a a))) (patch (/.f64 (PI.f64) (.f64 b (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (* (pow a 2) b)) (taylor 0 b) (#s(alt (/.f64 (PI.f64) (.f64 b (.f64 a a))) (patch (/.f64 (PI.f64) (.f64 b (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (* (pow a 2) b)) (taylor 0 b) (#s(alt (/.f64 (PI.f64) (.f64 b (.f64 a a))) (patch (/.f64 (PI.f64) (.f64 b (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (* (pow a 2) b)) (taylor 0 b) (#s(alt (/.f64 (PI.f64) (.f64 b (.f64 a a))) (patch (/.f64 (PI.f64) (.f64 b (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) (patch #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) (patch #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) (patch #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) (patch #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) b)) (taylor 0 b) (#s(alt (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (patch (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b) (taylor 0 b) (#s(alt (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (patch (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b) (taylor 0 b) (#s(alt (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (patch (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b) (taylor 0 b) (#s(alt (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (patch (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 b) (taylor 0 b) (#s(alt (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) (patch (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ b a))) b) (taylor 0 b) (#s(alt (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) (patch (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ b a))) b) (taylor 0 b) (#s(alt (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) (patch (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* -1/2 (/ b a))) b) (taylor 0 b) (#s(alt (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) (patch (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) (patch (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b) (taylor 0 b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) (patch (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b) (taylor 0 b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) (patch (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b) (taylor 0 b) (#s(alt (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) (patch (.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (pow a 2)) (taylor 0 b) (#s(alt (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (patch (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* b (PI)) (pow a 3))) (/ (PI) (pow a 2))) (taylor 0 b) (#s(alt (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (patch (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (+ (* b (- (/ (* b (PI)) (pow a 4)) (/ (PI) (pow a 3)))) (/ (PI) (pow a 2))) (taylor 0 b) (#s(alt (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (patch (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 5))) (* -1 (/ (PI) (pow a 4))))) (/ (PI) (pow a 3)))) (/ (PI) (pow a 2))) (taylor 0 b) (#s(alt (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (patch (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))))) (patch (fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b) (taylor 0 b) (#s(alt (fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))))) (patch (fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* (PI) (+ a (* -1 a))) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b) (taylor 0 b) (#s(alt (fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))))) (patch (fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)) (patch (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)) (patch (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* a b)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* a b)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* a b)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* a b)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor -inf a) (#s(alt (fma.f64 (neg.f64 b) b (.f64 a a)) (patch (fma.f64 (neg.f64 b) b (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor -inf a) (#s(alt (fma.f64 (neg.f64 b) b (.f64 a a)) (patch (fma.f64 (neg.f64 b) b (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor -inf a) (#s(alt (fma.f64 (neg.f64 b) b (.f64 a a)) (patch (fma.f64 (neg.f64 b) b (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor -inf a) (#s(alt (fma.f64 (neg.f64 b) b (.f64 a a)) (patch (fma.f64 (neg.f64 b) b (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) (patch (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 (/ (pow b 2) (pow a 2))) 1/2) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) (patch (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 (/ (pow b 4) (pow a 4))) (+ 1/2 (* 1/2 (/ (pow b 2) (pow a 2))))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) (patch (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 (/ (pow b 6) (pow a 6))) (+ 1/2 (+ (* 1/2 (/ (pow b 2) (pow a 2))) (* 1/2 (/ (pow b 4) (pow a 4)))))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) (patch (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
16.0ms	b	@	0	((* (/ (PI) (* (+ a b) (- b a))) (- b a)) (PI) (* (+ a b) (- b a)) (+ a b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) (* b (* a a))) 1/2) (/ (PI) (* b (* a a))) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (+ (/ 1/2 b) (/ -1/2 a)) (* (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/ 1 (* 2 (* a b)))) (* (pow a -1) (/ (PI) (+ a b))) (+ (* (* (pow a -1) (/ (PI) (+ a b))) (/ 1/2 (- b a))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a))))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a)))) (* (/ -1 b) (PI)) (/ (PI) (* (+ a b) (- b a))) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* b (* a a)) (/ (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (* a a)) (/ 1 (* 2 (* a b))) (+ (* (neg b) b) (* a a)) (/ -1/2 (+ (* (neg b) b) (* a a))))
9.0ms	a	@	0	((* (/ (PI) (* (+ a b) (- b a))) (- b a)) (PI) (* (+ a b) (- b a)) (+ a b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) (* b (* a a))) 1/2) (/ (PI) (* b (* a a))) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (+ (/ 1/2 b) (/ -1/2 a)) (* (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/ 1 (* 2 (* a b)))) (* (pow a -1) (/ (PI) (+ a b))) (+ (* (* (pow a -1) (/ (PI) (+ a b))) (/ 1/2 (- b a))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a))))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a)))) (* (/ -1 b) (PI)) (/ (PI) (* (+ a b) (- b a))) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* b (* a a)) (/ (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (* a a)) (/ 1 (* 2 (* a b))) (+ (* (neg b) b) (* a a)) (/ -1/2 (+ (* (neg b) b) (* a a))))
9.0ms	b	@	inf	((* (/ (PI) (* (+ a b) (- b a))) (- b a)) (PI) (* (+ a b) (- b a)) (+ a b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) (* b (* a a))) 1/2) (/ (PI) (* b (* a a))) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (+ (/ 1/2 b) (/ -1/2 a)) (* (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/ 1 (* 2 (* a b)))) (* (pow a -1) (/ (PI) (+ a b))) (+ (* (* (pow a -1) (/ (PI) (+ a b))) (/ 1/2 (- b a))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a))))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a)))) (* (/ -1 b) (PI)) (/ (PI) (* (+ a b) (- b a))) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* b (* a a)) (/ (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (* a a)) (/ 1 (* 2 (* a b))) (+ (* (neg b) b) (* a a)) (/ -1/2 (+ (* (neg b) b) (* a a))))
5.0ms	a	@	-inf	((* (/ (PI) (* (+ a b) (- b a))) (- b a)) (PI) (* (+ a b) (- b a)) (+ a b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) (* b (* a a))) 1/2) (/ (PI) (* b (* a a))) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (+ (/ 1/2 b) (/ -1/2 a)) (* (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/ 1 (* 2 (* a b)))) (* (pow a -1) (/ (PI) (+ a b))) (+ (* (* (pow a -1) (/ (PI) (+ a b))) (/ 1/2 (- b a))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a))))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a)))) (* (/ -1 b) (PI)) (/ (PI) (* (+ a b) (- b a))) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* b (* a a)) (/ (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (* a a)) (/ 1 (* 2 (* a b))) (+ (* (neg b) b) (* a a)) (/ -1/2 (+ (* (neg b) b) (* a a))))
5.0ms	b	@	-inf	((* (/ (PI) (* (+ a b) (- b a))) (- b a)) (PI) (* (+ a b) (- b a)) (+ a b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) (* b (* a a))) 1/2) (/ (PI) (* b (* a a))) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (+ (/ 1/2 b) (/ -1/2 a)) (* (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/ 1 (* 2 (* a b)))) (* (pow a -1) (/ (PI) (+ a b))) (+ (* (* (pow a -1) (/ (PI) (+ a b))) (/ 1/2 (- b a))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a))))) (* (* (/ -1 b) (PI)) (/ -1/2 (+ (* (neg b) b) (* a a)))) (* (/ -1 b) (PI)) (/ (PI) (* (+ a b) (- b a))) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* b (* a a)) (/ (* (PI) (+ (/ 1/2 b) (/ -1/2 a))) (* a a)) (/ 1 (* 2 (* a b))) (+ (* (neg b) b) (* a a)) (/ -1/2 (+ (* (neg b) b) (* a a))))

simplify280.0ms (3.2%)

Memory

-11.3MiB live, 342.0MiB allocated

Algorithm

1×	egg-herbie

Rules

26 648×	`lower-fma.f64`
26 648×	`lower-fma.f32`
4 824×	`lower-*.f64`
4 824×	`lower-*.f32`
3 456×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	834	7482
1	2519	6825
0	9168	6506

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 486

Calls

Call 1

Inputs
(/ (PI) a)
(+ (* -1 (/ (* b (PI)) (pow a 2))) (/ (PI) a))
(+ (* b (- (/ (* b (PI)) (pow a 3)) (/ (PI) (pow a 2)))) (/ (PI) a))
(+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 4))) (* -1 (/ (PI) (pow a 3))))) (/ (PI) (pow a 2)))) (/ (PI) a))
(* -1 (pow a 2))
(+ (* -1 (pow a 2)) (* b (+ a (* -1 a))))
(+ (* -1 (pow a 2)) (* b (+ a (+ b (* -1 a)))))
(+ (* -1 (pow a 2)) (* b (+ a (+ b (* -1 a)))))
a
(+ a b)
(+ a b)
(+ a b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* 1/2 (/ (PI) b))
(/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b)
(/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b)
(/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b)
(/ 1/2 b)
(/ (+ 1/2 (* -1/2 (/ b a))) b)
(/ (+ 1/2 (* -1/2 (/ b a))) b)
(/ (+ 1/2 (* -1/2 (/ b a))) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(/ (PI) (pow a 2))
(+ (* -1 (/ (* b (PI)) (pow a 3))) (/ (PI) (pow a 2)))
(+ (* b (- (/ (* b (PI)) (pow a 4)) (/ (PI) (pow a 3)))) (/ (PI) (pow a 2)))
(+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 5))) (* -1 (/ (PI) (pow a 4))))) (/ (PI) (pow a 3)))) (/ (PI) (pow a 2)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* (PI) (+ a (* -1 a))) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (* b (+ (/ (PI) (pow a 5)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) (pow a 7))))) (+ (* -1/2 (/ (* (PI) (+ a (* -1 a))) (pow a 5))) (* 1/2 (/ (PI) (pow a 4))))))))) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* 1/2 (/ (* (pow b 2) (PI)) (pow a 4)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* (pow b 2) (+ (* 1/2 (/ (PI) (pow a 4))) (* 1/2 (/ (* (pow b 2) (PI)) (pow a 6)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* (pow b 2) (+ (* 1/2 (/ (PI) (pow a 4))) (* (pow b 2) (+ (* 1/2 (/ (PI) (pow a 6))) (* 1/2 (/ (* (pow b 2) (PI)) (pow a 8)))))))) b)
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(* -1 (/ (PI) (pow a 2)))
(+ (* -1 (/ (PI) (pow a 2))) (* -1 (/ (* b (* (PI) (+ a (* -1 a)))) (pow a 4))))
(+ (* -1 (/ (PI) (pow a 2))) (* b (- (* -1 (* b (+ (/ (PI) (pow a 4)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) (pow a 6))))) (/ (* (PI) (+ a (* -1 a))) (pow a 4)))))
(+ (* -1 (/ (PI) (pow a 2))) (* b (- (* b (- (* -1 (* b (+ (/ (* (PI) (+ a (* -1 a))) (pow a 6)) (/ (* (+ a (* -1 a)) (+ (/ (PI) (pow a 4)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) (pow a 6)))) (pow a 2))))) (+ (/ (PI) (pow a 4)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) (pow a 6))))) (/ (* (PI) (+ a (* -1 a))) (pow a 4)))))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(/ -1/2 (pow a 2))
(- (* -1/2 (/ (pow b 2) (pow a 4))) (* 1/2 (/ 1 (pow a 2))))
(- (* (pow b 2) (- (* -1/2 (/ (pow b 2) (pow a 6))) (* 1/2 (/ 1 (pow a 4))))) (* 1/2 (/ 1 (pow a 2))))
(- (* (pow b 2) (- (* (pow b 2) (- (* -1/2 (/ (pow b 2) (pow a 8))) (* 1/2 (/ 1 (pow a 6))))) (* 1/2 (/ 1 (pow a 4))))) (* 1/2 (/ 1 (pow a 2))))
(/ (PI) b)
(/ (+ (PI) (* -1 (/ (* a (PI)) b))) b)
(/ (- (+ (PI) (/ (* (pow a 2) (PI)) (pow b 2))) (/ (* a (PI)) b)) b)
(/ (- (+ (PI) (* -1 (/ (* (pow a 3) (PI)) (pow b 3)))) (+ (* -1 (/ (* (pow a 2) (PI)) (pow b 2))) (/ (* a (PI)) b))) b)
(pow b 2)
(* (pow b 2) (+ 1 (+ (* -1 (/ a b)) (/ a b))))
(* (pow b 2) (+ 1 (+ (* -1 (/ a b)) (+ (* -1 (/ (pow a 2) (pow b 2))) (/ a b)))))
(* (pow b 2) (+ 1 (+ (* -1 (/ a b)) (+ (* -1 (/ (pow a 2) (pow b 2))) (/ a b)))))
b
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(* -1/2 (/ (PI) a))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(/ -1/2 a)
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(/ (PI) (* a b))
(/ (+ (* -1 (/ (PI) b)) (/ (PI) a)) b)
(/ (- (+ (/ (PI) a) (/ (* a (PI)) (pow b 2))) (/ (PI) b)) b)
(/ (- (+ (* -1 (/ (* (pow a 2) (PI)) (pow b 3))) (/ (PI) a)) (+ (* -1 (/ (* a (PI)) (pow b 2))) (/ (PI) b))) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (PI) (+ a (* -1 a))) (* a b))) (* 1/2 (/ (PI) a)))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (PI) (+ a (* -1 a))) (* a b))) (+ (* -1/2 (/ (+ (* -1 (* a (PI))) (* -1 (/ (* (PI) (pow (+ a (* -1 a)) 2)) a))) (pow b 2))) (* 1/2 (/ (PI) a))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (PI) (+ a (* -1 a))) (* a b))) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* -1/2 (/ (+ (* -1 (* a (PI))) (* -1 (/ (* (PI) (pow (+ a (* -1 a)) 2)) a))) (pow b 2))) (+ (* -1/2 (/ (+ (* -1 (* (+ a (* -1 a)) (+ (* -1 (* a (PI))) (* -1 (/ (* (PI) (pow (+ a (* -1 a)) 2)) a))))) (* a (* (PI) (+ a (* -1 a))))) (pow b 3))) (* 1/2 (/ (PI) a))))))) (pow b 2))
(* -1/2 (/ (PI) (pow b 3)))
(/ (+ (* -1/2 (PI)) (* -1/2 (/ (* (pow a 2) (PI)) (pow b 2)))) (pow b 3))
(/ (+ (* -1/2 (PI)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 2))) (* -1/2 (/ (* (pow a 4) (PI)) (pow b 4))))) (pow b 3))
(/ (+ (* -1/2 (PI)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 2))) (+ (* -1/2 (/ (* (pow a 4) (PI)) (pow b 4))) (* -1/2 (/ (* (pow a 6) (PI)) (pow b 6)))))) (pow b 3))
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(/ (PI) (pow b 2))
(/ (+ (PI) (* -1 (/ (* (PI) (+ a (* -1 a))) b))) (pow b 2))
(/ (- (+ (PI) (* -1 (/ (+ (* -1 (* (PI) (pow (+ a (* -1 a)) 2))) (* -1 (* (pow a 2) (PI)))) (pow b 2)))) (/ (* (PI) (+ a (* -1 a))) b)) (pow b 2))
(/ (- (+ (PI) (* -1 (/ (+ (* -1 (* (+ a (* -1 a)) (+ (* -1 (* (PI) (pow (+ a (* -1 a)) 2))) (* -1 (* (pow a 2) (PI)))))) (* (pow a 2) (* (PI) (+ a (* -1 a))))) (pow b 3)))) (+ (* -1 (/ (* (PI) (pow (+ a (* -1 a)) 2)) (pow b 2))) (+ (* -1 (/ (* (pow a 2) (PI)) (pow b 2))) (/ (* (PI) (+ a (* -1 a))) b)))) (pow b 2))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* -1/2 (/ (PI) (pow a 3)))
(+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (PI) (* (pow a 2) b))))
(+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (PI) (* (pow a 2) b))))
(+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (PI) (* (pow a 2) b))))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(/ 1/2 (pow b 2))
(/ (+ 1/2 (* 1/2 (/ (pow a 2) (pow b 2)))) (pow b 2))
(/ (- (+ 1/2 (* 1/2 (/ (pow a 4) (pow b 4)))) (* -1/2 (/ (pow a 2) (pow b 2)))) (pow b 2))
(/ (- (+ 1/2 (* 1/2 (/ (pow a 6) (pow b 6)))) (+ (* -1/2 (/ (pow a 2) (pow b 2))) (* -1/2 (/ (pow a 4) (pow b 4))))) (pow b 2))
(/ (PI) b)
(* -1 (/ (+ (* -1 (PI)) (/ (* a (PI)) b)) b))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (/ (* (pow a 2) (PI)) b) (* a (PI))) b))) b))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow a 3) (PI)) b) (* (pow a 2) (PI))) b)) (* a (PI))) b))) b))
(pow b 2)
(* (pow b 2) (+ 1 (+ (* -1 (/ a b)) (/ a b))))
(* (pow b 2) (+ 1 (* -1 (/ (+ (* -1 (+ a (* -1 a))) (/ (pow a 2) b)) b))))
(* (pow b 2) (+ 1 (* -1 (/ (+ (* -1 (+ a (* -1 a))) (/ (pow a 2) b)) b))))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* -1/2 (/ (PI) a))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(/ -1/2 a)
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (PI) (* a b))
(* -1 (/ (+ (* -1 (/ (PI) a)) (/ (PI) b)) b))
(* -1 (/ (+ (* -1 (/ (PI) a)) (* -1 (/ (- (/ (* a (PI)) b) (PI)) b))) b))
(* -1 (/ (+ (* -1 (/ (PI) a)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow a 2) (PI)) b) (* a (PI))) b)) (PI)) b))) b))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1 (/ (+ (* 1/2 (PI)) (* 1/2 (/ (* (PI) (+ a (* -1 a))) a))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* a (PI)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) a)) b)) (+ (* 1/2 (PI)) (* 1/2 (/ (* (PI) (+ a (* -1 a))) a)))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (* (pow a 2) (PI))) (* 1/2 (+ (* a (* (PI) (+ a (* -1 a)))) (* (+ a (* -1 a)) (+ (* a (PI)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) a)))))) b)) (* 1/2 (+ (* a (PI)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) a)))) b)) (+ (* 1/2 (PI)) (* 1/2 (/ (* (PI) (+ a (* -1 a))) a)))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* -1/2 (/ (PI) (pow b 3)))
(* -1 (/ (+ (* 1/2 (PI)) (* 1/2 (/ (* (pow a 2) (PI)) (pow b 2)))) (pow b 3)))
(* -1 (/ (+ (* 1/2 (PI)) (+ (* 1/2 (/ (* (pow a 2) (PI)) (pow b 2))) (* 1/2 (/ (* (pow a 4) (PI)) (pow b 4))))) (pow b 3)))
(* -1 (/ (+ (* 1/2 (PI)) (+ (* 1/2 (/ (* (pow a 2) (PI)) (pow b 2))) (+ (* 1/2 (/ (* (pow a 4) (PI)) (pow b 4))) (* 1/2 (/ (* (pow a 6) (PI)) (pow b 6)))))) (pow b 3)))
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(* -1 (/ (PI) b))
(/ (PI) (pow b 2))
(/ (+ (PI) (* -1 (/ (* (PI) (+ a (* -1 a))) b))) (pow b 2))
(/ (+ (PI) (* -1 (/ (+ (* -1 (/ (+ (* (PI) (pow (+ a (* -1 a)) 2)) (* (pow a 2) (PI))) b)) (* (PI) (+ a (* -1 a)))) b))) (pow b 2))
(/ (+ (PI) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* (+ a (* -1 a)) (+ (* (PI) (pow (+ a (* -1 a)) 2)) (* (pow a 2) (PI)))) (* (pow a 2) (* (PI) (+ a (* -1 a))))) b)) (+ (* (PI) (pow (+ a (* -1 a)) 2)) (* (pow a 2) (PI)))) b)) (* (PI) (+ a (* -1 a)))) b))) (pow b 2))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* -1/2 (/ (PI) (pow a 3)))
(+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (PI) (* (pow a 2) b))))
(+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (PI) (* (pow a 2) b))))
(+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (PI) (* (pow a 2) b))))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(/ 1/2 (pow b 2))
(/ (+ 1/2 (* 1/2 (/ (pow a 2) (pow b 2)))) (pow b 2))
(/ (- (+ 1/2 (* 1/2 (/ (pow a 4) (pow b 4)))) (* -1/2 (/ (pow a 2) (pow b 2)))) (pow b 2))
(/ (- (+ 1/2 (* 1/2 (/ (pow a 6) (pow b 6)))) (+ (* -1/2 (/ (pow a 2) (pow b 2))) (* -1/2 (/ (pow a 4) (pow b 4))))) (pow b 2))
(/ (PI) b)
(+ (* -1 (/ (* a (PI)) (pow b 2))) (/ (PI) b))
(+ (* a (- (/ (* a (PI)) (pow b 3)) (/ (PI) (pow b 2)))) (/ (PI) b))
(+ (* a (- (* a (- (* -1 (/ (* a (PI)) (pow b 4))) (* -1 (/ (PI) (pow b 3))))) (/ (PI) (pow b 2)))) (/ (PI) b))
(pow b 2)
(+ (* a (+ b (* -1 b))) (pow b 2))
(+ (* a (+ b (+ (* -1 a) (* -1 b)))) (pow b 2))
(+ (* a (+ b (+ (* -1 a) (* -1 b)))) (pow b 2))
b
(+ a b)
(+ a b)
(+ a b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(* -1/2 (/ (PI) a))
(/ (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b))) a)
(/ (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b))) a)
(/ (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b))) a)
(/ -1/2 a)
(/ (- (* 1/2 (/ a b)) 1/2) a)
(/ (- (* 1/2 (/ a b)) 1/2) a)
(/ (- (* 1/2 (/ a b)) 1/2) a)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(/ (PI) (* a b))
(/ (+ (* -1 (/ (* a (PI)) (pow b 2))) (/ (PI) b)) a)
(/ (+ (* a (- (/ (* a (PI)) (pow b 3)) (/ (PI) (pow b 2)))) (/ (PI) b)) a)
(/ (+ (* a (- (* a (- (* -1 (/ (* a (PI)) (pow b 4))) (* -1 (/ (PI) (pow b 3))))) (/ (PI) (pow b 2)))) (/ (PI) b)) a)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* -1/2 (/ (* (PI) (+ b (* -1 b))) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (* a (+ (* -1 (/ (PI) (pow b 4))) (* -1 (/ (* (PI) (pow (+ b (* -1 b)) 2)) (pow b 6)))))) (+ (* -1/2 (/ (PI) (pow b 3))) (* -1/2 (/ (* (PI) (+ b (* -1 b))) (pow b 4))))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (+ (* -1/2 (/ (* (PI) (+ b (* -1 b))) (pow b 4))) (* a (+ (* -1/2 (+ (* -1 (/ (PI) (pow b 4))) (* -1 (/ (* (PI) (pow (+ b (* -1 b)) 2)) (pow b 6))))) (* a (+ (* -1/2 (+ (* -1 (/ (* (+ b (* -1 b)) (+ (* -1 (/ (PI) (pow b 4))) (* -1 (/ (* (PI) (pow (+ b (* -1 b)) 2)) (pow b 6))))) (pow b 2))) (/ (* (PI) (+ b (* -1 b))) (pow b 6)))) (* -1/2 (/ (PI) (pow b 5))))))))))) a)
(* -1/2 (/ (PI) (pow b 3)))
(+ (* -1/2 (/ (PI) (pow b 3))) (* -1/2 (/ (* (pow a 2) (PI)) (pow b 5))))
(+ (* -1/2 (/ (PI) (pow b 3))) (* (pow a 2) (+ (* -1/2 (/ (PI) (pow b 5))) (* -1/2 (/ (* (pow a 2) (PI)) (pow b 7))))))
(+ (* -1/2 (/ (PI) (pow b 3))) (* (pow a 2) (+ (* -1/2 (/ (PI) (pow b 5))) (* (pow a 2) (+ (* -1/2 (/ (PI) (pow b 7))) (* -1/2 (/ (* (pow a 2) (PI)) (pow b 9))))))))
(/ (PI) (pow b 2))
(+ (* -1 (/ (* a (* (PI) (+ b (* -1 b)))) (pow b 4))) (/ (PI) (pow b 2)))
(+ (* a (- (* -1 (* a (+ (* -1 (/ (PI) (pow b 4))) (* -1 (/ (* (PI) (pow (+ b (* -1 b)) 2)) (pow b 6)))))) (/ (* (PI) (+ b (* -1 b))) (pow b 4)))) (/ (PI) (pow b 2)))
(+ (* a (- (* a (- (* -1 (* a (+ (* -1 (/ (* (+ b (* -1 b)) (+ (* -1 (/ (PI) (pow b 4))) (* -1 (/ (* (PI) (pow (+ b (* -1 b)) 2)) (pow b 6))))) (pow b 2))) (/ (* (PI) (+ b (* -1 b))) (pow b 6))))) (+ (* -1 (/ (PI) (pow b 4))) (* -1 (/ (* (PI) (pow (+ b (* -1 b)) 2)) (pow b 6)))))) (/ (* (PI) (+ b (* -1 b))) (pow b 4)))) (/ (PI) (pow b 2)))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* -1/2 (/ (PI) (pow a 3)))
(/ (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b))) (pow a 3))
(/ (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b))) (pow a 3))
(/ (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b))) (pow a 3))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(* -1 (pow b 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(/ 1/2 (pow b 2))
(+ (* 1/2 (/ (pow a 2) (pow b 4))) (* 1/2 (/ 1 (pow b 2))))
(+ (* (pow a 2) (+ (* 1/2 (/ (pow a 2) (pow b 6))) (* 1/2 (/ 1 (pow b 4))))) (* 1/2 (/ 1 (pow b 2))))
(+ (* (pow a 2) (+ (* (pow a 2) (+ (* 1/2 (/ (pow a 2) (pow b 8))) (* 1/2 (/ 1 (pow b 6))))) (* 1/2 (/ 1 (pow b 4))))) (* 1/2 (/ 1 (pow b 2))))
(/ (PI) a)
(/ (+ (PI) (* -1 (/ (* b (PI)) a))) a)
(/ (- (+ (PI) (/ (* (pow b 2) (PI)) (pow a 2))) (/ (* b (PI)) a)) a)
(/ (- (+ (PI) (* -1 (/ (* (pow b 3) (PI)) (pow a 3)))) (+ (* -1 (/ (* (pow b 2) (PI)) (pow a 2))) (/ (* b (PI)) a))) a)
(* -1 (pow a 2))
(* (pow a 2) (- (+ (* -1 (/ b a)) (/ b a)) 1))
(* (pow a 2) (- (+ (* -1 (/ b a)) (+ (/ b a) (/ (pow b 2) (pow a 2)))) 1))
(* (pow a 2) (- (+ (* -1 (/ b a)) (+ (/ b a) (/ (pow b 2) (pow a 2)))) 1))
a
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(* 1/2 (/ (PI) b))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(/ 1/2 b)
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(/ (PI) (pow a 2))
(/ (+ (PI) (* -1 (/ (* b (PI)) a))) (pow a 2))
(/ (- (+ (PI) (/ (* (pow b 2) (PI)) (pow a 2))) (/ (* b (PI)) a)) (pow a 2))
(/ (- (+ (PI) (* -1 (/ (* (pow b 3) (PI)) (pow a 3)))) (+ (* -1 (/ (* (pow b 2) (PI)) (pow a 2))) (/ (* b (PI)) a))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (PI) (+ b (* -1 b))) (pow a 2))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (PI) (+ b (* -1 b))) (pow a 2))) (+ (* -1/2 (/ (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI))) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))) (pow a 2))
(/ (+ (* 1/2 (/ (PI) b)) (+ (* 1/2 (/ (* b (PI)) (pow a 2))) (* 1/2 (/ (* (pow b 3) (PI)) (pow a 4))))) (pow a 2))
(/ (+ (* 1/2 (/ (PI) b)) (+ (* 1/2 (/ (* b (PI)) (pow a 2))) (+ (* 1/2 (/ (* (pow b 3) (PI)) (pow a 4))) (* 1/2 (/ (* (pow b 5) (PI)) (pow a 6)))))) (pow a 2))
(* -1 (/ (PI) (pow a 2)))
(/ (+ (* -1 (PI)) (* -1 (/ (* (PI) (+ b (* -1 b))) a))) (pow a 2))
(/ (- (+ (* -1 (PI)) (* -1 (/ (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI))) (pow a 2)))) (/ (* (PI) (+ b (* -1 b))) a)) (pow a 2))
(/ (- (+ (* -1 (PI)) (* -1 (/ (+ (* (+ b (* -1 b)) (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI)))) (* (pow b 2) (* (PI) (+ b (* -1 b))))) (pow a 3)))) (+ (/ (* (PI) (+ b (* -1 b))) a) (+ (/ (* (PI) (pow (+ b (* -1 b)) 2)) (pow a 2)) (/ (* (pow b 2) (PI)) (pow a 2))))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(/ -1/2 (pow a 2))
(/ (- (* -1/2 (/ (pow b 2) (pow a 2))) 1/2) (pow a 2))
(/ (- (* -1/2 (/ (pow b 4) (pow a 4))) (+ 1/2 (* 1/2 (/ (pow b 2) (pow a 2))))) (pow a 2))
(/ (- (* -1/2 (/ (pow b 6) (pow a 6))) (+ 1/2 (+ (* 1/2 (/ (pow b 2) (pow a 2))) (* 1/2 (/ (pow b 4) (pow a 4)))))) (pow a 2))
(/ (PI) a)
(* -1 (/ (+ (* -1 (PI)) (/ (* b (PI)) a)) a))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (/ (* (pow b 2) (PI)) a) (* b (PI))) a))) a))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow b 3) (PI)) a) (* (pow b 2) (PI))) a)) (* b (PI))) a))) a))
(* -1 (pow a 2))
(* (pow a 2) (- (* -1 (/ (+ b (* -1 b)) a)) 1))
(* (pow a 2) (- (* -1 (/ (+ b (+ (* -1 b) (* -1 (/ (pow b 2) a)))) a)) 1))
(* (pow a 2) (- (* -1 (/ (+ b (+ (* -1 b) (* -1 (/ (pow b 2) a)))) a)) 1))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(/ (PI) (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* 1/2 (/ (PI) b))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(/ 1/2 b)
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (PI) (pow a 2))
(/ (+ (PI) (* -1 (/ (* b (PI)) a))) (pow a 2))
(/ (+ (PI) (* -1 (/ (+ (* -1 (/ (* (pow b 2) (PI)) a)) (* b (PI))) a))) (pow a 2))
(/ (+ (PI) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (pow b 3) (PI)) a)) (* (pow b 2) (PI))) a)) (* b (PI))) a))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (* b (PI))) (* 1/2 (* (PI) (+ b (* -1 b))))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI))) a)) (+ (* 1/2 (* b (PI))) (* 1/2 (* (PI) (+ b (* -1 b)))))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))) (pow a 2))
(/ (+ (* 1/2 (/ (PI) b)) (+ (* 1/2 (/ (* b (PI)) (pow a 2))) (* 1/2 (/ (* (pow b 3) (PI)) (pow a 4))))) (pow a 2))
(/ (+ (* 1/2 (/ (PI) b)) (+ (* 1/2 (/ (* b (PI)) (pow a 2))) (+ (* 1/2 (/ (* (pow b 3) (PI)) (pow a 4))) (* 1/2 (/ (* (pow b 5) (PI)) (pow a 6)))))) (pow a 2))
(* -1 (/ (PI) (pow a 2)))
(/ (+ (* -1 (PI)) (/ (* (PI) (+ b (* -1 b))) a)) (pow a 2))
(/ (+ (* -1 (PI)) (* -1 (/ (- (+ (/ (* (PI) (pow (+ b (* -1 b)) 2)) a) (/ (* (pow b 2) (PI)) a)) (* (PI) (+ b (* -1 b)))) a))) (pow a 2))
(/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ b (* -1 b)) (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI)))) a) (/ (* (pow b 2) (* (PI) (+ b (* -1 b)))) a)) (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI)))) a)) (* (PI) (+ b (* -1 b)))) a))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(/ -1/2 (pow a 2))
(/ (- (* -1/2 (/ (pow b 2) (pow a 2))) 1/2) (pow a 2))
(/ (- (* -1/2 (/ (pow b 4) (pow a 4))) (+ 1/2 (* 1/2 (/ (pow b 2) (pow a 2))))) (pow a 2))
(/ (- (* -1/2 (/ (pow b 6) (pow a 6))) (+ 1/2 (+ (* 1/2 (/ (pow b 2) (pow a 2))) (* 1/2 (/ (pow b 4) (pow a 4)))))) (pow a 2))

Outputs
(/ (PI) a)
(/.f64 (PI.f64) a)
(+ (* -1 (/ (* b (PI)) (pow a 2))) (/ (PI) a))
(fma.f64 (neg.f64 b) (/.f64 (/.f64 (PI.f64) a) a) (/.f64 (PI.f64) a))
(+ (* b (- (/ (* b (PI)) (pow a 3)) (/ (PI) (pow a 2)))) (/ (PI) a))
(fma.f64 (-.f64 (*.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))) b) (/.f64 (/.f64 (PI.f64) a) a)) b (/.f64 (PI.f64) a))
(+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 4))) (* -1 (/ (PI) (pow a 3))))) (/ (PI) (pow a 2)))) (/ (PI) a))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 b) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64)))) b (/.f64 (/.f64 (neg.f64 (PI.f64)) a) a)) b (/.f64 (PI.f64) a))
(* -1 (pow a 2))
(*.f64 (neg.f64 a) a)
(+ (* -1 (pow a 2)) (* b (+ a (* -1 a))))
(*.f64 (neg.f64 a) a)
(+ (* -1 (pow a 2)) (* b (+ a (+ b (* -1 a)))))
(fma.f64 (neg.f64 a) a (*.f64 b b))
(+ (* -1 (pow a 2)) (* b (+ a (+ b (* -1 a)))))
(fma.f64 (neg.f64 a) a (*.f64 b b))
a
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64)))) b (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64)) b (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))))) b (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) b) (/.f64 (PI.f64) (pow.f64 a #s(literal 5 binary64))) (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64))) b (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))))) b (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (PI) (* (pow a 2) b))
(/.f64 (/.f64 (/.f64 (PI.f64) a) a) b)
(/ (PI) (* (pow a 2) b))
(/.f64 (/.f64 (/.f64 (PI.f64) a) a) b)
(/ (PI) (* (pow a 2) b))
(/.f64 (/.f64 (/.f64 (PI.f64) a) a) b)
(/ (PI) (* (pow a 2) b))
(/.f64 (/.f64 (/.f64 (PI.f64) a) a) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64)))) b (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64)) b (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))))) b (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) b) (/.f64 (PI.f64) (pow.f64 a #s(literal 5 binary64))) (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64))) b (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))))) b (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(* 1/2 (/ (PI) b))
(*.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b)
(/.f64 (fma.f64 (.f64 b (/.f64 (PI.f64) a)) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) b)
(/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b)
(/.f64 (fma.f64 (.f64 b (/.f64 (PI.f64) a)) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) b)
(/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) b)
(/.f64 (fma.f64 (.f64 b (/.f64 (PI.f64) a)) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) b)
(/ 1/2 b)
(/.f64 #s(literal 1/2 binary64) b)
(/ (+ 1/2 (* -1/2 (/ b a))) b)
(/.f64 (fma.f64 (/.f64 b a) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) b)
(/ (+ 1/2 (* -1/2 (/ b a))) b)
(/.f64 (fma.f64 (/.f64 b a) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) b)
(/ (+ 1/2 (* -1/2 (/ b a))) b)
(/.f64 (fma.f64 (/.f64 b a) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64)))) b (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64)) b (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))))) b (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) b) (/.f64 (PI.f64) (pow.f64 a #s(literal 5 binary64))) (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64))) b (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))))) b (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (PI) (pow a 2))
(/.f64 (/.f64 (PI.f64) a) a)
(+ (* -1 (/ (* b (PI)) (pow a 3))) (/ (PI) (pow a 2)))
(fma.f64 (neg.f64 b) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))) (/.f64 (/.f64 (PI.f64) a) a))
(+ (* b (- (/ (* b (PI)) (pow a 4)) (/ (PI) (pow a 3)))) (/ (PI) (pow a 2)))
(fma.f64 (fma.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) b (/.f64 (neg.f64 (PI.f64)) (pow.f64 a #s(literal 3 binary64)))) b (/.f64 (/.f64 (PI.f64) a) a))
(+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 5))) (* -1 (/ (PI) (pow a 4))))) (/ (PI) (pow a 3)))) (/ (PI) (pow a 2)))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 b) (/.f64 (PI.f64) (pow.f64 a #s(literal 5 binary64))) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64)))) b (/.f64 (neg.f64 (PI.f64)) (pow.f64 a #s(literal 3 binary64)))) b (/.f64 (/.f64 (PI.f64) a) a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64)))) b (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* (PI) (+ a (* -1 a))) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(/.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 0 binary64) (pow.f64 a #s(literal 5 binary64))) (PI.f64) (fma.f64 (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64)) b (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64)))))) b (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (* b (+ (/ (PI) (pow a 5)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) (pow a 7))))) (+ (* -1/2 (/ (* (PI) (+ a (* -1 a))) (pow a 5))) (* 1/2 (/ (PI) (pow a 4))))))))) b)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) b) (fma.f64 (/.f64 #s(literal 0 binary64) (pow.f64 a #s(literal 7 binary64))) (PI.f64) (/.f64 (PI.f64) (pow.f64 a #s(literal 5 binary64)))) (fma.f64 (/.f64 #s(literal 0 binary64) (pow.f64 a #s(literal 5 binary64))) (PI.f64) (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64)))) b (.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 3 binary64))))) b (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* 1/2 (/ (* (pow b 2) (PI)) (pow a 4)))) b)
(.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 b b) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) (/.f64 (/.f64 (PI.f64) a) a)) b))
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* (pow b 2) (+ (* 1/2 (/ (PI) (pow a 4))) (* 1/2 (/ (* (pow b 2) (PI)) (pow a 6)))))) b)
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) b) b) (fma.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 6 binary64))) (.f64 b b) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (PI.f64) a) a))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* (pow b 2) (+ (* 1/2 (/ (PI) (pow a 4))) (* (pow b 2) (+ (* 1/2 (/ (PI) (pow a 6))) (* 1/2 (/ (* (pow b 2) (PI)) (pow a 8)))))))) b)
(/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (PI.f64) a) (.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) b) b) (fma.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 8 binary64))) (.f64 b b) (/.f64 (PI.f64) (pow.f64 a #s(literal 6 binary64)))) (.f64 (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/2 binary64))) (.f64 b b))) b)
(* -1 (/ (PI) b))
(/.f64 (neg.f64 (PI.f64)) b)
(* -1 (/ (PI) b))
(/.f64 (neg.f64 (PI.f64)) b)
(* -1 (/ (PI) b))
(/.f64 (neg.f64 (PI.f64)) b)
(* -1 (/ (PI) b))
(/.f64 (neg.f64 (PI.f64)) b)
(* -1 (/ (PI) (pow a 2)))
(/.f64 (/.f64 (neg.f64 (PI.f64)) a) a)
(+ (* -1 (/ (PI) (pow a 2))) (* -1 (/ (* b (* (PI) (+ a (* -1 a)))) (pow a 4))))
(neg.f64 (fma.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) (/.f64 (/.f64 (PI.f64) a) a)))
(+ (* -1 (/ (PI) (pow a 2))) (* b (- (* -1 (* b (+ (/ (PI) (pow a 4)) (/ (* (PI) (pow (+ a (* -1 a)) 2)) (pow a 6))))) (/ (* (PI) (+ a (* -1 a))) (pow a 4)))))
(fma.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 6 binary64))) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64)))) b (*.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64)))))) b (/.f64 (/.f64 (neg.f64 (PI.f64)) a) a))
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(/.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a))) a) a)
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 b (/.f64 (PI.f64) a)) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) (neg.f64 a))) (*.f64 a a))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 (fma.f64 (.f64 b (.f64 b (/.f64 (PI.f64) a))) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) b)) a)) (neg.f64 a))) (.f64 a a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (PI) (* (pow a 2) b))
(/.f64 (/.f64 (/.f64 (PI.f64) a) a) b)
(/ (PI) (* (pow a 2) b))
(/.f64 (/.f64 (/.f64 (PI.f64) a) a) b)
(/ (PI) (* (pow a 2) b))
(/.f64 (/.f64 (/.f64 (PI.f64) a) a) b)
(/ (PI) (* (pow a 2) b))
(/.f64 (/.f64 (/.f64 (PI.f64) a) a) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a))) a) a)
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 b (/.f64 (PI.f64) a)) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) (neg.f64 a))) (*.f64 a a))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 (fma.f64 (.f64 b (.f64 b (/.f64 (PI.f64) a))) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) b)) a)) (neg.f64 a))) (.f64 a a))
(* 1/2 (/ (PI) b))
(*.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a)))
(+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b)))
(fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a)))
(/ 1/2 b)
(/.f64 #s(literal 1/2 binary64) b)
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(-.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal 1/2 binary64) a))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(-.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal 1/2 binary64) a))
(- (* 1/2 (/ 1 b)) (* 1/2 (/ 1 a)))
(-.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal 1/2 binary64) a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a))) a) a)
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 b (/.f64 (PI.f64) a)) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) (neg.f64 a))) (*.f64 a a))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 (fma.f64 (.f64 b (.f64 b (/.f64 (PI.f64) a))) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) b)) a)) (neg.f64 a))) (.f64 a a))
(/ (PI) (pow a 2))
(/.f64 (/.f64 (PI.f64) a) a)
(/ (+ (PI) (* -1 (/ (* b (PI)) a))) (pow a 2))
(/.f64 (/.f64 (fma.f64 (neg.f64 b) (/.f64 (PI.f64) a) (PI.f64)) a) a)
(/ (+ (PI) (* -1 (/ (+ (* -1 (/ (* (pow b 2) (PI)) a)) (* b (PI))) a))) (pow a 2))
(/.f64 (-.f64 (PI.f64) (/.f64 (fma.f64 (.f64 (neg.f64 b) b) (/.f64 (PI.f64) a) (.f64 b (PI.f64))) a)) (*.f64 a a))
(/ (+ (PI) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (pow b 3) (PI)) a)) (* (pow b 2) (PI))) a)) (* b (PI))) a))) (pow a 2))
(/.f64 (-.f64 (PI.f64) (/.f64 (fma.f64 b (PI.f64) (/.f64 (fma.f64 (pow.f64 b #s(literal 3 binary64)) (/.f64 (neg.f64 (PI.f64)) a) (.f64 (.f64 b b) (PI.f64))) (neg.f64 a))) a)) (*.f64 a a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a))) a) a)
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (* b (PI))) (* 1/2 (* (PI) (+ b (* -1 b))))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (PI.f64) (+.f64 #s(literal 0 binary64) b))) a)) (neg.f64 a))) (*.f64 a a))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI))) a)) (+ (* 1/2 (* b (PI))) (* 1/2 (* (PI) (+ b (* -1 b)))))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) b) b) (/.f64 (PI.f64) a) (.f64 (.f64 (PI.f64) (+.f64 #s(literal 0 binary64) b)) #s(literal 1/2 binary64))) (neg.f64 a))) (neg.f64 a))) (*.f64 a a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))) (pow a 2))
(*.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (fma.f64 (/.f64 (/.f64 (PI.f64) a) a) b (/.f64 (PI.f64) b)) a))
(/ (+ (* 1/2 (/ (PI) b)) (+ (* 1/2 (/ (* b (PI)) (pow a 2))) (* 1/2 (/ (* (pow b 3) (PI)) (pow a 4))))) (pow a 2))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 (pow.f64 b #s(literal 3 binary64)) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))) (.f64 (/.f64 b a) (/.f64 (PI.f64) a))) (/.f64 (PI.f64) b))) (*.f64 a a))
(/ (+ (* 1/2 (/ (PI) b)) (+ (* 1/2 (/ (* b (PI)) (pow a 2))) (+ (* 1/2 (/ (* (pow b 3) (PI)) (pow a 4))) (* 1/2 (/ (* (pow b 5) (PI)) (pow a 6)))))) (pow a 2))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 (/.f64 (/.f64 (PI.f64) a) a) b (/.f64 (PI.f64) b)) (fma.f64 (pow.f64 b #s(literal 5 binary64)) (/.f64 (PI.f64) (pow.f64 a #s(literal 6 binary64))) (.f64 (pow.f64 b #s(literal 3 binary64)) (/.f64 (PI.f64) (pow.f64 a #s(literal 4 binary64))))))) (*.f64 a a))
(* -1 (/ (PI) (pow a 2)))
(/.f64 (/.f64 (neg.f64 (PI.f64)) a) a)
(/ (+ (* -1 (PI)) (/ (* (PI) (+ b (* -1 b))) a)) (pow a 2))
(/.f64 (/.f64 (neg.f64 (PI.f64)) a) a)
(/ (+ (* -1 (PI)) (* -1 (/ (- (+ (/ (* (PI) (pow (+ b (* -1 b)) 2)) a) (/ (* (pow b 2) (PI)) a)) (* (PI) (+ b (* -1 b)))) a))) (pow a 2))
(/.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (PI.f64) (.f64 b (.f64 b (/.f64 (PI.f64) a)))) a) (PI.f64))) (*.f64 a a))
(/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ b (* -1 b)) (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI)))) a) (/ (* (pow b 2) (* (PI) (+ b (* -1 b)))) a)) (+ (* (PI) (pow (+ b (* -1 b)) 2)) (* (pow b 2) (PI)))) a)) (* (PI) (+ b (* -1 b)))) a))) (pow a 2))
(/.f64 (-.f64 (/.f64 (fma.f64 #s(literal 0 binary64) (PI.f64) (neg.f64 (.f64 (.f64 (neg.f64 b) b) (/.f64 (PI.f64) a)))) (neg.f64 a)) (PI.f64)) (*.f64 a a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a))) a) a)
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 b (/.f64 (PI.f64) a)) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) (neg.f64 a))) (*.f64 a a))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (/.f64 (fma.f64 (.f64 b (.f64 b (/.f64 (PI.f64) a))) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) b)) a)) (neg.f64 a))) (.f64 a a))
(* (pow a 2) b)
(.f64 (.f64 a a) b)
(* (pow a 2) b)
(.f64 (.f64 a a) b)
(* (pow a 2) b)
(.f64 (.f64 a a) b)
(* (pow a 2) b)
(.f64 (.f64 a a) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(*.f64 (/.f64 (/.f64 (/.f64 (PI.f64) a) a) b) #s(literal 1/2 binary64))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a))) a) a)
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a))) a) a)
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) a))) a) a)
(/ 1/2 (* a b))
(/.f64 #s(literal 1/2 binary64) (*.f64 b a))
(/ 1/2 (* a b))
(/.f64 #s(literal 1/2 binary64) (*.f64 b a))
(/ 1/2 (* a b))
(/.f64 #s(literal 1/2 binary64) (*.f64 b a))
(/ 1/2 (* a b))
(/.f64 #s(literal 1/2 binary64) (*.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 b a) (/.f64 b a))) (*.f64 a a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 b a) (/.f64 b a))) (*.f64 a a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 b a) (/.f64 b a))) (*.f64 a a))
(/ -1/2 (pow a 2))
(/.f64 (/.f64 #s(literal -1/2 binary64) a) a)
(/ (- (* -1/2 (/ (pow b 2) (pow a 2))) 1/2) (pow a 2))
(/.f64 (.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (.f64 a a))
(/ (- (* -1/2 (/ (pow b 4) (pow a 4))) (+ 1/2 (* 1/2 (/ (pow b 2) (pow a 2))))) (pow a 2))
(/.f64 (-.f64 (/.f64 (.f64 (pow.f64 b #s(literal 4 binary64)) #s(literal -1/2 binary64)) (pow.f64 a #s(literal 4 binary64))) (.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal 1 binary64)) #s(literal 1/2 binary64))) (*.f64 a a))
(/ (- (* -1/2 (/ (pow b 6) (pow a 6))) (+ 1/2 (+ (* 1/2 (/ (pow b 2) (pow a 2))) (* 1/2 (/ (pow b 4) (pow a 4)))))) (pow a 2))
(/.f64 (-.f64 (/.f64 (.f64 (pow.f64 b #s(literal 6 binary64)) #s(literal -1/2 binary64)) (pow.f64 a #s(literal 6 binary64))) (fma.f64 (fma.f64 (/.f64 b a) (/.f64 b a) (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (.f64 a a))

rewrite171.0ms (1.9%)

Memory

-1.5MiB live, 320.5MiB allocated

Rules

4 338×	`lower-/.f32`
4 316×	`lower-/.f64`
3 814×	`lower-*.f32`
3 790×	`lower-*.f64`
2 320×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	271
0	84	263
1	372	254
2	3525	254
0	8135	254

Stop Event

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

Counts

22 → 1 170

Calls

Call 1

Inputs
(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))
(PI.f64)
(*.f64 (+.f64 a b) (-.f64 b a))
(+.f64 a b)
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))
(.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64))
(/.f64 (PI.f64) (.f64 b (.f64 a a)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)))
(*.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a)))
(+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))
(.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 a b))))
(*.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b)))
(fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a))))
(*.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64))
(/.f64 (PI.f64) (*.f64 (+.f64 a b) (-.f64 b a)))
(/.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
(.f64 b (.f64 a a))
(/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 a b)))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a)))

Outputs
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eval574.0ms (6.5%)

Memory: 33.4MiB live, 573.4MiB allocated
Compiler: Compiled 57 277 to 5 309 computations (90.7% saved)

prune175.0ms (2%)

Memory

0.5MiB live, 195.2MiB allocated

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	2 218	15	2 233
Fresh	8	4	12
Picked	4	1	5
Done	0	0	0
Total	2 230	20	2 250

Accuracy

100.0%

Counts

2 250 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	89.0%	(fma.f64 (.f64 (PI.f64) (pow.f64 (.f64 (+.f64 b a) a) #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a)))))
▶	90.3%	(/.f64 (/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a))) (.f64 #s(literal 2 binary64) (.f64 a b)))
	99.4%	(/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (-.f64 b a)) (.f64 (-.f64 b a) (.f64 (.f64 b a) #s(literal 2 binary64))))
▶	99.6%	(/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a))
	52.5%	(/.f64 (.f64 (/.f64 (PI.f64) #s(approx ( (+ a b) (- b a)) (.f64 b b))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (*.f64 a b)))
▶	84.7%	(/.f64 (.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 b a) (*.f64 (-.f64 b a) (+.f64 b a))))
	86.3%	(/.f64 (.f64 (.f64 (-.f64 b a) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))) (.f64 a b))
	65.1%	(/.f64 #s(approx (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/.f64 (PI.f64) b)) (.f64 #s(literal 2 binary64) (.f64 a b)))
	63.2%	(/.f64 #s(approx (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
	90.8%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 b a) #s(literal 2 binary64)) (*.f64 (/.f64 (/.f64 (PI.f64) (-.f64 b a)) (+.f64 b a)) (-.f64 b a))))
	83.4%	(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (-.f64 b a) a) b)))
	65.1%	#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64)))
	63.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 b a)) a))
▶	59.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)))
	51.6%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 #s(literal -1/2 binary64) b))) (.f64 b b)))
	59.6%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64)))
	62.9%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) a)) #s(literal 1/2 binary64)))
✓	59.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))
	63.0%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (.f64 (pow.f64 (/.f64 (*.f64 b a) (sqrt.f64 (PI.f64))) #s(literal -1 binary64)) (pow.f64 (/.f64 a (sqrt.f64 (PI.f64))) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
▶	59.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b))))

Compiler

Compiled 596 to 443 computations (25.7% saved)

simplify221.0ms (2.5%)

Memory

21.8MiB live, 211.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 b a)
cost-diff	0	(*.f64 (-.f64 b a) (PI.f64))
cost-diff	384	(/.f64 (/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a))) (.f64 #s(literal 2 binary64) (.f64 a b)))
cost-diff	1024	(/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a)))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) (PI.f64))
cost-diff	0	(-.f64 b a)
cost-diff	0	(.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64)))
cost-diff	1024	(/.f64 (.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 b a) (*.f64 (-.f64 b a) (+.f64 b a))))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) b)
cost-diff	0	(*.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)))
cost-diff	0	(.f64 (.f64 a a) b)
cost-diff	0	(PI.f64)
cost-diff	0	(.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b)))
cost-diff	0	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b))))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) (+.f64 b a))
cost-diff	0	(.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a)))
cost-diff	2176	(/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a))

Rules

6 128×	`lower-fma.f64`
6 128×	`lower-fma.f32`
4 434×	`lower-*.f32`
4 406×	`lower-*.f64`
3 540×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	302
0	72	294
1	162	272
2	626	266
3	3003	250
4	6432	250
0	8569	250

Stop Event

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

Calls

Call 1

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

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

localize165.0ms (1.9%)

Memory

-36.3MiB live, 131.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(PI.f64)
accuracy	0.1484375	(/.f64 (/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a))) (.f64 #s(literal 2 binary64) (.f64 a b)))
accuracy	0.23828125	(*.f64 (-.f64 b a) (PI.f64))
accuracy	27.422728934930987	(/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a)))
accuracy	0	(PI.f64)
accuracy	0.23828125	(.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64)))
accuracy	1.453957915907595	(.f64 (.f64 b a) (*.f64 (-.f64 b a) (+.f64 b a)))
accuracy	8.288892459135358	(/.f64 (.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 b a) (*.f64 (-.f64 b a) (+.f64 b a))))
accuracy	0	(PI.f64)
accuracy	0.25390625	(/.f64 (PI.f64) b)
accuracy	5.422735478110075	(/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a))
accuracy	23.430333761737135	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)))
accuracy	0.19140625	(.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b)))
accuracy	0.2993155455788509	(/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b))
accuracy	5.400889743003612	(.f64 (.f64 a a) b)
accuracy	23.430333761737135	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b))))
accuracy	0.16796875	(/.f64 (/.f64 #s(literal 1/2 binary64) b) a)
accuracy	0.25390625	(/.f64 (PI.f64) (+.f64 b a))
accuracy	0.265625	(.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a)))
accuracy	15.575094257742128	(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))

Samples

105.0ms

256×

valid

Compiler

Compiled 284 to 43 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-mult: 46.0ms (53.4% of total)

ival-div: 34.0ms (39.5% of total)

ival-sub: 3.0ms (3.5% of total)

ival-pi: 1.0ms (1.2% of total)

ival-add: 1.0ms (1.2% of total)

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

exact: 0.0ms (0% of total)

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

series77.0ms (0.9%)

Memory

5.3MiB live, 42.3MiB allocated

Counts

22 → 456

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a)) (patch (/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (patch (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) #<representation binary64>) () ())
#s(alt (/.f64 (PI.f64) (+.f64 b a)) (patch (/.f64 (PI.f64) (+.f64 b a)) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b)))) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b))) (patch (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 a a) b) (patch (.f64 (.f64 a a) b) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a))) (patch #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (PI.f64) b) (patch (/.f64 (PI.f64) b) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a)))) (patch (/.f64 (.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a)))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64))) (patch (.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64))) #<representation binary64>) () ())
#s(alt (-.f64 b a) (patch (-.f64 b a) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (PI.f64)) (patch (.f64 #s(literal 1/2 binary64) (PI.f64)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a))) (patch (/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a))) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 (/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a))) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 b a) (PI.f64)) (patch (.f64 (-.f64 b a) (PI.f64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a)) (patch (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (patch (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) (patch (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) (patch (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a)) (patch (/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b) (taylor 0 b) (#s(alt (/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a)) (patch (/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a)) #<representation binary64>) () ())) ())
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#s(alt (/ 1/2 (* a b)) (taylor -inf a) (#s(alt (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (patch (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* (pow a 2) b)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* (pow a 2) b)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* (pow a 2) b)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* (pow a 2) b)) (taylor -inf a) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a a) b)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) (patch (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) (patch (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) (patch (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) (patch (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow a 3) b)) (taylor -inf a) (#s(alt (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) (patch (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow a 3) (+ b (/ (* b (+ b (* -1 b))) a)))) (taylor -inf a) (#s(alt (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) (patch (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow a 3) (+ b (* -1 (/ (+ (* -1 (* b (+ b (* -1 b)))) (/ (pow b 3) a)) a))))) (taylor -inf a) (#s(alt (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) (patch (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow a 3) (+ b (* -1 (/ (+ (* -1 (* b (+ b (* -1 b)))) (/ (pow b 3) a)) a))))) (taylor -inf a) (#s(alt (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) (patch (.f64 (.f64 b a) (.f64 (-.f64 b a) (+.f64 b a))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
40.0ms	b	@	inf	((/ (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (- b a)) (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (/ (PI) (+ b a)) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a a) b))) (* (* a a) b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) b) 1/2) (/ (PI) b) (/ (* (- b a) (* 1/2 (PI))) (* (* b a) (* (- b a) (+ b a)))) (* (- b a) (* 1/2 (PI))) (- b a) (* 1/2 (PI)) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (* (- b a) (PI)) (* (/ (/ 1/2 b) a) (- b a)) (/ (/ 1/2 b) a) (/ 1/2 (* (* a a) b)) (/ (* (/ (PI) b) 1/2) (* a a)) (* (* b a) (* (- b a) (+ b a))))
9.0ms	b	@	0	((/ (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (- b a)) (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (/ (PI) (+ b a)) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a a) b))) (* (* a a) b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) b) 1/2) (/ (PI) b) (/ (* (- b a) (* 1/2 (PI))) (* (* b a) (* (- b a) (+ b a)))) (* (- b a) (* 1/2 (PI))) (- b a) (* 1/2 (PI)) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (* (- b a) (PI)) (* (/ (/ 1/2 b) a) (- b a)) (/ (/ 1/2 b) a) (/ 1/2 (* (* a a) b)) (/ (* (/ (PI) b) 1/2) (* a a)) (* (* b a) (* (- b a) (+ b a))))
4.0ms	b	@	-inf	((/ (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (- b a)) (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (/ (PI) (+ b a)) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a a) b))) (* (* a a) b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) b) 1/2) (/ (PI) b) (/ (* (- b a) (* 1/2 (PI))) (* (* b a) (* (- b a) (+ b a)))) (* (- b a) (* 1/2 (PI))) (- b a) (* 1/2 (PI)) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (* (- b a) (PI)) (* (/ (/ 1/2 b) a) (- b a)) (/ (/ 1/2 b) a) (/ 1/2 (* (* a a) b)) (/ (* (/ (PI) b) 1/2) (* a a)) (* (* b a) (* (- b a) (+ b a))))
3.0ms	a	@	inf	((/ (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (- b a)) (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (/ (PI) (+ b a)) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a a) b))) (* (* a a) b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) b) 1/2) (/ (PI) b) (/ (* (- b a) (* 1/2 (PI))) (* (* b a) (* (- b a) (+ b a)))) (* (- b a) (* 1/2 (PI))) (- b a) (* 1/2 (PI)) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (* (- b a) (PI)) (* (/ (/ 1/2 b) a) (- b a)) (/ (/ 1/2 b) a) (/ 1/2 (* (* a a) b)) (/ (* (/ (PI) b) 1/2) (* a a)) (* (* b a) (* (- b a) (+ b a))))
3.0ms	a	@	-inf	((/ (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (- b a)) (* (/ (PI) (+ b a)) (* (/ (/ 1/2 b) a) (- b a))) (/ (PI) (+ b a)) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a a) b))) (* (* a a) b) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (/ (PI) b) 1/2) (/ (PI) b) (/ (* (- b a) (* 1/2 (PI))) (* (* b a) (* (- b a) (+ b a)))) (* (- b a) (* 1/2 (PI))) (- b a) (* 1/2 (PI)) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (* (- b a) (PI)) (* (/ (/ 1/2 b) a) (- b a)) (/ (/ 1/2 b) a) (/ 1/2 (* (* a a) b)) (/ (* (/ (PI) b) 1/2) (* a a)) (* (* b a) (* (- b a) (+ b a))))

simplify396.0ms (4.5%)

Memory

14.1MiB live, 164.8MiB allocated

Algorithm

1×	egg-herbie

Rules

11 182×	`lower-fma.f64`
11 182×	`lower-fma.f32`
5 184×	`lower-*.f64`
5 184×	`lower-*.f32`
2 696×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	495	5948
1	1513	5649
2	4567	5383
0	8354	5177

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 453

Calls

Call 1

Inputs
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* -1/2 (/ (PI) (* a b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (* b (- (/ (PI) (pow a 2)) (* -1 (/ (PI) (pow a 2))))))) b)
(/ (+ (* -1/2 (/ (PI) a)) (* b (+ (* 1/2 (* b (- (* -1 (/ (PI) (pow a 3))) (/ (PI) (pow a 3))))) (* 1/2 (- (/ (PI) (pow a 2)) (* -1 (/ (PI) (pow a 2)))))))) b)
(/ (+ (* -1/2 (/ (PI) a)) (* b (+ (* 1/2 (- (/ (PI) (pow a 2)) (* -1 (/ (PI) (pow a 2))))) (* b (+ (* 1/2 (* b (- (/ (PI) (pow a 4)) (* -1 (/ (PI) (pow a 4)))))) (* 1/2 (- (* -1 (/ (PI) (pow a 3))) (/ (PI) (pow a 3))))))))) b)
(/ (PI) a)
(+ (* -1 (/ (* b (PI)) (pow a 2))) (/ (PI) a))
(+ (* b (- (/ (* b (PI)) (pow a 3)) (/ (PI) (pow a 2)))) (/ (PI) a))
(+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 4))) (* -1 (/ (PI) (pow a 3))))) (/ (PI) (pow a 2)))) (/ (PI) a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(/ (PI) b)
(/ (PI) b)
(/ (PI) b)
(/ (PI) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* -1/2 (* a (PI)))
(+ (* -1/2 (* a (PI))) (* 1/2 (* b (PI))))
(+ (* -1/2 (* a (PI))) (* 1/2 (* b (PI))))
(+ (* -1/2 (* a (PI))) (* 1/2 (* b (PI))))
(* -1 a)
(- b a)
(- b a)
(- b a)
(/ (PI) a)
(+ (* -1 (/ (* b (PI)) (pow a 2))) (/ (PI) a))
(+ (* b (- (/ (* b (PI)) (pow a 3)) (/ (PI) (pow a 2)))) (/ (PI) a))
(+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 4))) (* -1 (/ (PI) (pow a 3))))) (/ (PI) (pow a 2)))) (/ (PI) a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* -1 (* a (PI)))
(+ (* -1 (* a (PI))) (* b (PI)))
(+ (* -1 (* a (PI))) (* b (PI)))
(+ (* -1 (* a (PI))) (* b (PI)))
(/ -1/2 b)
(/ (- (* 1/2 (/ b a)) 1/2) b)
(/ (- (* 1/2 (/ b a)) 1/2) b)
(/ (- (* 1/2 (/ b a)) 1/2) b)
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* -1 (* (pow a 3) b))
(* b (+ (* -1 (pow a 3)) (* a (* b (+ a (* -1 a))))))
(* b (+ (* -1 (pow a 3)) (* b (+ (* a b) (* a (+ a (* -1 a)))))))
(* b (+ (* -1 (pow a 3)) (* b (+ (* a b) (* a (+ a (* -1 a)))))))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(* 1/2 (/ (PI) (* a b)))
(/ (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (- (* -1 (PI)) (PI)) b))) b)
(/ (+ (* -1/2 (/ (* a (- (* -1 (PI)) (PI))) (pow b 2))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (- (* -1 (PI)) (PI)) b)))) b)
(/ (+ (* -1/2 (/ (* a (- (* -1 (PI)) (PI))) (pow b 2))) (+ (* 1/2 (/ (PI) a)) (+ (* 1/2 (/ (* (pow a 2) (- (* -1 (PI)) (PI))) (pow b 3))) (* 1/2 (/ (- (* -1 (PI)) (PI)) b))))) b)
(/ (PI) b)
(/ (+ (PI) (* -1 (/ (* a (PI)) b))) b)
(/ (- (+ (PI) (/ (* (pow a 2) (PI)) (pow b 2))) (/ (* a (PI)) b)) b)
(/ (- (+ (PI) (* -1 (/ (* (pow a 3) (PI)) (pow b 3)))) (+ (* -1 (/ (* (pow a 2) (PI)) (pow b 2))) (/ (* a (PI)) b))) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(/ (PI) b)
(/ (PI) b)
(/ (PI) b)
(/ (PI) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(* 1/2 (* b (PI)))
(* b (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))))
(* b (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))))
(* b (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))))
b
(* b (+ 1 (* -1 (/ a b))))
(* b (+ 1 (* -1 (/ a b))))
(* b (+ 1 (* -1 (/ a b))))
(/ (PI) b)
(/ (+ (PI) (* -1 (/ (* a (PI)) b))) b)
(/ (- (+ (PI) (/ (* (pow a 2) (PI)) (pow b 2))) (/ (* a (PI)) b)) b)
(/ (- (+ (PI) (* -1 (/ (* (pow a 3) (PI)) (pow b 3)))) (+ (* -1 (/ (* (pow a 2) (PI)) (pow b 2))) (/ (* a (PI)) b))) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2))))) (pow b 2))
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* (pow a 2) (PI)) (pow b 3))) (+ (* 1/2 (/ (PI) a)) (* 1/2 (/ (* a (PI)) (pow b 2)))))) (pow b 2))
(* b (PI))
(* b (+ (PI) (* -1 (/ (* a (PI)) b))))
(* b (+ (PI) (* -1 (/ (* a (PI)) b))))
(* b (+ (PI) (* -1 (/ (* a (PI)) b))))
(/ 1/2 a)
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* a (pow b 3))
(* (pow b 3) (+ a (/ (* a (+ a (* -1 a))) b)))
(* (pow b 3) (+ a (+ (* -1 (/ (pow a 3) (pow b 2))) (/ (* a (+ a (* -1 a))) b))))
(* (pow b 3) (+ a (+ (* -1 (/ (pow a 3) (pow b 2))) (/ (* a (+ a (* -1 a))) b))))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* 1/2 (/ (PI) (* a b)))
(* -1 (/ (+ (* -1/2 (/ (PI) a)) (* -1/2 (/ (- (* -1 (PI)) (PI)) b))) b))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (- (* -1 (PI)) (PI))) b)) (* 1/2 (- (* -1 (PI)) (PI)))) b)) (* -1/2 (/ (PI) a))) b))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (- (* -1 (PI)) (PI))) b)) (* 1/2 (* a (- (* -1 (PI)) (PI))))) b)) (* 1/2 (- (* -1 (PI)) (PI)))) b)) (* -1/2 (/ (PI) a))) b))
(/ (PI) b)
(* -1 (/ (+ (* -1 (PI)) (/ (* a (PI)) b)) b))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (/ (* (pow a 2) (PI)) b) (* a (PI))) b))) b))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow a 3) (PI)) b) (* (pow a 2) (PI))) b)) (* a (PI))) b))) b))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(* 1/2 (/ (PI) b))
(/ (PI) b)
(/ (PI) b)
(/ (PI) b)
(/ (PI) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* 1/2 (* b (PI)))
(* -1 (* b (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b)))))
(* -1 (* b (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b)))))
(* -1 (* b (+ (* -1/2 (PI)) (* 1/2 (/ (* a (PI)) b)))))
b
(* -1 (* b (- (/ a b) 1)))
(* -1 (* b (- (/ a b) 1)))
(* -1 (* b (- (/ a b) 1)))
(/ (PI) b)
(* -1 (/ (+ (* -1 (PI)) (/ (* a (PI)) b)) b))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (/ (* (pow a 2) (PI)) b) (* a (PI))) b))) b))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow a 3) (PI)) b) (* (pow a 2) (PI))) b)) (* a (PI))) b))) b))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* a (PI)) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow a 2) (PI)) b)) (* 1/2 (* a (PI)))) b)) (* 1/2 (PI))) b)) (* 1/2 (/ (PI) a))) (pow b 2))
(* b (PI))
(* -1 (* b (+ (* -1 (PI)) (/ (* a (PI)) b))))
(* -1 (* b (+ (* -1 (PI)) (/ (* a (PI)) b))))
(* -1 (* b (+ (* -1 (PI)) (/ (* a (PI)) b))))
(/ 1/2 a)
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* a (pow b 3))
(* -1 (* (pow b 3) (+ (* -1 a) (* -1 (/ (* a (+ a (* -1 a))) b)))))
(* -1 (* (pow b 3) (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (pow a 3) b)) (* a (+ a (* -1 a)))) b)))))
(* -1 (* (pow b 3) (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (pow a 3) b)) (* a (+ a (* -1 a)))) b)))))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(* 1/2 (/ (PI) (* a b)))
(/ (+ (* 1/2 (* a (- (* -1 (/ (PI) (pow b 2))) (/ (PI) (pow b 2))))) (* 1/2 (/ (PI) b))) a)
(/ (+ (* 1/2 (/ (PI) b)) (* a (+ (* 1/2 (* a (- (/ (PI) (pow b 3)) (* -1 (/ (PI) (pow b 3)))))) (* 1/2 (- (* -1 (/ (PI) (pow b 2))) (/ (PI) (pow b 2))))))) a)
(/ (+ (* 1/2 (/ (PI) b)) (* a (+ (* 1/2 (- (* -1 (/ (PI) (pow b 2))) (/ (PI) (pow b 2)))) (* a (+ (* 1/2 (* a (- (* -1 (/ (PI) (pow b 4))) (/ (PI) (pow b 4))))) (* 1/2 (- (/ (PI) (pow b 3)) (* -1 (/ (PI) (pow b 3)))))))))) a)
(/ (PI) b)
(+ (* -1 (/ (* a (PI)) (pow b 2))) (/ (PI) b))
(+ (* a (- (/ (* a (PI)) (pow b 3)) (/ (PI) (pow b 2)))) (/ (PI) b))
(+ (* a (- (* a (- (* -1 (/ (* a (PI)) (pow b 4))) (* -1 (/ (PI) (pow b 3))))) (/ (PI) (pow b 2)))) (/ (PI) b))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(* 1/2 (* b (PI)))
(+ (* -1/2 (* a (PI))) (* 1/2 (* b (PI))))
(+ (* -1/2 (* a (PI))) (* 1/2 (* b (PI))))
(+ (* -1/2 (* a (PI))) (* 1/2 (* b (PI))))
b
(+ b (* -1 a))
(+ b (* -1 a))
(+ b (* -1 a))
(/ (PI) b)
(+ (* -1 (/ (* a (PI)) (pow b 2))) (/ (PI) b))
(+ (* a (- (/ (* a (PI)) (pow b 3)) (/ (PI) (pow b 2)))) (/ (PI) b))
(+ (* a (- (* a (- (* -1 (/ (* a (PI)) (pow b 4))) (* -1 (/ (PI) (pow b 3))))) (/ (PI) (pow b 2)))) (/ (PI) b))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (+ (* -1/2 (/ (* a (PI)) (pow b 3))) (* 1/2 (/ (PI) (pow b 2)))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* 1/2 (/ (* a (PI)) (pow b 4)))))) a)
(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
(* b (PI))
(+ (* -1 (* a (PI))) (* b (PI)))
(+ (* -1 (* a (PI))) (* b (PI)))
(+ (* -1 (* a (PI))) (* b (PI)))
(/ 1/2 a)
(/ (+ 1/2 (* -1/2 (/ a b))) a)
(/ (+ 1/2 (* -1/2 (/ a b))) a)
(/ (+ 1/2 (* -1/2 (/ a b))) a)
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* a (pow b 3))
(* a (+ (* a (* b (+ b (* -1 b)))) (pow b 3)))
(* a (+ (* a (+ (* -1 (* a b)) (* b (+ b (* -1 b))))) (pow b 3)))
(* a (+ (* a (+ (* -1 (* a b)) (* b (+ b (* -1 b))))) (pow b 3)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(* -1/2 (/ (PI) (* a b)))
(/ (+ (* -1/2 (/ (PI) b)) (* 1/2 (/ (- (PI) (* -1 (PI))) a))) a)
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* b (- (PI) (* -1 (PI)))) (pow a 2))) (* 1/2 (/ (- (PI) (* -1 (PI))) a)))) a)
(/ (+ (* -1/2 (/ (PI) b)) (+ (* -1/2 (/ (* b (- (PI) (* -1 (PI)))) (pow a 2))) (+ (* 1/2 (/ (* (pow b 2) (- (PI) (* -1 (PI)))) (pow a 3))) (* 1/2 (/ (- (PI) (* -1 (PI))) a))))) a)
(/ (PI) a)
(/ (+ (PI) (* -1 (/ (* b (PI)) a))) a)
(/ (- (+ (PI) (/ (* (pow b 2) (PI)) (pow a 2))) (/ (* b (PI)) a)) a)
(/ (- (+ (PI) (* -1 (/ (* (pow b 3) (PI)) (pow a 3)))) (+ (* -1 (/ (* (pow b 2) (PI)) (pow a 2))) (/ (* b (PI)) a))) a)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(* -1/2 (* a (PI)))
(* a (+ (* -1/2 (PI)) (* 1/2 (/ (* b (PI)) a))))
(* a (+ (* -1/2 (PI)) (* 1/2 (/ (* b (PI)) a))))
(* a (+ (* -1/2 (PI)) (* 1/2 (/ (* b (PI)) a))))
(* -1 a)
(* a (- (/ b a) 1))
(* a (- (/ b a) 1))
(* a (- (/ b a) 1))
(/ (PI) a)
(/ (+ (PI) (* -1 (/ (* b (PI)) a))) a)
(/ (- (+ (PI) (/ (* (pow b 2) (PI)) (pow a 2))) (/ (* b (PI)) a)) a)
(/ (- (+ (PI) (* -1 (/ (* (pow b 3) (PI)) (pow a 3)))) (+ (* -1 (/ (* (pow b 2) (PI)) (pow a 2))) (/ (* b (PI)) a))) a)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2))))) (pow a 2))
(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(* -1 (* a (PI)))
(* a (+ (* -1 (PI)) (/ (* b (PI)) a)))
(* a (+ (* -1 (PI)) (/ (* b (PI)) a)))
(* a (+ (* -1 (PI)) (/ (* b (PI)) a)))
(/ -1/2 b)
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* -1 (* (pow a 3) b))
(* (pow a 3) (+ (* -1 b) (/ (* b (+ b (* -1 b))) a)))
(* (pow a 3) (+ (* -1 b) (+ (/ (* b (+ b (* -1 b))) a) (/ (pow b 3) (pow a 2)))))
(* (pow a 3) (+ (* -1 b) (+ (/ (* b (+ b (* -1 b))) a) (/ (pow b 3) (pow a 2)))))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* -1/2 (/ (PI) (* a b)))
(* -1 (/ (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (- (* -1 (PI)) (PI)) a))) a))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (- (* -1 (PI)) (PI))) (* 1/2 (/ (* b (- (* -1 (PI)) (PI))) a))) a)) (* 1/2 (/ (PI) b))) a))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* b (- (* -1 (PI)) (PI)))) (* 1/2 (/ (* (pow b 2) (- (* -1 (PI)) (PI))) a))) a)) (* -1/2 (- (* -1 (PI)) (PI)))) a)) (* 1/2 (/ (PI) b))) a))
(/ (PI) a)
(* -1 (/ (+ (* -1 (PI)) (/ (* b (PI)) a)) a))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (/ (* (pow b 2) (PI)) a) (* b (PI))) a))) a))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow b 3) (PI)) a) (* (pow b 2) (PI))) a)) (* b (PI))) a))) a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* -1/2 (* a (PI)))
(* -1 (* a (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI)))))
(* -1 (* a (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI)))))
(* -1 (* a (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI)))))
(* -1 a)
(* -1 (* a (+ 1 (* -1 (/ b a)))))
(* -1 (* a (+ 1 (* -1 (/ b a)))))
(* -1 (* a (+ 1 (* -1 (/ b a)))))
(/ (PI) a)
(* -1 (/ (+ (* -1 (PI)) (/ (* b (PI)) a)) a))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (/ (* (pow b 2) (PI)) a) (* b (PI))) a))) a))
(* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow b 3) (PI)) a) (* (pow b 2) (PI))) a)) (* b (PI))) a))) a))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(* -1 (* a (PI)))
(* -1 (* a (+ (PI) (* -1 (/ (* b (PI)) a)))))
(* -1 (* a (+ (PI) (* -1 (/ (* b (PI)) a)))))
(* -1 (* a (+ (PI) (* -1 (/ (* b (PI)) a)))))
(/ -1/2 b)
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(- (* 1/2 (/ 1 a)) (* 1/2 (/ 1 b)))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* a b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* -1 (* (pow a 3) b))
(* -1 (* (pow a 3) (+ b (/ (* b (+ b (* -1 b))) a))))
(* -1 (* (pow a 3) (+ b (* -1 (/ (+ (* -1 (* b (+ b (* -1 b)))) (/ (pow b 3) a)) a)))))
(* -1 (* (pow a 3) (+ b (* -1 (/ (+ (* -1 (* b (+ b (* -1 b)))) (/ (pow b 3) a)) a)))))

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

rewrite296.0ms (3.4%)

Memory

-9.2MiB live, 151.1MiB allocated

Rules

5 398×	`lower-/.f32`
5 378×	`lower-/.f64`
4 030×	`lower-*.f32`
4 002×	`lower-*.f64`
2 234×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	234
0	72	222
1	321	182
2	3038	182
0	8709	182

Stop Event

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

Counts

22 → 1 712

Calls

Call 1

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

Outputs
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eval579.0ms (6.6%)

Memory: -0.5MiB live, 542.6MiB allocated
Compiler: Compiled 62 505 to 5 381 computations (91.4% saved)

prune106.0ms (1.2%)

Memory

-27.9MiB live, 272.9MiB allocated

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	2 781	10	2 791
Fresh	10	4	14
Picked	4	1	5
Done	0	1	1
Total	2 795	16	2 811

Accuracy

100.0%

Counts

2 811 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b)))
	95.6%	(/.f64 (/.f64 #s(literal 1/2 binary64) b) (*.f64 (/.f64 (+.f64 a b) (PI.f64)) a))
	69.8%	(/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) #s(approx ( (/ (/ 1/2 b) a) (- b a)) (/.f64 #s(literal 1/2 binary64) a))) (-.f64 b a))
	99.6%	(/.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 1/2 binary64) b) a)) (+.f64 a b))
▶	95.7%	(/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a)))
	99.4%	(/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (+.f64 a b) (*.f64 a b)))
	65.1%	(/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) b)) (.f64 #s(literal 2 binary64) (.f64 a b)))
▶	63.2%	(/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
	99.3%	(/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (+.f64 a b) (PI.f64)) (.f64 a b)))
▶	65.1%	#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64)))
	63.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 b a)) a))
✓	59.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)))
	59.6%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64)))
	62.9%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) a)) #s(literal 1/2 binary64)))
✓	59.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))
▶	62.9%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a))))

Compiler

Compiled 326 to 280 computations (14.1% saved)

simplify113.0ms (1.3%)

Memory

33.7MiB live, 225.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (+.f64 a b) (neg.f64 a))
cost-diff	0	(/.f64 #s(literal -1/2 binary64) b)
cost-diff	0	(PI.f64)
cost-diff	0	(*.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) a)
cost-diff	0	#s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a))
cost-diff	0	(/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) (.f64 (.f64 b a) b))
cost-diff	0	(.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))
cost-diff	0	(PI.f64)
cost-diff	0	(.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a)))
cost-diff	0	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a))))
cost-diff	0	(PI.f64)
cost-diff	0	(+.f64 a b)
cost-diff	0	(/.f64 (+.f64 a b) (PI.f64))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64)))

Rules

4 744×	`lower-*.f32`
4 726×	`lower-*.f64`
3 548×	`lower-/.f32`
3 530×	`lower-/.f64`
3 048×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	247
0	76	248
1	167	222
2	481	216
3	1783	208
4	5318	208
0	8543	208

Stop Event

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

Calls

Call 1

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

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

localize115.0ms (1.3%)

Memory

19.2MiB live, 290.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(PI.f64)
accuracy	0.015625	(*.f64 (+.f64 a b) (neg.f64 a))
accuracy	0.328125	(*.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b))
accuracy	2.6637297807986466	(/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a)))
accuracy	0	(PI.f64)
accuracy	0.1484375	(/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
accuracy	0.28125	(/.f64 (PI.f64) a)
accuracy	33.829778147243786	#s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a))
accuracy	0	(PI.f64)
accuracy	0.11328125	(.f64 (.f64 b a) b)
accuracy	0.15360128162065376	(/.f64 (PI.f64) (.f64 (.f64 b a) b))
accuracy	22.26146987704615	#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64)))
accuracy	0.11328125	(.f64 (.f64 a b) a)
accuracy	0.19140625	(.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a)))
accuracy	0.2993155455788509	(/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))
accuracy	23.430333761737135	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a))))
accuracy	0	(PI.f64)
accuracy	0.1484375	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b)))
accuracy	0.2421875	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64)))
accuracy	0.2734375	(/.f64 (+.f64 a b) (PI.f64))

Samples

89.0ms

256×

valid

Compiler

Compiled 221 to 48 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-div: 30.0ms (46.5% of total)

ival-mult: 26.0ms (40.3% of total)

ival-add: 3.0ms (4.6% of total)

ival-sub: 3.0ms (4.6% of total)

ival-pi: 1.0ms (1.5% of total)

ival-neg: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series40.0ms (0.5%)

Memory

-13.8MiB live, 96.1MiB allocated

Counts

20 → 420

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 a b) (PI.f64)) (patch (/.f64 (+.f64 a b) (PI.f64)) #<representation binary64>) () ())
#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())
#s(alt (PI.f64) (patch (PI.f64) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a)))) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) (patch (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (PI.f64) (.f64 (.f64 b a) b)) (patch (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (patch #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) #<representation binary64>) () ())
#s(alt (/.f64 (PI.f64) a) (patch (/.f64 (PI.f64) a) #<representation binary64>) () ())
#s(alt (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (patch (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/2 binary64) b) (patch (/.f64 #s(literal -1/2 binary64) b) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 a b) (neg.f64 a)) (patch (.f64 (+.f64 a b) (neg.f64 a)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 a b) a) (patch (.f64 (.f64 a b) a) #<representation binary64>) () ())
#s(alt (.f64 (.f64 b a) b) (patch (.f64 (.f64 b a) b) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) (patch (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) #<representation binary64>) () ())

Outputs
#s(alt (/ (PI) a) (taylor 0 b) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* b (PI)) (pow a 2))) (/ (PI) a)) (taylor 0 b) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (+ (* b (- (/ (* b (PI)) (pow a 3)) (/ (PI) (pow a 2)))) (/ (PI) a)) (taylor 0 b) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 4))) (* -1 (/ (PI) (pow a 3))))) (/ (PI) (pow a 2)))) (/ (PI) a)) (taylor 0 b) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) #<representation binary64>) () ())) ())
#s(alt (/ a (PI)) (taylor 0 b) (#s(alt (/.f64 (+.f64 a b) (PI.f64)) (patch (/.f64 (+.f64 a b) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (/ a (PI)) (/ b (PI))) (taylor 0 b) (#s(alt (/.f64 (+.f64 a b) (PI.f64)) (patch (/.f64 (+.f64 a b) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (/ a (PI)) (/ b (PI))) (taylor 0 b) (#s(alt (/.f64 (+.f64 a b) (PI.f64)) (patch (/.f64 (+.f64 a b) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt (+ (/ a (PI)) (/ b (PI))) (taylor 0 b) (#s(alt (/.f64 (+.f64 a b) (PI.f64)) (patch (/.f64 (+.f64 a b) (PI.f64)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b) (taylor 0 b) (#s(alt #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) (patch #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) (patch (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) (patch (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) (patch (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) (patch (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* (pow a 2) b)) (taylor 0 b) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* (pow a 2) b)) (taylor 0 b) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* (pow a 2) b)) (taylor 0 b) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (* (pow a 2) b)) (taylor 0 b) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) (patch (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor 0 b) (#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b) (taylor 0 b) (#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b) (taylor 0 b) (#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b) (taylor 0 b) (#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* a (pow b 2)))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* a (pow b 2)))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* a (pow b 2)))) (taylor 0 b) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt #s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64))) (patch #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* a (pow b 2)))) (taylor -inf a) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* a (pow b 2)))) (taylor -inf a) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* a (pow b 2)))) (taylor -inf a) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* a (pow b 2)))) (taylor -inf a) (#s(alt (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) (patch (.f64 (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (* a (pow b 2))) (taylor -inf a) (#s(alt (/.f64 (PI.f64) (.f64 (.f64 b a) b)) (patch (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (* a (pow b 2))) (taylor -inf a) (#s(alt (/.f64 (PI.f64) (.f64 (.f64 b a) b)) (patch (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (* a (pow b 2))) (taylor -inf a) (#s(alt (/.f64 (PI.f64) (.f64 (.f64 b a) b)) (patch (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #<representation binary64>) () ())) ())
#s(alt (/ (PI) (* a (pow b 2))) (taylor -inf a) (#s(alt (/.f64 (PI.f64) (.f64 (.f64 b a) b)) (patch (/.f64 (PI.f64) (.f64 (.f64 b a) b)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ (PI) a) (taylor -inf a) (#s(alt #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (patch #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (PI)) (/ (* b (PI)) a)) a)) (taylor -inf a) (#s(alt #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (patch #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (/ (* (pow b 2) (PI)) a) (* b (PI))) a))) a)) (taylor -inf a) (#s(alt #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (patch #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (PI)) (* -1 (/ (- (* -1 (/ (- (/ (* (pow b 3) (PI)) a) (* (pow b 2) (PI))) a)) (* b (PI))) a))) a)) (taylor -inf a) (#s(alt #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (patch #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) #<representation binary64>) () ())) ())
#s(alt (/ (PI) a) (taylor -inf a) (#s(alt (/.f64 (PI.f64) a) (patch (/.f64 (PI.f64) a) #<representation binary64>) () ())) ())
#s(alt (/ (PI) a) (taylor -inf a) (#s(alt (/.f64 (PI.f64) a) (patch (/.f64 (PI.f64) a) #<representation binary64>) () ())) ())
#s(alt (/ (PI) a) (taylor -inf a) (#s(alt (/.f64 (PI.f64) a) (patch (/.f64 (PI.f64) a) #<representation binary64>) () ())) ())
#s(alt (/ (PI) a) (taylor -inf a) (#s(alt (/.f64 (PI.f64) a) (patch (/.f64 (PI.f64) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow a 2)) (taylor -inf a) (#s(alt (.f64 (+.f64 a b) (neg.f64 a)) (patch (.f64 (+.f64 a b) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (* -1 (/ b a)) 1)) (taylor -inf a) (#s(alt (.f64 (+.f64 a b) (neg.f64 a)) (patch (.f64 (+.f64 a b) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (* -1 (/ b a)) 1)) (taylor -inf a) (#s(alt (.f64 (+.f64 a b) (neg.f64 a)) (patch (.f64 (+.f64 a b) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (- (* -1 (/ b a)) 1)) (taylor -inf a) (#s(alt (.f64 (+.f64 a b) (neg.f64 a)) (patch (.f64 (+.f64 a b) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) b) (taylor -inf a) (#s(alt (.f64 (.f64 a b) a) (patch (.f64 (.f64 a b) a) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) b) (taylor -inf a) (#s(alt (.f64 (.f64 a b) a) (patch (.f64 (.f64 a b) a) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) b) (taylor -inf a) (#s(alt (.f64 (.f64 a b) a) (patch (.f64 (.f64 a b) a) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) b) (taylor -inf a) (#s(alt (.f64 (.f64 a b) a) (patch (.f64 (.f64 a b) a) #<representation binary64>) () ())) ())
#s(alt (* a (pow b 2)) (taylor -inf a) (#s(alt (.f64 (.f64 b a) b) (patch (.f64 (.f64 b a) b) #<representation binary64>) () ())) ())
#s(alt (* a (pow b 2)) (taylor -inf a) (#s(alt (.f64 (.f64 b a) b) (patch (.f64 (.f64 b a) b) #<representation binary64>) () ())) ())
#s(alt (* a (pow b 2)) (taylor -inf a) (#s(alt (.f64 (.f64 b a) b) (patch (.f64 (.f64 b a) b) #<representation binary64>) () ())) ())
#s(alt (* a (pow b 2)) (taylor -inf a) (#s(alt (.f64 (.f64 b a) b) (patch (.f64 (.f64 b a) b) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ (PI) (* (pow a 2) b))) (taylor -inf a) (#s(alt (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) (patch (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) (patch (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) (patch (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2)) (taylor -inf a) (#s(alt (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) (patch (/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	a	@	0	((/ 1 (/ (+ a b) (PI))) (/ (+ a b) (PI)) (+ a b) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a b) a))) (/ 1/2 (* (* a b) a)) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* (/ (PI) (* (* b a) b)) 1/2) (/ (PI) (* (* b a) b)) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (PI) a) (* (PI) (/ -1/2 b)) (/ -1/2 b) (* (+ a b) (neg a)) (/ (/ 1 (/ (+ a b) (PI))) (* 2 (* a b))) (* (* a b) a) (* (* b a) b) (/ (* (PI) (/ -1/2 b)) (* (+ a b) (neg a))))
3.0ms	b	@	-inf	((/ 1 (/ (+ a b) (PI))) (/ (+ a b) (PI)) (+ a b) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a b) a))) (/ 1/2 (* (* a b) a)) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* (/ (PI) (* (* b a) b)) 1/2) (/ (PI) (* (* b a) b)) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (PI) a) (* (PI) (/ -1/2 b)) (/ -1/2 b) (* (+ a b) (neg a)) (/ (/ 1 (/ (+ a b) (PI))) (* 2 (* a b))) (* (* a b) a) (* (* b a) b) (/ (* (PI) (/ -1/2 b)) (* (+ a b) (neg a))))
3.0ms	b	@	0	((/ 1 (/ (+ a b) (PI))) (/ (+ a b) (PI)) (+ a b) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a b) a))) (/ 1/2 (* (* a b) a)) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* (/ (PI) (* (* b a) b)) 1/2) (/ (PI) (* (* b a) b)) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (PI) a) (* (PI) (/ -1/2 b)) (/ -1/2 b) (* (+ a b) (neg a)) (/ (/ 1 (/ (+ a b) (PI))) (* 2 (* a b))) (* (* a b) a) (* (* b a) b) (/ (* (PI) (/ -1/2 b)) (* (+ a b) (neg a))))
3.0ms	a	@	-inf	((/ 1 (/ (+ a b) (PI))) (/ (+ a b) (PI)) (+ a b) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a b) a))) (/ 1/2 (* (* a b) a)) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* (/ (PI) (* (* b a) b)) 1/2) (/ (PI) (* (* b a) b)) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (PI) a) (* (PI) (/ -1/2 b)) (/ -1/2 b) (* (+ a b) (neg a)) (/ (/ 1 (/ (+ a b) (PI))) (* 2 (* a b))) (* (* a b) a) (* (* b a) b) (/ (* (PI) (/ -1/2 b)) (* (+ a b) (neg a))))
3.0ms	b	@	inf	((/ 1 (/ (+ a b) (PI))) (/ (+ a b) (PI)) (+ a b) (PI) (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (* (PI) (/ 1/2 (* (* a b) a))) (/ 1/2 (* (* a b) a)) (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (* (/ (PI) (* (* b a) b)) 1/2) (/ (PI) (* (* b a) b)) (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/ (PI) a) (* (PI) (/ -1/2 b)) (/ -1/2 b) (* (+ a b) (neg a)) (/ (/ 1 (/ (+ a b) (PI))) (* 2 (* a b))) (* (* a b) a) (* (* b a) b) (/ (* (PI) (/ -1/2 b)) (* (+ a b) (neg a))))

simplify229.0ms (2.6%)

Memory

-33.3MiB live, 226.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 734×	`lower-fma.f64`
11 734×	`lower-fma.f32`
4 706×	`lower-*.f64`
4 706×	`lower-*.f32`
2 158×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	288	4900
1	827	4748
2	2241	4648
3	6513	4640
0	8341	4456

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 414

Calls

Call 1

Inputs
(/ (PI) a)
(+ (* -1 (/ (* b (PI)) (pow a 2))) (/ (PI) a))
(+ (* b (- (/ (* b (PI)) (pow a 3)) (/ (PI) (pow a 2)))) (/ (PI) a))
(+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 4))) (* -1 (/ (PI) (pow a 3))))) (/ (PI) (pow a 2)))) (/ (PI) a))
(/ a (PI))
(+ (/ a (PI)) (/ b (PI)))
(+ (/ a (PI)) (/ b (PI)))
(+ (/ a (PI)) (/ b (PI)))
a
(+ a b)
(+ a b)
(+ a b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(/ 1/2 (* (pow a 2) b))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* 1/2 (/ (PI) (* a (pow b 2))))
(* 1/2 (/ (PI) (* a (pow b 2))))
(* 1/2 (/ (PI) (* a (pow b 2))))
(* 1/2 (/ (PI) (* a (pow b 2))))
(/ (PI) (* a (pow b 2)))
(/ (PI) (* a (pow b 2)))
(/ (PI) (* a (pow b 2)))
(/ (PI) (* a (pow b 2)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(/ (PI) a)
(+ (* -1 (/ (* b (PI)) (pow a 2))) (/ (PI) a))
(+ (* b (- (/ (* b (PI)) (pow a 3)) (/ (PI) (pow a 2)))) (/ (PI) a))
(+ (* b (- (* b (- (* -1 (/ (* b (PI)) (pow a 4))) (* -1 (/ (PI) (pow a 3))))) (/ (PI) (pow a 2)))) (/ (PI) a))
(* -1/2 (/ (PI) b))
(* -1/2 (/ (PI) b))
(* -1/2 (/ (PI) b))
(* -1/2 (/ (PI) b))
(/ -1/2 b)
(/ -1/2 b)
(/ -1/2 b)
(/ -1/2 b)
(* -1 (pow a 2))
(+ (* -1 (* a b)) (* -1 (pow a 2)))
(+ (* -1 (* a b)) (* -1 (pow a 2)))
(+ (* -1 (* a b)) (* -1 (pow a 2)))
(* 1/2 (/ (PI) (* (pow a 2) b)))
(/ (+ (* -1/2 (/ (* b (PI)) (pow a 3))) (* 1/2 (/ (PI) (pow a 2)))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* 1/2 (/ (* b (PI)) (pow a 4)))))) b)
(/ (+ (* 1/2 (/ (PI) (pow a 2))) (* b (+ (* -1/2 (/ (PI) (pow a 3))) (* b (+ (* -1/2 (/ (* b (PI)) (pow a 5))) (* 1/2 (/ (PI) (pow a 4)))))))) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* (pow a 2) b)
(* a (pow b 2))
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b
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b
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b
(+ a b)
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(* (pow a 2) b)
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(/ (+ (* 1/2 (/ (PI) (pow b 2))) (* a (+ (* -1/2 (/ (PI) (pow b 3))) (* a (+ (* -1/2 (/ (* a (PI)) (pow b 5))) (* 1/2 (/ (PI) (pow b 4)))))))) a)
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(/ a (PI))
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a
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(* (pow a 2) b)
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(/ (+ (* -1/2 (/ (PI) a)) (+ (* -1/2 (/ (* (pow b 2) (PI)) (pow a 3))) (+ (* 1/2 (/ (PI) b)) (* 1/2 (/ (* b (PI)) (pow a 2)))))) (pow a 2))
(/ (PI) a)
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(/ a (PI))
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(* -1 (* a (- (* -1 (/ b (* a (PI)))) (/ 1 (PI)))))
a
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(/ (+ (* -1/2 (/ (PI) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1/2 (/ (* b (PI)) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (* (pow b 2) (PI)) a)) (* 1/2 (* b (PI)))) a)) (* 1/2 (PI))) a)) (* 1/2 (/ (PI) b))) (pow a 2))

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

rewrite148.0ms (1.7%)

Memory

31.3MiB live, 225.7MiB allocated

Rules

5 266×	`lower-/.f32`
5 248×	`lower-/.f64`
3 500×	`lower-*.f32`
3 482×	`lower-*.f64`
1 758×	`frac-2neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	200
0	76	199
1	339	161
2	3002	161
0	8176	161

Stop Event

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

Counts

20 → 1 100

Calls

Call 1

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

Outputs
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eval275.0ms (3.1%)

Memory: -14.5MiB live, 458.7MiB allocated
Compiler: Compiled 33 091 to 3 851 computations (88.4% saved)

prune122.0ms (1.4%)

Memory

6.7MiB live, 207.4MiB allocated

Pruning

19 alts after pruning (14 fresh and 5 done)

	Pruned	Kept	Total
New	1 815	9	1 824
Fresh	4	5	9
Picked	2	3	5
Done	0	2	2
Total	1 821	19	1 840

Accuracy

100.0%

Counts

1 840 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.2%	(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ a b) (PI)) (/.f64 a (PI.f64)))) (.f64 #s(literal 2 binary64) (.f64 a b)))
	69.8%	(/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) #s(approx ( (/ (/ 1/2 b) a) (- b a)) (/.f64 #s(literal 1/2 binary64) a))) (-.f64 b a))
	99.6%	(/.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 1/2 binary64) b) a)) (+.f64 a b))
	99.6%	(/.f64 (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 b a))) (+.f64 b a))
	65.0%	(/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) #s(approx ( (+ a b) (neg a)) (*.f64 (neg.f64 b) a)))
	99.4%	(/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (+.f64 a b) (*.f64 a b)))
	65.1%	(/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) b)) (.f64 #s(literal 2 binary64) (.f64 a b)))
✓	63.2%	(/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
	99.3%	(/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (+.f64 a b) (PI.f64)) (.f64 a b)))
	59.6%	#s(approx (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64)))
	65.1%	#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (/.f64 (*.f64 (/.f64 (/.f64 (PI.f64) a) b) #s(literal 1/2 binary64)) b))
	65.0%	#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (/.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 b a) b) (PI.f64))))
✓	65.1%	#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64)))
	65.0%	#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 b a) b))))
✓	59.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)))
	63.2%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 b a)) (PI.f64)) a))
	62.9%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (*.f64 b a) a)))
✓	59.3%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))
✓	62.9%	#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a))))

Compiler

Compiled 999 to 395 computations (60.5% saved)

regimes46.0ms (0.5%)

Memory

22.2MiB live, 101.7MiB allocated

Counts

52 → 1

Calls

Call 1

Inputs
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b))))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a))))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 b (*.f64 a a))) #s(literal 1/2 binary64)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) a)) #s(literal 1/2 binary64)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (*.f64 b a) a)))
#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 b a) b))))
#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64)))
#s(approx (/ (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (+.f64 a b) (*.f64 a b)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 b a)) (PI.f64)) a))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (/.f64 (PI.f64) b) #s(literal 1/2 binary64)) (.f64 a a)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 b a)) a))
#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (/.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 b a) b) (PI.f64))))
(/.f64 #s(approx (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 #s(approx (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (/.f64 (PI.f64) b)) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 #s(approx (/ (* (- b a) (PI)) (* (- b a) (+ b a))) (/.f64 (PI.f64) b)) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) #s(approx ( (+ a b) (neg a)) (*.f64 (neg.f64 b) a)))
(/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (+.f64 a b) (PI.f64)) (.f64 a b)))
(/.f64 (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 b a))) (+.f64 b a))
(/.f64 (.f64 (PI.f64) (/.f64 #s(literal -1/2 binary64) b)) (.f64 (+.f64 a b) (neg.f64 a)))
#s(approx (/ (* (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (/.f64 (*.f64 (/.f64 (/.f64 (PI.f64) a) b) #s(literal 1/2 binary64)) b))
(/.f64 (*.f64 (PI.f64) (/.f64 (/.f64 #s(literal 1/2 binary64) b) a)) (+.f64 a b))
(/.f64 (/.f64 #s(literal 1/2 binary64) b) (*.f64 (/.f64 (+.f64 a b) (PI.f64)) a))
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ a b) (PI)) (/.f64 a (PI.f64)))) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) #s(approx ( (/ (/ 1/2 b) a) (- b a)) (/.f64 #s(literal 1/2 binary64) a))) (-.f64 b a))
(/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (.f64 (.f64 a b) #s(literal 2 binary64)) (*.f64 (+.f64 a b) (-.f64 b a))))
(/.f64 (.f64 (-.f64 b a) (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (.f64 b a) (*.f64 (-.f64 b a) (+.f64 b a))))
(/.f64 (.f64 (/.f64 (PI.f64) #s(approx ( (+ a b) (- b a)) (.f64 b b))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (*.f64 a b)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 #s(literal -1/2 binary64) b))) (.f64 b b)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (/.f64 (.f64 (PI.f64) (+.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 #s(literal -1/2 binary64) a))) (.f64 a a)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) (-.f64 b a)))) (.f64 (.f64 (fma.f64 (neg.f64 b) b (*.f64 a a)) a) b))
(.f64 (.f64 (-.f64 b a) (PI.f64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 a b) #s(literal 2 binary64)) (.f64 (+.f64 a b) (-.f64 b a)))))
(/.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (-.f64 b a)) (.f64 (-.f64 b a) (.f64 (.f64 b a) #s(literal 2 binary64))))
(/.f64 (/.f64 (.f64 (-.f64 b a) (PI.f64)) (.f64 (-.f64 b a) (+.f64 b a))) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 (.f64 (.f64 (-.f64 b a) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))) (.f64 a b))
(.f64 (.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 a b))))
(.f64 #s(approx ( (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (*.f64 (/.f64 (/.f64 (PI.f64) b) b) #s(literal 1/2 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))
(.f64 (/.f64 (PI.f64) (.f64 (+.f64 a b) (-.f64 b a))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (-.f64 b a) a) b)))
(.f64 (.f64 (/.f64 (/.f64 (-.f64 b a) a) b) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)))
(/.f64 (.f64 (/.f64 (PI.f64) (+.f64 b a)) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) a) (-.f64 b a))) (-.f64 b a))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 b a) #s(literal 2 binary64)) (*.f64 (/.f64 (/.f64 (PI.f64) (-.f64 b a)) (+.f64 b a)) (-.f64 b a))))
(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))
(fma.f64 (.f64 (PI.f64) (pow.f64 (.f64 (+.f64 b a) a) #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (*.f64 a a)))))
(fma.f64 (.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (PI.f64) (+.f64 a b))) (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (PI.f64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 b) b (.f64 a a)))))
(fma.f64 (/.f64 (PI.f64) (+.f64 a b)) (.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (pow.f64 a #s(literal -1 binary64))) (/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 a b)) (/.f64 (PI.f64) (-.f64 b a))) (neg.f64 b)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (.f64 (pow.f64 (/.f64 (*.f64 b a) (sqrt.f64 (PI.f64))) #s(literal -1 binary64)) (pow.f64 (/.f64 a (sqrt.f64 (PI.f64))) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 a b) (.f64 a b)) (.f64 (/.f64 (PI.f64) (+.f64 a b)) (*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal -2 binary64)) (pow.f64 b #s(literal -2 binary64)))))))
(.f64 (.f64 (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (*.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))

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

Calls

3 calls:

15.0ms	a
15.0ms	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))
14.0ms	b

Results

Accuracy	Segments	Branch
99.7%	1	`a`
99.7%	1	`b`
99.7%	1	`(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))`

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes30.0ms (0.3%)

Memory

-6.3MiB live, 70.7MiB allocated

Counts

32 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	b
9.0ms	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))
9.0ms	a

Results

Accuracy	Segments	Branch
99.6%	1	`a`
99.6%	1	`b`
99.6%	1	`(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))`

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes24.0ms (0.3%)

Memory

-22.8MiB live, 35.0MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	b
6.0ms	a
5.0ms	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))

Results

Accuracy	Segments	Branch
99.4%	1	`a`
99.4%	1	`b`
99.4%	1	`(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))`

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes11.0ms (0.1%)

Memory

18.4MiB live, 18.5MiB allocated

Counts

9 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

3.0ms	a
3.0ms	b
3.0ms	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))

Results

Accuracy	Segments	Branch
90.7%	2	`a`
88.8%	2	`b`
68.5%	2	`(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))`

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes9.0ms (0.1%)

Memory

-30.7MiB live, 8.5MiB allocated

Counts

7 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
90.7%	2	`a`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes6.0ms (0.1%)

Memory

14.7MiB live, 14.7MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

3.0ms	a
3.0ms	b

Results

Accuracy	Segments	Branch
83.3%	2	`b`
85.3%	2	`a`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes7.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	b
2.0ms	a
2.0ms	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))

Results

Accuracy	Segments	Branch
62.9%	1	`(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))`
62.9%	1	`b`
62.9%	1	`a`

Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes6.0ms (0.1%)

Memory

-26.0MiB live, 12.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	a
1.0ms	b
1.0ms	(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))

Results

Accuracy	Segments	Branch
59.3%	1	`b`
59.3%	1	`(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b)))`
59.3%	1	`a`

Compiler

Compiled 23 to 19 computations (17.4% saved)

bsearch20.0ms (0.2%)

Memory

9.5MiB live, 46.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	-0.13818124328178416	-0.00010732115302233544

Samples

13.0ms

128×

valid

Compiler

Compiled 184 to 180 computations (2.2% saved)

Precisions

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

ival-mult: 5.0ms (50.2% of total)

ival-div: 3.0ms (30.1% of total)

ival-pi: 1.0ms (10% of total)

ival-sub: 1.0ms (10% of total)

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

exact: 0.0ms (0% of total)

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

bsearch22.0ms (0.2%)

Memory

1.1MiB live, 40.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	-1.1876857329389035e-39	-5.971134710004489e-42

Samples

15.0ms

112×

valid

Compiler

Compiled 164 to 160 computations (2.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 3.0ms (44.7% of total)

ival-mult: 2.0ms (29.8% of total)

ival-sub: 1.0ms (14.9% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.1876857329389035e-39	-5.971134710004489e-42

Compiler

Compiled 164 to 160 computations (2.4% saved)

simplify27.0ms (0.3%)

Memory

-7.0MiB live, 69.1MiB allocated

Algorithm

1×	egg-herbie

Rules

28×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	291
1	86	291

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 b a))) (+.f64 b a))
(/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (+.f64 a b) (*.f64 a b)))
(if (<=.f64 a #s(literal -7566047373982433/72057594037927936 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))))
(if (<=.f64 a #s(literal -3432790011539591/3064991081731777716716694054300618367237478244367204352 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 b a) b)))))
(if (<=.f64 a #s(literal -3432790011539591/3064991081731777716716694054300618367237478244367204352 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64))))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a))))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b))))

Outputs
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a b) (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 a b)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 b a) (PI.f64))) (.f64 (.f64 b a) #s(literal 2 binary64)))
(/.f64 (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 b a))) (+.f64 b a))
(/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 b a)) (PI.f64)) (+.f64 b a))
(/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (+.f64 a b) (*.f64 a b)))
(/.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (*.f64 b a) (+.f64 b a)))
(if (<=.f64 a #s(literal -7566047373982433/72057594037927936 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))))
(if (<=.f64 a #s(literal -7566047373982433/72057594037927936 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 b a) a)) (PI.f64))) #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b a) b)) #s(literal 1/2 binary64))))
(if (<=.f64 a #s(literal -3432790011539591/3064991081731777716716694054300618367237478244367204352 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 b a) b)))))
(if (<=.f64 a #s(literal -3432790011539591/3064991081731777716716694054300618367237478244367204352 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 b a) a)) (PI.f64))) #s(approx (/ ( (/ (PI) (* (+ a b) (- b a))) (- b a)) (* 2 (* a b))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 b a) b)) (PI.f64))))
(if (<=.f64 a #s(literal -3432790011539591/3064991081731777716716694054300618367237478244367204352 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 a b) a)))) #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64))))
(if (<=.f64 a #s(literal -3432790011539591/3064991081731777716716694054300618367237478244367204352 binary64)) #s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 b a) a)) (PI.f64))) #s(approx ( (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 (PI.f64) (.f64 (*.f64 b b) a)) #s(literal 1/2 binary64))))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a b) a))))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 b a) a)) (PI.f64)))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (PI.f64) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b))))
#s(approx (* (* (/ (PI) 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 a a) b)) (PI.f64)))

soundness1.4s (16.1%)

Memory

25.2MiB live, 1 023.7MiB allocated

Rules

26 648×	`lower-fma.f64`
26 648×	`lower-fma.f32`
12 618×	`lower-fma.f64`
12 618×	`lower-fma.f32`
6 700×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	291	1696
1	768	1666
2	2293	1612
3	6395	1612
0	8352	1525
0	45	234
0	72	222
1	321	182
2	3038	182
0	8709	182
0	834	7482
1	2519	6825
0	9168	6506
0	15	53
0	26	49
1	124	49
2	1123	49
0	9193	49
0	53	200
0	76	199
1	339	161
2	3002	161
0	8176	161
0	51	271
0	84	263
1	372	254
2	3525	254
0	8135	254

Stop Event

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

Compiler

Compiled 661 to 392 computations (40.7% saved)

preprocess126.0ms (1.4%)

Memory: -20.5MiB live, 187.6MiB allocated
Remove: (sort a b)
Compiler: Compiled 452 to 254 computations (43.8% saved)

end0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

start0.0ms (0%)

analyze90.0ms (1%)

sample1.4s (16%)

explain164.0ms (1.9%)

preprocess156.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify163.0ms (1.9%)

localize61.0ms (0.7%)

series31.0ms (0.4%)

simplify204.0ms (2.3%)

rewrite204.0ms (2.3%)

eval93.0ms (1.1%)

prune29.0ms (0.3%)

simplify133.0ms (1.5%)

localize142.0ms (1.6%)

series71.0ms (0.8%)

simplify280.0ms (3.2%)

rewrite171.0ms (1.9%)

eval574.0ms (6.5%)

prune175.0ms (2%)

simplify221.0ms (2.5%)

localize165.0ms (1.9%)

series77.0ms (0.9%)

simplify396.0ms (4.5%)

rewrite296.0ms (3.4%)

eval579.0ms (6.6%)

prune106.0ms (1.2%)

simplify113.0ms (1.3%)

localize115.0ms (1.3%)

series40.0ms (0.5%)

simplify229.0ms (2.6%)

rewrite148.0ms (1.7%)

eval275.0ms (3.1%)

prune122.0ms (1.4%)

regimes46.0ms (0.5%)

regimes30.0ms (0.3%)

regimes24.0ms (0.3%)

regimes11.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch20.0ms (0.2%)

bsearch22.0ms (0.2%)

bsearch1.0ms (0%)

simplify27.0ms (0.3%)

soundness1.4s (16.1%)

preprocess126.0ms (1.4%)

end0.0ms (0%)

Profiling