Metrics for Data.Colour.CIE:cieLABView from colour-2.3.3, A

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 11 to 10 computations (9.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

const: 0.0ms (0% of total)

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

sample771.0ms (11.4%)

Results

524.0ms	8252×	0	valid
0.0ms	3×	1	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 308.0ms

ival-div: 147.0ms (47.8% of total)

ival-add: 71.0ms (23.1% of total)

ival-mult: 66.0ms (21.5% of total)

const: 20.0ms (6.5% of total)

backward-pass: 3.0ms (1% of total)

Bogosity

preprocess24.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

148×	`fmsub-define`
148×	`fnmadd-define`
144×	`fnmsub-define`
94×	`fmm-def`
64×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	15
1	32	13
2	67	12
3	153	12
4	262	12
5	385	12
6	477	12
7	501	12
8	515	12
9	519	12
0	11	4
1	14	4
2	15	4
0	15	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (* (/ 841 108) x) (/ 4 29))

Outputs
(+ (* (/ 841 108) x) (/ 4 29))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))

Call 2

Inputs
(+ (* (/ 841 108) x) (/ 4 29))
(+ (* (/ 841 108) (neg x)) (/ 4 29))
(neg (+ (* (/ 841 108) (neg x)) (/ 4 29)))

Outputs
(+ (* (/ 841 108) x) (/ 4 29))
(fnmsub x -841/108 -4/29)
(+ (* (/ 841 108) (neg x)) (/ 4 29))
(fnmsub 841/108 x -4/29)
(neg (+ (* (/ 841 108) (neg x)) (/ 4 29)))
(fnmsub x -841/108 4/29)

explain95.0ms (1.4%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`#s(literal 29 binary64)`
-	-	`(+.f64 (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) (/.f64 #s(literal 4 binary64) #s(literal 29 binary64)))`
-	-	`#s(literal 4 binary64)`
-	-	`(/.f64 #s(literal 841 binary64) #s(literal 108 binary64))`
-	-	`(/.f64 #s(literal 4 binary64) #s(literal 29 binary64))`
-	-	`#s(literal 841 binary64)`
-	-	`(*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x)`
-	-	`#s(literal 108 binary64)`

Results

57.0ms	510×	0	valid
1.0ms	2×	5	exit

Compiler

Compiled 64 to 29 computations (54.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-div: 13.0ms (59.8% of total)

ival-mult: 4.0ms (18.4% of total)

ival-add: 3.0ms (13.8% of total)

const: 1.0ms (4.6% of total)

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

eval0.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 841/108 binary64) x)
✓	cost-diff	0	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))

Rules

4×	`fma-lowering-fma.f32`
4×	`fma-define`
4×	`+-lowering-+.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	8	10
2	9	10
0	9	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* 841/108 x) 4/29)
(* 841/108 x)
841/108
x
4/29

Outputs
(+ (* 841/108 x) 4/29)
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
841/108
#s(literal 841/108 binary64)
x
4/29
#s(literal 4/29 binary64)

localize45.0ms (0.7%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)

Results

34.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 13 to 6 computations (53.8% saved)

Precisions

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

...c/correct-round.rkt:119:19: 8.0ms (64.8% of total)

ival-mult: 2.0ms (16.2% of total)

ival-add: 2.0ms (16.2% of total)

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

const: 0.0ms (0% of total)

series2.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (+ (* 841/108 x) 4/29)>
#<alt (* 841/108 x)>

Outputs
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* 841/108 x) 4/29)
0.0ms	x	@	-inf	(* 841/108 x)
0.0ms	x	@	inf	(* 841/108 x)
0.0ms	x	@	0	(* 841/108 x)
0.0ms	x	@	0	(+ (* 841/108 x) 4/29)

rewrite533.0ms (7.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4122×	`/-lowering-/.f32`
4122×	`/-lowering-/.f64`
3440×	`-lowering-.f32`
3440×	`-lowering-.f64`
1716×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	23	7
2	157	7
3	1416	7
0	8145	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 185

Calls

Call 1

Inputs
(+ (* 841/108 x) 4/29)
(* 841/108 x)

Outputs
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(+.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)))) #s(literal -1 binary64)))
(-.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(-.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64))) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))) (/.f64 (/.f64 #s(literal 4096/594823321 binary64) (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64))) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (/.f64 #s(literal 4096/594823321 binary64) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (/.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))) (/.f64 (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal 64/24389 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal 4/29 binary64))) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal 4/29 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (.f64 (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))) (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64)))) (/.f64 #s(literal 4096/594823321 binary64) (.f64 (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))) (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64)))))) (/.f64 #s(literal 4096/594823321 binary64) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64)))))))
(-.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64)))) (/.f64 #s(literal 256/707281 binary64) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))) (/.f64 (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))))) (+.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))) (+.f64 (/.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 (/.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 16/841 binary64)) #s(literal 29/4 binary64))) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 (/.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 16/841 binary64)) #s(literal 29/4 binary64)))))) (/.f64 (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 (/.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 16/841 binary64)) #s(literal 29/4 binary64)))) (+.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))) (+.f64 (/.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 (/.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 16/841 binary64)) #s(literal 29/4 binary64))) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 (/.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 16/841 binary64)) #s(literal 29/4 binary64)))))))
(-.f64 (/.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))) (/.f64 (/.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 (/.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 16/841 binary64)) #s(literal 29/4 binary64))) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))))
(fma.f64 #s(literal 841/108 binary64) x #s(literal 4/29 binary64))
(fma.f64 #s(literal 841/108 binary64) (/.f64 (.f64 #s(literal 841/108 binary64) (.f64 x x)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 x #s(literal 841/108 binary64) #s(literal 4/29 binary64))
(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 (.f64 #s(literal 841/108 binary64) x) (/.f64 (.f64 #s(literal 841/108 binary64) x) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 #s(literal 707281/11664 binary64) (/.f64 (.f64 x x) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 707281/11664 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 (.f64 #s(literal 841/108 binary64) (.f64 x x)) (/.f64 #s(literal 841/108 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
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(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) #s(literal -4096/594823321 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal 64/24389 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))))) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) #s(literal -4096/594823321 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 #s(literal -64/24389 binary64) (neg.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) #s(literal -4096/594823321 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))))) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal 4/29 binary64))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) #s(literal -4096/594823321 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))))) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64)) (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64)) (*.f64 x #s(literal 29/27 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal 64/24389 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 #s(literal -64/24389 binary64) (neg.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal 4/29 binary64))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal 64/24389 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 #s(literal -64/24389 binary64) (neg.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal 4/29 binary64))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
(exp.f64 (log.f64 (*.f64 #s(literal 841/108 binary64) x)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 841/108 binary64) x)) #s(literal 1 binary64)))
(pow.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 841/108 binary64) x)
(*.f64 #s(literal 841/108 binary64) (pow.f64 x #s(literal 1 binary64)))
(*.f64 x #s(literal 841/108 binary64))
(*.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal 841/108 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 #s(literal 841/108 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal 841/108 binary64))) (exp.f64 (log.f64 x)))

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

44×	`-lowering-.f32`
44×	`-lowering-.f64`
40×	`fma-define`
28×	`fma-lowering-fma.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	88
1	25	79
2	46	79
3	68	79
4	68	79
5	83	79
6	91	79
7	97	79
8	99	79
0	99	79

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)

Outputs
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)

eval23.0ms (0.3%)

Compiler: Compiled 6893 to 558 computations (91.9% saved)

prune56.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	197	12	209
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	197	13	210

Accuracy

100.0%

Counts

210 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
	99.7%	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
▶	68.1%	(/.f64 (-.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
	75.7%	(/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
	63.2%	(/.f64 (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64)) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))))
▶	75.7%	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
	63.3%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64))))
▶	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))))
	75.7%	(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
▶	75.7%	(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
	52.8%	(*.f64 #s(literal 841/108 binary64) x)
▶	48.3%	#s(literal 4/29 binary64)

Compiler

Compiled 394 to 279 computations (29.2% saved)

simplify214.0ms (3.1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(.f64 #s(literal 594823321/1259712 binary64) (.f64 x (*.f64 x x)))
✓	cost-diff	0	(-.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (*.f64 x x))) #s(literal -64/24389 binary64))
✓	cost-diff	0	(/.f64 (-.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
✓	cost-diff	128	(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
✓	cost-diff	0	(*.f64 #s(literal 841/108 binary64) x)
✓	cost-diff	0	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))))

Rules

2140×	`fma-lowering-fma.f32`
2140×	`fma-lowering-fma.f64`
1854×	`fmsub-define`
1746×	`fnmsub-define`
1566×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	160
1	76	149
2	153	149
3	268	149
4	400	149
5	645	149
6	1170	149
7	2051	149
8	3956	149
9	6891	149
0	8128	149

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (/ 1 (+ (* 841/108 x) 4/29)))
1
(/ 1 (+ (* 841/108 x) 4/29))
(+ (* 841/108 x) 4/29)
(* 841/108 x)
841/108
x
4/29
4/29
(/ (+ 16/841 (* -707281/11664 (* x x))) (+ 4/29 (* x -841/108)))
(+ 16/841 (* -707281/11664 (* x x)))
16/841
(* -707281/11664 (* x x))
-707281/11664
(* x x)
x
(+ 4/29 (* x -841/108))
4/29
(* x -841/108)
-841/108
(* (+ 16/841 (* -707281/11664 (* x x))) (/ 1 (+ 4/29 (* x -841/108))))
(+ 16/841 (* -707281/11664 (* x x)))
16/841
(* -707281/11664 (* x x))
-707281/11664
(* x x)
x
(/ 1 (+ 4/29 (* x -841/108)))
1
(+ 4/29 (* x -841/108))
4/29
(* x -841/108)
-841/108
(/ (- (* 594823321/1259712 (* x (* x x))) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
(- (* 594823321/1259712 (* x (* x x))) -64/24389)
(* 594823321/1259712 (* x (* x x)))
594823321/1259712
(* x (* x x))
x
(* x x)
-64/24389
(+ 16/841 (* x (+ (* x 707281/11664) -29/27)))
16/841
(* x (+ (* x 707281/11664) -29/27))
(+ (* x 707281/11664) -29/27)
(* x 707281/11664)
707281/11664
-29/27

Outputs
(/ 1 (/ 1 (+ (* 841/108 x) 4/29)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
1
#s(literal 1 binary64)
(/ 1 (+ (* 841/108 x) 4/29))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)))
(+ (* 841/108 x) 4/29)
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
841/108
#s(literal 841/108 binary64)
x
4/29
#s(literal 4/29 binary64)
4/29
#s(literal 4/29 binary64)
(/ (+ 16/841 (* -707281/11664 (* x x))) (+ 4/29 (* x -841/108)))
(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64)))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
(+ 16/841 (* -707281/11664 (* x x)))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
16/841
#s(literal 16/841 binary64)
(* -707281/11664 (* x x))
(.f64 x (.f64 x #s(literal -707281/11664 binary64)))
-707281/11664
#s(literal -707281/11664 binary64)
(* x x)
(*.f64 x x)
x
(+ 4/29 (* x -841/108))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64)))
4/29
#s(literal 4/29 binary64)
(* x -841/108)
(*.f64 x #s(literal -841/108 binary64))
-841/108
#s(literal -841/108 binary64)
(* (+ 16/841 (* -707281/11664 (* x x))) (/ 1 (+ 4/29 (* x -841/108))))
(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64)))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
(+ 16/841 (* -707281/11664 (* x x)))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
16/841
#s(literal 16/841 binary64)
(* -707281/11664 (* x x))
(.f64 x (.f64 x #s(literal -707281/11664 binary64)))
-707281/11664
#s(literal -707281/11664 binary64)
(* x x)
(*.f64 x x)
x
(/ 1 (+ 4/29 (* x -841/108)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
1
#s(literal 1 binary64)
(+ 4/29 (* x -841/108))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64)))
4/29
#s(literal 4/29 binary64)
(* x -841/108)
(*.f64 x #s(literal -841/108 binary64))
-841/108
#s(literal -841/108 binary64)
(/ (- (* 594823321/1259712 (* x (* x x))) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
(/.f64 (+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal 64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
(- (* 594823321/1259712 (* x (* x x))) -64/24389)
(+.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (*.f64 x x))) #s(literal 64/24389 binary64))
(* 594823321/1259712 (* x (* x x)))
(.f64 #s(literal 594823321/1259712 binary64) (.f64 x (*.f64 x x)))
594823321/1259712
#s(literal 594823321/1259712 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
-64/24389
#s(literal -64/24389 binary64)
(+ 16/841 (* x (+ (* x 707281/11664) -29/27)))
(+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))
16/841
#s(literal 16/841 binary64)
(* x (+ (* x 707281/11664) -29/27))
(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
(+ (* x 707281/11664) -29/27)
(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
(* x 707281/11664)
(*.f64 x #s(literal 707281/11664 binary64))
707281/11664
#s(literal 707281/11664 binary64)
-29/27
#s(literal -29/27 binary64)

localize235.0ms (3.5%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 #s(literal 594823321/1259712 binary64) (.f64 x (*.f64 x x)))
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	99.5%	(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
✓	accuracy	68.8%	(/.f64 (-.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
✓	accuracy	99.8%	(*.f64 x #s(literal -841/108 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
✓	accuracy	99.7%	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	accuracy	75.8%	(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64)))
✓	accuracy	99.8%	(*.f64 x #s(literal -841/108 binary64))
✓	accuracy	99.7%	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	accuracy	75.7%	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
✓	accuracy	100.0%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)))
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))))

Results

174.0ms	255×	0	valid
5.0ms	1×	5	exit

Compiler

Compiled 196 to 32 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 104.0ms

...c/correct-round.rkt:119:19: 67.0ms (64.3% of total)

ival-mult: 20.0ms (19.2% of total)

ival-div: 9.0ms (8.6% of total)

ival-add: 6.0ms (5.8% of total)

ival-sub: 1.0ms (1% of total)

backward-pass: 1.0ms (1% of total)

const: 0.0ms (0% of total)

series14.0ms (0.2%)

Counts

18 → 216

Calls

Call 1

Inputs
#<alt (/ 1 (/ 1 (+ (* 841/108 x) 4/29)))>
#<alt (/ 1 (+ (* 841/108 x) 4/29))>
#<alt (+ (* 841/108 x) 4/29)>
#<alt (* 841/108 x)>
#<alt (/ (+ 16/841 (* -707281/11664 (* x x))) (+ 4/29 (* x -841/108)))>
#<alt (+ 16/841 (* -707281/11664 (* x x)))>
#<alt (* -707281/11664 (* x x))>
#<alt (* x x)>
#<alt (* (+ 16/841 (* -707281/11664 (* x x))) (/ 1 (+ 4/29 (* x -841/108))))>
#<alt (/ (- (* 594823321/1259712 (* x (* x x))) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))>
#<alt (- (* 594823321/1259712 (* x (* x x))) -64/24389)>
#<alt (* 594823321/1259712 (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (* x -841/108)>
#<alt (+ 4/29 (* x -841/108))>
#<alt (/ 1 (+ 4/29 (* x -841/108)))>
#<alt (* x (+ (* x 707281/11664) -29/27))>
#<alt (* x 707281/11664)>

Outputs
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt 29/4>
#<alt (+ 29/4 (* -707281/1728 x))>
#<alt (+ 29/4 (* x (- (* 17249876309/746496 x) 707281/1728)))>
#<alt (+ 29/4 (* x (- (* x (+ 17249876309/746496 (* -420707233300201/322486272 x))) 707281/1728)))>
#<alt (/ 108/841 x)>
#<alt (/ (- 108/841 (* 46656/20511149 (/ 1 x))) x)>
#<alt (/ (- (+ 108/841 (/ 20155392/500246412961 (pow x 2))) (* 46656/20511149 (/ 1 x))) x)>
#<alt (/ (- (+ 108/841 (/ 20155392/500246412961 (pow x 2))) (+ (* 46656/20511149 (/ 1 x)) (* 8707129344/12200509765705829 (/ 1 (pow x 3))))) x)>
#<alt (/ 108/841 x)>
#<alt (* -1 (/ (- (* 46656/20511149 (/ 1 x)) 108/841) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 20155392/500246412961 (/ 1 x)) 46656/20511149) x)) 108/841) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8707129344/12200509765705829 (/ 1 x)) 20155392/500246412961) x)) 46656/20511149) x)) 108/841) x))>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt 16/841>
#<alt (+ 16/841 (* -707281/11664 (pow x 2)))>
#<alt (+ 16/841 (* -707281/11664 (pow x 2)))>
#<alt (+ 16/841 (* -707281/11664 (pow x 2)))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt 64/24389>
#<alt (+ 64/24389 (* 594823321/1259712 (pow x 3)))>
#<alt (+ 64/24389 (* 594823321/1259712 (pow x 3)))>
#<alt (+ 64/24389 (* 594823321/1259712 (pow x 3)))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt 4/29>
#<alt (+ 4/29 (* -841/108 x))>
#<alt (+ 4/29 (* -841/108 x))>
#<alt (+ 4/29 (* -841/108 x))>
#<alt (* -841/108 x)>
#<alt (* x (- (* 4/29 (/ 1 x)) 841/108))>
#<alt (* x (- (* 4/29 (/ 1 x)) 841/108))>
#<alt (* x (- (* 4/29 (/ 1 x)) 841/108))>
#<alt (* -841/108 x)>
#<alt (* -1 (* x (- 841/108 (* 4/29 (/ 1 x)))))>
#<alt (* -1 (* x (- 841/108 (* 4/29 (/ 1 x)))))>
#<alt (* -1 (* x (- 841/108 (* 4/29 (/ 1 x)))))>
#<alt 29/4>
#<alt (+ 29/4 (* 707281/1728 x))>
#<alt (+ 29/4 (* x (+ 707281/1728 (* 17249876309/746496 x))))>
#<alt (+ 29/4 (* x (+ 707281/1728 (* x (+ 17249876309/746496 (* 420707233300201/322486272 x))))))>
#<alt (/ -108/841 x)>
#<alt (* -1 (/ (+ 108/841 (* 46656/20511149 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 46656/20511149 (* 20155392/500246412961 (/ 1 x))) x)) 108/841) x)>
#<alt (/ (- (* -1 (/ (+ 20155392/500246412961 (* 8707129344/12200509765705829 (/ 1 x))) (pow x 2))) (+ 108/841 (* 46656/20511149 (/ 1 x)))) x)>
#<alt (/ -108/841 x)>
#<alt (* -1 (/ (+ 108/841 (* 46656/20511149 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 108/841 (+ (/ 20155392/500246412961 (pow x 2)) (* 46656/20511149 (/ 1 x)))) x))>
#<alt (* -1 (/ (+ 108/841 (* -1 (/ (- (* -1 (/ (+ 20155392/500246412961 (* 8707129344/12200509765705829 (/ 1 x))) x)) 46656/20511149) x))) x))>
#<alt (* -29/27 x)>
#<alt (* x (- (* 707281/11664 x) 29/27))>
#<alt (* x (- (* 707281/11664 x) 29/27))>
#<alt (* x (- (* 707281/11664 x) 29/27))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>

Calls

54 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(/ 1 (+ 4/29 (* x -841/108)))
1.0ms	x	@	inf	(/ (- (* 594823321/1259712 (* x (* x x))) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
1.0ms	x	@	0	(/ (- (* 594823321/1259712 (* x (* x x))) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
1.0ms	x	@	0	(/ (+ 16/841 (* -707281/11664 (* x x))) (+ 4/29 (* x -841/108)))
1.0ms	x	@	inf	(+ 16/841 (* -707281/11664 (* x x)))

rewrite417.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3884×	`/-lowering-/.f32`
3884×	`/-lowering-/.f64`
3020×	`-lowering-.f32`
3020×	`-lowering-.f64`
1832×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	104
1	182	96
2	1459	96
0	8391	96

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 778

Calls

Call 1

Inputs
(/ 1 (/ 1 (+ (* 841/108 x) 4/29)))
(/ 1 (+ (* 841/108 x) 4/29))
(+ (* 841/108 x) 4/29)
(* 841/108 x)
(/ (+ 16/841 (* -707281/11664 (* x x))) (+ 4/29 (* x -841/108)))
(+ 16/841 (* -707281/11664 (* x x)))
(* -707281/11664 (* x x))
(* x x)
(* (+ 16/841 (* -707281/11664 (* x x))) (/ 1 (+ 4/29 (* x -841/108))))
(/ (- (* 594823321/1259712 (* x (* x x))) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
(- (* 594823321/1259712 (* x (* x x))) -64/24389)
(* 594823321/1259712 (* x (* x x)))
(* x (* x x))
(* x -841/108)
(+ 4/29 (* x -841/108))
(/ 1 (+ 4/29 (* x -841/108)))
(* x (+ (* x 707281/11664) -29/27))
(* x 707281/11664)

Outputs
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+.f64 #s(literal 4/29 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -841/108 binary64))))
(+.f64 #s(literal 4/29 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -841/108 binary64)))
(+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(exp.f64 (log.f64 (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64)))
(-.f64 #s(literal 4/29 binary64) (/.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -4/29 binary64) (*.f64 #s(literal 841/108 binary64) x)))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(-.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))) (/.f64 #s(literal -64/24389 binary64) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (*.f64 x #s(literal 707281/11664 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 210457284365172120330305161/1999004627104432128 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) #s(literal 4096/594823321 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -24389/19683 binary64)))) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))) (/.f64 (/.f64 #s(literal -262144/14507145975869 binary64) (+.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) #s(literal 4096/594823321 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -24389/19683 binary64)))) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (*.f64 x #s(literal 707281/11664 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) #s(literal -64/24389 binary64))) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))) (/.f64 (/.f64 #s(literal 4096/594823321 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) #s(literal -64/24389 binary64))) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal 29/27 binary64))))) (/.f64 #s(literal -64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (*.f64 x #s(literal 29/27 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 210457284365172120330305161/1999004627104432128 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) #s(literal 4096/594823321 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -24389/19683 binary64)))) (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal 29/27 binary64))))) (/.f64 (/.f64 #s(literal -262144/14507145975869 binary64) (+.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) #s(literal 4096/594823321 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -24389/19683 binary64)))) (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (*.f64 x #s(literal 29/27 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) #s(literal -64/24389 binary64))) (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal 29/27 binary64))))) (/.f64 (/.f64 #s(literal 4096/594823321 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) #s(literal -64/24389 binary64))) (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal 29/27 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))))) (-.f64 #s(literal -4/29 binary64) (.f64 #s(literal 841/108 binary64) x)))
(-.f64 (/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(fma.f64 #s(literal 841/108 binary64) x #s(literal 4/29 binary64))
(fma.f64 x #s(literal 841/108 binary64) #s(literal 4/29 binary64))
(fma.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 1 binary64) #s(literal 4/29 binary64))
(neg.f64 (-.f64 #s(literal -4/29 binary64) (*.f64 #s(literal 841/108 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal 29/27 binary64)))) (+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) #s(literal 64/24389 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x (*.f64 x #s(literal 707281/11664 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))) (-.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal 594823321/1259712 binary64))))))
(/.f64 (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) #s(literal 64/24389 binary64)) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) #s(literal 64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal 29/27 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))) #s(literal 64/24389 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64)))) #s(literal -64/24389 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal 29/27 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64)))) #s(literal -64/24389 binary64)) (neg.f64 (+.f64 #s(literal 16/841 binary64) (-.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal 29/27 binary64))))))
(/.f64 (-.f64 #s(literal -4/29 binary64) (*.f64 #s(literal 841/108 binary64) x)) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
(/.f64 (-.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))) (-.f64 #s(literal -4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
(/.f64 (-.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64)))) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) #s(literal 16/841 binary64))) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x x) (.f64 x #s(literal 594823321/1259712 binary64))))) (-.f64 #s(literal -16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
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(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal -24389/19683 binary64))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))) (-.f64 (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x #s(literal -29/27 binary64))) (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (*.f64 x #s(literal -29/27 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))) (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x #s(literal -29/27 binary64)))) (.f64 (.f64 x #s(literal -841/108 binary64)) (+.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal -4/29 binary64))))
(/.f64 (.f64 x (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) #s(literal -24389/19683 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) (-.f64 #s(literal 841/729 binary64) (*.f64 x #s(literal -20511149/314928 binary64)))))
(/.f64 (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) #s(literal -841/729 binary64))) (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal 29/27 binary64)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) #s(literal -24389/19683 binary64)) x) (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) (-.f64 #s(literal 841/729 binary64) (*.f64 x #s(literal -20511149/314928 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) #s(literal -841/729 binary64)) x) (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal 29/27 binary64)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal -24389/19683 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))) (-.f64 (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x #s(literal -29/27 binary64))) (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (*.f64 x #s(literal -29/27 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))) (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x #s(literal -29/27 binary64))))) (neg.f64 (.f64 (.f64 x #s(literal -841/108 binary64)) (+.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal -4/29 binary64)))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) #s(literal -24389/19683 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) (-.f64 #s(literal 841/729 binary64) (*.f64 x #s(literal -20511149/314928 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) #s(literal -841/729 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal 29/27 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) #s(literal -24389/19683 binary64)) x)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) (-.f64 #s(literal 841/729 binary64) (*.f64 x #s(literal -20511149/314928 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) #s(literal -841/729 binary64)) x)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal 29/27 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -24389/19683 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)))) (+.f64 (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x #s(literal -29/27 binary64))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))) (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x (*.f64 x #s(literal 707281/11664 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x #s(literal -29/27 binary64))) (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))) (-.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x (*.f64 x #s(literal 707281/11664 binary64)))))
(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
(.f64 (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)) x)
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal -24389/19683 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))) (-.f64 (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x #s(literal -29/27 binary64))) (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal -29/27 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))) (.f64 (.f64 x #s(literal -29/27 binary64)) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -841/108 binary64)) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal -4/29 binary64)))))
(.f64 (.f64 x (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) #s(literal -24389/19683 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) (-.f64 #s(literal 841/729 binary64) (.f64 x #s(literal -20511149/314928 binary64))))))
(.f64 (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) #s(literal -841/729 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal 29/27 binary64))))
(.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) #s(literal -24389/19683 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) (-.f64 #s(literal 841/729 binary64) (.f64 x #s(literal -20511149/314928 binary64))))))
(.f64 (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) #s(literal -841/729 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal 29/27 binary64))))
(*.f64 x #s(literal 707281/11664 binary64))
(*.f64 #s(literal 707281/11664 binary64) x)

simplify232.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1866×	`-lowering-.f32`
1866×	`-lowering-.f64`
1740×	`fnmsub-define`
1534×	`sum3-define`
1350×	`sum4-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	1047
1	413	914
2	1002	908
3	2372	906
4	5785	906
0	8189	906

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
29/4
(+ 29/4 (* -707281/1728 x))
(+ 29/4 (* x (- (* 17249876309/746496 x) 707281/1728)))
(+ 29/4 (* x (- (* x (+ 17249876309/746496 (* -420707233300201/322486272 x))) 707281/1728)))
(/ 108/841 x)
(/ (- 108/841 (* 46656/20511149 (/ 1 x))) x)
(/ (- (+ 108/841 (/ 20155392/500246412961 (pow x 2))) (* 46656/20511149 (/ 1 x))) x)
(/ (- (+ 108/841 (/ 20155392/500246412961 (pow x 2))) (+ (* 46656/20511149 (/ 1 x)) (* 8707129344/12200509765705829 (/ 1 (pow x 3))))) x)
(/ 108/841 x)
(* -1 (/ (- (* 46656/20511149 (/ 1 x)) 108/841) x))
(* -1 (/ (- (* -1 (/ (- (* 20155392/500246412961 (/ 1 x)) 46656/20511149) x)) 108/841) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8707129344/12200509765705829 (/ 1 x)) 20155392/500246412961) x)) 46656/20511149) x)) 108/841) x))
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
16/841
(+ 16/841 (* -707281/11664 (pow x 2)))
(+ 16/841 (* -707281/11664 (pow x 2)))
(+ 16/841 (* -707281/11664 (pow x 2)))
(* -707281/11664 (pow x 2))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* -707281/11664 (pow x 2))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
64/24389
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(* 594823321/1259712 (pow x 3))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* 594823321/1259712 (pow x 3))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
4/29
(+ 4/29 (* -841/108 x))
(+ 4/29 (* -841/108 x))
(+ 4/29 (* -841/108 x))
(* -841/108 x)
(* x (- (* 4/29 (/ 1 x)) 841/108))
(* x (- (* 4/29 (/ 1 x)) 841/108))
(* x (- (* 4/29 (/ 1 x)) 841/108))
(* -841/108 x)
(* -1 (* x (- 841/108 (* 4/29 (/ 1 x)))))
(* -1 (* x (- 841/108 (* 4/29 (/ 1 x)))))
(* -1 (* x (- 841/108 (* 4/29 (/ 1 x)))))
29/4
(+ 29/4 (* 707281/1728 x))
(+ 29/4 (* x (+ 707281/1728 (* 17249876309/746496 x))))
(+ 29/4 (* x (+ 707281/1728 (* x (+ 17249876309/746496 (* 420707233300201/322486272 x))))))
(/ -108/841 x)
(* -1 (/ (+ 108/841 (* 46656/20511149 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 46656/20511149 (* 20155392/500246412961 (/ 1 x))) x)) 108/841) x)
(/ (- (* -1 (/ (+ 20155392/500246412961 (* 8707129344/12200509765705829 (/ 1 x))) (pow x 2))) (+ 108/841 (* 46656/20511149 (/ 1 x)))) x)
(/ -108/841 x)
(* -1 (/ (+ 108/841 (* 46656/20511149 (/ 1 x))) x))
(* -1 (/ (+ 108/841 (+ (/ 20155392/500246412961 (pow x 2)) (* 46656/20511149 (/ 1 x)))) x))
(* -1 (/ (+ 108/841 (* -1 (/ (- (* -1 (/ (+ 20155392/500246412961 (* 8707129344/12200509765705829 (/ 1 x))) x)) 46656/20511149) x))) x))
(* -29/27 x)
(* x (- (* 707281/11664 x) 29/27))
(* x (- (* 707281/11664 x) 29/27))
(* x (- (* 707281/11664 x) 29/27))
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)

Outputs
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
29/4
#s(literal 29/4 binary64)
(+ 29/4 (* -707281/1728 x))
(+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64)))
(+ 29/4 (* x (- (* 17249876309/746496 x) 707281/1728)))
(+.f64 #s(literal 29/4 binary64) (.f64 x (+.f64 #s(literal -707281/1728 binary64) (.f64 x #s(literal 17249876309/746496 binary64)))))
(+ 29/4 (* x (- (* x (+ 17249876309/746496 (* -420707233300201/322486272 x))) 707281/1728)))
(+.f64 #s(literal 29/4 binary64) (.f64 x (+.f64 #s(literal -707281/1728 binary64) (.f64 x (+.f64 #s(literal 17249876309/746496 binary64) (*.f64 x #s(literal -420707233300201/322486272 binary64)))))))
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ (- 108/841 (* 46656/20511149 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 108/841 binary64) (/.f64 #s(literal -46656/20511149 binary64) x)) x)
(/ (- (+ 108/841 (/ 20155392/500246412961 (pow x 2))) (* 46656/20511149 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 108/841 binary64) (/.f64 (+.f64 (/.f64 #s(literal 20155392/500246412961 binary64) x) #s(literal -46656/20511149 binary64)) x)) x)
(/ (- (+ 108/841 (/ 20155392/500246412961 (pow x 2))) (+ (* 46656/20511149 (/ 1 x)) (* 8707129344/12200509765705829 (/ 1 (pow x 3))))) x)
(/.f64 (+.f64 #s(literal 108/841 binary64) (/.f64 (-.f64 #s(literal -46656/20511149 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8707129344/12200509765705829 binary64) x) #s(literal -20155392/500246412961 binary64)) x)) x)) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(* -1 (/ (- (* 46656/20511149 (/ 1 x)) 108/841) x))
(/.f64 (+.f64 #s(literal 108/841 binary64) (/.f64 #s(literal -46656/20511149 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 20155392/500246412961 (/ 1 x)) 46656/20511149) x)) 108/841) x))
(/.f64 (+.f64 #s(literal 108/841 binary64) (/.f64 (+.f64 (/.f64 #s(literal 20155392/500246412961 binary64) x) #s(literal -46656/20511149 binary64)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8707129344/12200509765705829 (/ 1 x)) 20155392/500246412961) x)) 46656/20511149) x)) 108/841) x))
(/.f64 (+.f64 #s(literal 108/841 binary64) (/.f64 (-.f64 #s(literal -46656/20511149 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8707129344/12200509765705829 binary64) x) #s(literal -20155392/500246412961 binary64)) x)) x)) x)
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
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(* 707281/11664 x)
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(* 707281/11664 x)
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eval391.0ms (5.8%)

Compiler: Compiled 33130 to 2151 computations (93.5% saved)

prune104.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1164	6	1170
Fresh	5	2	7
Picked	4	1	5
Done	0	1	1
Total	1173	10	1183

Accuracy

100.0%

Counts

1183 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
▶	68.1%	(/.f64 (-.f64 (.f64 (.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x) x) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
	28.1%	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (*.f64 x #s(literal -841/108 binary64)))
	52.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
▶	48.1%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64))))
▶	48.8%	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
	28.1%	(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x))) (/.f64 #s(literal -108/841 binary64) x))
▶	52.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	48.3%	#s(literal 4/29 binary64)

Compiler

Compiled 196 to 147 computations (25% saved)

simplify289.0ms (4.3%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x)
✓	cost-diff	0	(.f64 (.f64 (*.f64 x #s(literal 594823321/1259712 binary64)) x) x)
✓	cost-diff	0	(-.f64 (.f64 (.f64 (*.f64 x #s(literal 594823321/1259712 binary64)) x) x) #s(literal -64/24389 binary64))
✓	cost-diff	0	(/.f64 (-.f64 (.f64 (.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x) x) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
✓	cost-diff	0	(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
✓	cost-diff	0	(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
✓	cost-diff	0	(*.f64 x #s(literal -707281/1728 binary64))
✓	cost-diff	0	(+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64))))
✓	cost-diff	0	(*.f64 #s(literal 841/108 binary64) x)
✓	cost-diff	0	(/.f64 x (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal 707281/11664 binary64))
✓	cost-diff	64	(neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
✓	cost-diff	6336	(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))

Rules

1912×	`fmsub-define`
1864×	`fnmsub-define`
1606×	`sum3-define`
1584×	`fma-lowering-fma.f32`
1584×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	175
1	79	165
2	155	161
3	288	161
4	478	161
5	840	161
6	1905	161
7	4457	161
8	6726	161
0	8042	161

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (* x 707281/11664) (/ x (+ (* 841/108 x) -4/29))) (neg (/ 16/841 (+ (* 841/108 x) -4/29))))
(* x 707281/11664)
x
707281/11664
(/ x (+ (* 841/108 x) -4/29))
(+ (* 841/108 x) -4/29)
(* 841/108 x)
841/108
-4/29
(neg (/ 16/841 (+ (* 841/108 x) -4/29)))
(/ 16/841 (+ (* 841/108 x) -4/29))
16/841
(* 841/108 x)
841/108
x
(/ 1 (+ 29/4 (* x -707281/1728)))
1
(+ 29/4 (* x -707281/1728))
29/4
(* x -707281/1728)
x
-707281/1728
(/ 64/24389 (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
64/24389
(+ 16/841 (* x (+ (* x 707281/11664) -29/27)))
16/841
(* x (+ (* x 707281/11664) -29/27))
x
(+ (* x 707281/11664) -29/27)
(* x 707281/11664)
707281/11664
-29/27
(/ (- (* (* (* x 594823321/1259712) x) x) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
(- (* (* (* x 594823321/1259712) x) x) -64/24389)
(* (* (* x 594823321/1259712) x) x)
(* (* x 594823321/1259712) x)
(* x 594823321/1259712)
x
594823321/1259712
-64/24389
(+ 16/841 (* x (+ (* x 707281/11664) -29/27)))
16/841
(* x (+ (* x 707281/11664) -29/27))
(+ (* x 707281/11664) -29/27)
(* x 707281/11664)
707281/11664
-29/27

Outputs
(+ (* (* x 707281/11664) (/ x (+ (* 841/108 x) -4/29))) (neg (/ 16/841 (+ (* 841/108 x) -4/29))))
(+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal 4/29 binary64))))
(* x 707281/11664)
(*.f64 x #s(literal 707281/11664 binary64))
x
707281/11664
#s(literal 707281/11664 binary64)
(/ x (+ (* 841/108 x) -4/29))
(/.f64 x (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))
(+ (* 841/108 x) -4/29)
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))
(* 841/108 x)
(*.f64 x #s(literal 841/108 binary64))
841/108
#s(literal 841/108 binary64)
-4/29
#s(literal -4/29 binary64)
(neg (/ 16/841 (+ (* 841/108 x) -4/29)))
(/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal 4/29 binary64)))
(/ 16/841 (+ (* 841/108 x) -4/29))
(/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))
16/841
#s(literal 16/841 binary64)
(* 841/108 x)
(*.f64 x #s(literal 841/108 binary64))
841/108
#s(literal 841/108 binary64)
x
(/ 1 (+ 29/4 (* x -707281/1728)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64))))
1
#s(literal 1 binary64)
(+ 29/4 (* x -707281/1728))
(+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64)))
29/4
#s(literal 29/4 binary64)
(* x -707281/1728)
(*.f64 x #s(literal -707281/1728 binary64))
x
-707281/1728
#s(literal -707281/1728 binary64)
(/ 64/24389 (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
64/24389
#s(literal 64/24389 binary64)
(+ 16/841 (* x (+ (* x 707281/11664) -29/27)))
(+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))
16/841
#s(literal 16/841 binary64)
(* x (+ (* x 707281/11664) -29/27))
(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
x
(+ (* x 707281/11664) -29/27)
(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
(* x 707281/11664)
(*.f64 x #s(literal 707281/11664 binary64))
707281/11664
#s(literal 707281/11664 binary64)
-29/27
#s(literal -29/27 binary64)
(/ (- (* (* (* x 594823321/1259712) x) x) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
(/.f64 (+.f64 #s(literal 64/24389 binary64) (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x)))) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
(- (* (* (* x 594823321/1259712) x) x) -64/24389)
(+.f64 #s(literal 64/24389 binary64) (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (*.f64 x x))))
(* (* (* x 594823321/1259712) x) x)
(.f64 x (.f64 #s(literal 594823321/1259712 binary64) (*.f64 x x)))
(* (* x 594823321/1259712) x)
(.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))
(* x 594823321/1259712)
(*.f64 x #s(literal 594823321/1259712 binary64))
x
594823321/1259712
#s(literal 594823321/1259712 binary64)
-64/24389
#s(literal -64/24389 binary64)
(+ 16/841 (* x (+ (* x 707281/11664) -29/27)))
(+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))
16/841
#s(literal 16/841 binary64)
(* x (+ (* x 707281/11664) -29/27))
(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
(+ (* x 707281/11664) -29/27)
(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
(* x 707281/11664)
(*.f64 x #s(literal 707281/11664 binary64))
707281/11664
#s(literal 707281/11664 binary64)
-29/27
#s(literal -29/27 binary64)

localize482.0ms (7.1%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x)
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	99.5%	(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
✓	accuracy	68.8%	(/.f64 (-.f64 (.f64 (.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x) x) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
✓	accuracy	99.9%	(+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))))
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	99.5%	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
✓	accuracy	99.5%	(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64))))
✓	accuracy	99.4%	(*.f64 x #s(literal -707281/1728 binary64))
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.7%	(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	99.5%	(/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))

Results

279.0ms	255×	0	valid
5.0ms	1×	5	exit

Compiler

Compiled 196 to 32 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 209.0ms

...c/correct-round.rkt:119:19: 171.0ms (81.9% of total)

ival-mult: 15.0ms (7.2% of total)

ival-div: 9.0ms (4.3% of total)

ival-add: 6.0ms (2.9% of total)

compiled-spec: 4.0ms (1.9% of total)

ival-neg: 2.0ms (1% of total)

ival-sub: 1.0ms (0.5% of total)

const: 1.0ms (0.5% of total)

backward-pass: 1.0ms (0.5% of total)

series12.0ms (0.2%)

Counts

17 → 204

Calls

Call 1

Inputs
#<alt (+ (* (* x 707281/11664) (/ x (+ (* 841/108 x) -4/29))) (neg (/ 16/841 (+ (* 841/108 x) -4/29))))>
#<alt (neg (/ 16/841 (+ (* 841/108 x) -4/29)))>
#<alt (* x 707281/11664)>
#<alt (/ x (+ (* 841/108 x) -4/29))>
#<alt (* 841/108 x)>
#<alt (/ 1 (+ 29/4 (* x -707281/1728)))>
#<alt (+ 29/4 (* x -707281/1728))>
#<alt (* x -707281/1728)>
#<alt (/ 64/24389 (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))>
#<alt (+ 16/841 (* x (+ (* x 707281/11664) -29/27)))>
#<alt (* x (+ (* x 707281/11664) -29/27))>
#<alt (+ (* x 707281/11664) -29/27)>
#<alt (/ (- (* (* (* x 594823321/1259712) x) x) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))>
#<alt (- (* (* (* x 594823321/1259712) x) x) -64/24389)>
#<alt (* (* (* x 594823321/1259712) x) x)>
#<alt (* (* x 594823321/1259712) x)>
#<alt (/ 16/841 (+ (* 841/108 x) -4/29))>

Outputs
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* x (+ 841/108 (* 20511149/46656 x))))>
#<alt (+ 4/29 (* x (+ 841/108 (* x (+ 20511149/46656 (* 500246412961/20155392 x))))))>
#<alt (/ -1728/707281 x)>
#<alt (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x)>
#<alt (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) (pow x 2))) (+ 1728/707281 (* 746496/17249876309 (/ 1 x)))) x)>
#<alt (/ -1728/707281 x)>
#<alt (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x))>
#<alt (* -1 (/ (+ 1728/707281 (* -1 (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) x)) 746496/17249876309) x))) x))>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* -29/4 x)>
#<alt (* x (- (* -707281/1728 x) 29/4))>
#<alt (* x (- (* x (- (* -17249876309/746496 x) 707281/1728)) 29/4))>
#<alt (* x (- (* x (- (* x (- (* -420707233300201/322486272 x) 17249876309/746496)) 707281/1728)) 29/4))>
#<alt 108/841>
#<alt (+ 108/841 (* 46656/20511149 (/ 1 x)))>
#<alt (+ 108/841 (+ (/ 20155392/500246412961 (pow x 2)) (* 46656/20511149 (/ 1 x))))>
#<alt (+ 108/841 (+ (/ 20155392/500246412961 (pow x 2)) (+ (* 46656/20511149 (/ 1 x)) (* 8707129344/12200509765705829 (/ 1 (pow x 3))))))>
#<alt 108/841>
#<alt (+ 108/841 (* 46656/20511149 (/ 1 x)))>
#<alt (+ 108/841 (+ (/ 20155392/500246412961 (pow x 2)) (* 46656/20511149 (/ 1 x))))>
#<alt (+ 108/841 (* -1 (/ (- (* -1 (/ (+ 20155392/500246412961 (* 8707129344/12200509765705829 (/ 1 x))) x)) 46656/20511149) x)))>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* x (+ 841/108 (* 20511149/46656 x))))>
#<alt (+ 4/29 (* x (+ 841/108 (* x (+ 20511149/46656 (* 500246412961/20155392 x))))))>
#<alt (/ -1728/707281 x)>
#<alt (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x)>
#<alt (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) (pow x 2))) (+ 1728/707281 (* 746496/17249876309 (/ 1 x)))) x)>
#<alt (/ -1728/707281 x)>
#<alt (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x))>
#<alt (* -1 (/ (+ 1728/707281 (* -1 (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) x)) 746496/17249876309) x))) x))>
#<alt 29/4>
#<alt (+ 29/4 (* -707281/1728 x))>
#<alt (+ 29/4 (* -707281/1728 x))>
#<alt (+ 29/4 (* -707281/1728 x))>
#<alt (* -707281/1728 x)>
#<alt (* x (- (* 29/4 (/ 1 x)) 707281/1728))>
#<alt (* x (- (* 29/4 (/ 1 x)) 707281/1728))>
#<alt (* x (- (* 29/4 (/ 1 x)) 707281/1728))>
#<alt (* -707281/1728 x)>
#<alt (* -1 (* x (- 707281/1728 (* 29/4 (/ 1 x)))))>
#<alt (* -1 (* x (- 707281/1728 (* 29/4 (/ 1 x)))))>
#<alt (* -1 (* x (- 707281/1728 (* 29/4 (/ 1 x)))))>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt (* -707281/1728 x)>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* x (+ 841/108 (* -500246412961/20155392 (pow x 2)))))>
#<alt (+ 4/29 (* x (+ 841/108 (* (pow x 2) (- (* -12200509765705829/8707129344 x) 500246412961/20155392)))))>
#<alt (/ 746496/17249876309 (pow x 2))>
#<alt (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) (/ 60183678025728/250246473680347348787521 (pow x 3))) (pow x 2))>
#<alt (/ (+ 746496/17249876309 (+ (* -1 (/ (+ 60183678025728/250246473680347348787521 (* 25999348907114496/6103261246589991489578849669 (/ 1 x))) (pow x 3))) (* 322486272/420707233300201 (/ 1 x)))) (pow x 2))>
#<alt (/ 746496/17249876309 (pow x 2))>
#<alt (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 746496/17249876309 (* -1 (/ (- (* 60183678025728/250246473680347348787521 (/ 1 (pow x 2))) 322486272/420707233300201) x))) (pow x 2))>
#<alt (/ (+ 746496/17249876309 (* -1 (/ (- (+ (/ 25999348907114496/6103261246589991489578849669 (pow x 3)) (* 60183678025728/250246473680347348787521 (/ 1 (pow x 2)))) 322486272/420707233300201) x))) (pow x 2))>
#<alt 16/841>
#<alt (+ 16/841 (* -29/27 x))>
#<alt (+ 16/841 (* x (- (* 707281/11664 x) 29/27)))>
#<alt (+ 16/841 (* x (- (* 707281/11664 x) 29/27)))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 707281/11664 (/ 16/841 (pow x 2))) (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 707281/11664 (/ 16/841 (pow x 2))) (* 29/27 (/ 1 x))))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (+ 707281/11664 (* -1 (/ (- 29/27 (* 16/841 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 707281/11664 (* -1 (/ (- 29/27 (* 16/841 (/ 1 x))) x))))>
#<alt (* -29/27 x)>
#<alt (* x (- (* 707281/11664 x) 29/27))>
#<alt (* x (- (* 707281/11664 x) 29/27))>
#<alt (* x (- (* 707281/11664 x) 29/27))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt -29/27>
#<alt (- (* 707281/11664 x) 29/27)>
#<alt (- (* 707281/11664 x) 29/27)>
#<alt (- (* 707281/11664 x) 29/27)>
#<alt (* 707281/11664 x)>
#<alt (* x (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* x (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* x (- 707281/11664 (* 29/27 (/ 1 x))))>
#<alt (* 707281/11664 x)>
#<alt (* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))>
#<alt (* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))>
#<alt (* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt 64/24389>
#<alt (+ 64/24389 (* 594823321/1259712 (pow x 3)))>
#<alt (+ 64/24389 (* 594823321/1259712 (pow x 3)))>
#<alt (+ 64/24389 (* 594823321/1259712 (pow x 3)))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 3))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt (* 594823321/1259712 (pow x 2))>
#<alt -4/29>
#<alt (- (* -841/108 x) 4/29)>
#<alt (- (* x (- (* -20511149/46656 x) 841/108)) 4/29)>
#<alt (- (* x (- (* x (- (* -500246412961/20155392 x) 20511149/46656)) 841/108)) 4/29)>
#<alt (/ 1728/707281 x)>
#<alt (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)>
#<alt (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x)>
#<alt (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (+ (* 746496/17249876309 (/ 1 x)) (* 139314069504/10260628712958602189 (/ 1 (pow x 3)))))) x)>
#<alt (/ 1728/707281 x)>
#<alt (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (+ (/ 139314069504/10260628712958602189 (pow x 2)) (* 322486272/420707233300201 (/ 1 x)))) x)) 1728/707281) x))>

Calls

51 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/ 64/24389 (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
1.0ms	x	@	0	(+ (* (* x 707281/11664) (/ x (+ (* 841/108 x) -4/29))) (neg (/ 16/841 (+ (* 841/108 x) -4/29))))
1.0ms	x	@	inf	(+ (* (* x 707281/11664) (/ x (+ (* 841/108 x) -4/29))) (neg (/ 16/841 (+ (* 841/108 x) -4/29))))
1.0ms	x	@	-inf	(+ (* (* x 707281/11664) (/ x (+ (* 841/108 x) -4/29))) (neg (/ 16/841 (+ (* 841/108 x) -4/29))))
0.0ms	x	@	inf	(* x -707281/1728)

rewrite451.0ms (6.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3564×	`/-lowering-/.f32`
3564×	`/-lowering-/.f64`
2810×	`-lowering-.f32`
2810×	`-lowering-.f64`
2118×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	119
1	188	98
2	1590	95
0	8392	95

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 698

Calls

Call 1

Inputs
(+ (* (* x 707281/11664) (/ x (+ (* 841/108 x) -4/29))) (neg (/ 16/841 (+ (* 841/108 x) -4/29))))
(neg (/ 16/841 (+ (* 841/108 x) -4/29)))
(* x 707281/11664)
(/ x (+ (* 841/108 x) -4/29))
(* 841/108 x)
(/ 1 (+ 29/4 (* x -707281/1728)))
(+ 29/4 (* x -707281/1728))
(* x -707281/1728)
(/ 64/24389 (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
(+ 16/841 (* x (+ (* x 707281/11664) -29/27)))
(* x (+ (* x 707281/11664) -29/27))
(+ (* x 707281/11664) -29/27)
(/ (- (* (* (* x 594823321/1259712) x) x) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
(- (* (* (* x 594823321/1259712) x) x) -64/24389)
(* (* (* x 594823321/1259712) x) x)
(* (* x 594823321/1259712) x)
(/ 16/841 (+ (* 841/108 x) -4/29))

Outputs
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64))
(+.f64 (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)) (/.f64 #s(literal -16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))
(+.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)))
(+.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)) (+.f64 (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))) #s(literal 16/841 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))))
(+.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)) (fma.f64 #s(literal -16/841 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))))
(+.f64 (fma.f64 x (/.f64 #s(literal 707281/11664 binary64) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)) (neg.f64 (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 x (/.f64 #s(literal 707281/11664 binary64) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64))))) #s(literal -16/841 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64)))))) #s(literal -16/841 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64))))) #s(literal -16/841 binary64))))
(+.f64 (fma.f64 x (/.f64 #s(literal 707281/11664 binary64) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)) (neg.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64)))))) (fma.f64 (neg.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64))))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (*.f64 x x))) #s(literal -64/24389 binary64))))))
(+.f64 (fma.f64 x (/.f64 #s(literal 707281/11664 binary64) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)) (neg.f64 (.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)))))) (fma.f64 (neg.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))) (.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))))))
(+.f64 (fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) (.f64 x #s(literal 707281/11664 binary64))) (neg.f64 (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) (.f64 x #s(literal 707281/11664 binary64))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64))))) #s(literal -16/841 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64)))))) #s(literal -16/841 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64))))) #s(literal -16/841 binary64))))
(+.f64 (fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) (.f64 x #s(literal 707281/11664 binary64))) (neg.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64)))))) (fma.f64 (neg.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64))))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (*.f64 x x))) #s(literal -64/24389 binary64))))))
(+.f64 (fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) (.f64 x #s(literal 707281/11664 binary64))) (neg.f64 (.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)))))) (fma.f64 (neg.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))) (.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))))))
(+.f64 (fma.f64 #s(literal 707281/11664 binary64) (.f64 x (/.f64 x (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))) (neg.f64 (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 #s(literal 707281/11664 binary64) (.f64 x (/.f64 x (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64))))) #s(literal -16/841 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64)))))) #s(literal -16/841 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (*.f64 x #s(literal 841/108 binary64))))) #s(literal -16/841 binary64))))
(+.f64 (fma.f64 #s(literal 707281/11664 binary64) (.f64 x (/.f64 x (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))) (neg.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64)))))) (fma.f64 (neg.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64))))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64))))))
(+.f64 (fma.f64 #s(literal 707281/11664 binary64) (.f64 x (/.f64 x (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))) (neg.f64 (.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)))))) (fma.f64 (neg.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))) (.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))))))
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(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 210457284365172120330305161/1999004627104432128 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal 4096/594823321 binary64)) (.f64 #s(literal -24389/19683 binary64) (.f64 x (.f64 x x))))) (.f64 (+.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal 4096/594823321 binary64)) (.f64 #s(literal -24389/19683 binary64) (.f64 x (.f64 x x)))) #s(literal -262144/14507145975869 binary64))) (.f64 (+.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal 4096/594823321 binary64)) (.f64 #s(literal -24389/19683 binary64) (.f64 x (.f64 x x)))) (+.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal 4096/594823321 binary64)) (.f64 #s(literal -24389/19683 binary64) (.f64 x (.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64))) (.f64 (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64)) #s(literal 4096/594823321 binary64))) (.f64 (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64)) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (*.f64 x x))) #s(literal -64/24389 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 210457284365172120330305161/1999004627104432128 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 262144/14507145975869 binary64)))) (neg.f64 (neg.f64 (+.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal 4096/594823321 binary64)) (.f64 #s(literal -24389/19683 binary64) (.f64 x (.f64 x x)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal -4096/594823321 binary64)))) (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (*.f64 x x))) #s(literal -64/24389 binary64)))))
(pow.f64 (/.f64 (+.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal 4096/594823321 binary64)) (.f64 #s(literal -24389/19683 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 210457284365172120330305161/1999004627104432128 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 262144/14507145975869 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64)) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (*.f64 x x))) #s(literal -4096/594823321 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 210457284365172120330305161/1999004627104432128 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 262144/14507145975869 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal 4096/594823321 binary64)) (.f64 #s(literal -24389/19683 binary64) (.f64 x (*.f64 x x))))))
(.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)) (.f64 x (.f64 x x))) #s(literal -4096/594823321 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 841/108 binary64))) #s(literal 3 binary64)))
(pow.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal 3 binary64))
(pow.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (*.f64 x #s(literal 841/108 binary64)))) #s(literal 3 binary64))
(.f64 x (.f64 #s(literal 594823321/1259712 binary64) (*.f64 x x)))
(.f64 (.f64 x #s(literal 841/108 binary64)) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))
(.f64 #s(literal 594823321/1259712 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x #s(literal 594823321/1259712 binary64)) (*.f64 x x))
(.f64 (.f64 #s(literal 594823321/1259712 binary64) (*.f64 x x)) x)
(.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (.f64 x #s(literal 841/108 binary64)))
(.f64 (.f64 x x) (*.f64 x #s(literal 594823321/1259712 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 3/2 binary64)) (pow.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal 3/2 binary64)))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x)
(.f64 (.f64 x x) #s(literal 594823321/1259712 binary64))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))
(/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))
(/.f64 #s(literal 16/841 binary64) (neg.f64 (+.f64 #s(literal 4/29 binary64) (neg.f64 (*.f64 x #s(literal 841/108 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -16/841 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (*.f64 x #s(literal 841/108 binary64)))))
(/.f64 #s(literal -16/841 binary64) (neg.f64 (neg.f64 (+.f64 #s(literal 4/29 binary64) (neg.f64 (*.f64 x #s(literal 841/108 binary64)))))))
(pow.f64 (/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 16/841 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))
(.f64 #s(literal -16/841 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (neg.f64 (.f64 x #s(literal 841/108 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))) #s(literal 16/841 binary64))
(.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 #s(literal 594823321/1259712 binary64) (.f64 x x))) #s(literal -64/24389 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (-.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))))
(.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal 4/29 binary64)))

simplify311.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

2586×	`-lowering-.f32`
2586×	`-lowering-.f64`
1630×	`sum3-define`
1626×	`+-lowering-+.f64`
1626×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	1232
1	611	1104
2	1551	1067
3	3598	1063
4	7548	1063
0	8325	1063

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* x (+ 841/108 (* 20511149/46656 x))))
(+ 4/29 (* x (+ 841/108 (* x (+ 20511149/46656 (* 500246412961/20155392 x))))))
(/ -1728/707281 x)
(* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x)
(/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) (pow x 2))) (+ 1728/707281 (* 746496/17249876309 (/ 1 x)))) x)
(/ -1728/707281 x)
(* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))
(* -1 (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x))
(* -1 (/ (+ 1728/707281 (* -1 (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) x)) 746496/17249876309) x))) x))
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* -29/4 x)
(* x (- (* -707281/1728 x) 29/4))
(* x (- (* x (- (* -17249876309/746496 x) 707281/1728)) 29/4))
(* x (- (* x (- (* x (- (* -420707233300201/322486272 x) 17249876309/746496)) 707281/1728)) 29/4))
108/841
(+ 108/841 (* 46656/20511149 (/ 1 x)))
(+ 108/841 (+ (/ 20155392/500246412961 (pow x 2)) (* 46656/20511149 (/ 1 x))))
(+ 108/841 (+ (/ 20155392/500246412961 (pow x 2)) (+ (* 46656/20511149 (/ 1 x)) (* 8707129344/12200509765705829 (/ 1 (pow x 3))))))
108/841
(+ 108/841 (* 46656/20511149 (/ 1 x)))
(+ 108/841 (+ (/ 20155392/500246412961 (pow x 2)) (* 46656/20511149 (/ 1 x))))
(+ 108/841 (* -1 (/ (- (* -1 (/ (+ 20155392/500246412961 (* 8707129344/12200509765705829 (/ 1 x))) x)) 46656/20511149) x)))
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* x (+ 841/108 (* 20511149/46656 x))))
(+ 4/29 (* x (+ 841/108 (* x (+ 20511149/46656 (* 500246412961/20155392 x))))))
(/ -1728/707281 x)
(* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x)
(/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) (pow x 2))) (+ 1728/707281 (* 746496/17249876309 (/ 1 x)))) x)
(/ -1728/707281 x)
(* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))
(* -1 (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x))
(* -1 (/ (+ 1728/707281 (* -1 (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) x)) 746496/17249876309) x))) x))
29/4
(+ 29/4 (* -707281/1728 x))
(+ 29/4 (* -707281/1728 x))
(+ 29/4 (* -707281/1728 x))
(* -707281/1728 x)
(* x (- (* 29/4 (/ 1 x)) 707281/1728))
(* x (- (* 29/4 (/ 1 x)) 707281/1728))
(* x (- (* 29/4 (/ 1 x)) 707281/1728))
(* -707281/1728 x)
(* -1 (* x (- 707281/1728 (* 29/4 (/ 1 x)))))
(* -1 (* x (- 707281/1728 (* 29/4 (/ 1 x)))))
(* -1 (* x (- 707281/1728 (* 29/4 (/ 1 x)))))
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
(* -707281/1728 x)
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* x (+ 841/108 (* -500246412961/20155392 (pow x 2)))))
(+ 4/29 (* x (+ 841/108 (* (pow x 2) (- (* -12200509765705829/8707129344 x) 500246412961/20155392)))))
(/ 746496/17249876309 (pow x 2))
(/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) (pow x 2))
(/ (- (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) (/ 60183678025728/250246473680347348787521 (pow x 3))) (pow x 2))
(/ (+ 746496/17249876309 (+ (* -1 (/ (+ 60183678025728/250246473680347348787521 (* 25999348907114496/6103261246589991489578849669 (/ 1 x))) (pow x 3))) (* 322486272/420707233300201 (/ 1 x)))) (pow x 2))
(/ 746496/17249876309 (pow x 2))
(/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) (pow x 2))
(/ (+ 746496/17249876309 (* -1 (/ (- (* 60183678025728/250246473680347348787521 (/ 1 (pow x 2))) 322486272/420707233300201) x))) (pow x 2))
(/ (+ 746496/17249876309 (* -1 (/ (- (+ (/ 25999348907114496/6103261246589991489578849669 (pow x 3)) (* 60183678025728/250246473680347348787521 (/ 1 (pow x 2)))) 322486272/420707233300201) x))) (pow x 2))
16/841
(+ 16/841 (* -29/27 x))
(+ 16/841 (* x (- (* 707281/11664 x) 29/27)))
(+ 16/841 (* x (- (* 707281/11664 x) 29/27)))
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- (+ 707281/11664 (/ 16/841 (pow x 2))) (* 29/27 (/ 1 x))))
(* (pow x 2) (- (+ 707281/11664 (/ 16/841 (pow x 2))) (* 29/27 (/ 1 x))))
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (+ 707281/11664 (* -1 (/ (- 29/27 (* 16/841 (/ 1 x))) x))))
(* (pow x 2) (+ 707281/11664 (* -1 (/ (- 29/27 (* 16/841 (/ 1 x))) x))))
(* -29/27 x)
(* x (- (* 707281/11664 x) 29/27))
(* x (- (* 707281/11664 x) 29/27))
(* x (- (* 707281/11664 x) 29/27))
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
(* (pow x 2) (- 707281/11664 (* 29/27 (/ 1 x))))
-29/27
(- (* 707281/11664 x) 29/27)
(- (* 707281/11664 x) 29/27)
(- (* 707281/11664 x) 29/27)
(* 707281/11664 x)
(* x (- 707281/11664 (* 29/27 (/ 1 x))))
(* x (- 707281/11664 (* 29/27 (/ 1 x))))
(* x (- 707281/11664 (* 29/27 (/ 1 x))))
(* 707281/11664 x)
(* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))
(* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))
(* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
64/24389
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(* 594823321/1259712 (pow x 3))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* 594823321/1259712 (pow x 3))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 3))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
(* 594823321/1259712 (pow x 2))
-4/29
(- (* -841/108 x) 4/29)
(- (* x (- (* -20511149/46656 x) 841/108)) 4/29)
(- (* x (- (* x (- (* -500246412961/20155392 x) 20511149/46656)) 841/108)) 4/29)
(/ 1728/707281 x)
(/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)
(/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x)
(/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (+ (* 746496/17249876309 (/ 1 x)) (* 139314069504/10260628712958602189 (/ 1 (pow x 3)))))) x)
(/ 1728/707281 x)
(/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x))
(* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (+ (/ 139314069504/10260628712958602189 (pow x 2)) (* 322486272/420707233300201 (/ 1 x)))) x)) 1728/707281) x))

Outputs
4/29
#s(literal 4/29 binary64)
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(+ 4/29 (* 841/108 x))
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(+ 4/29 (* 841/108 x))
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(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
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(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
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(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
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(/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) (pow x 2))) (+ 1728/707281 (* 746496/17249876309 (/ 1 x)))) x)
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(/ -1728/707281 x)
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(* 707281/11664 x)
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(* 707281/11664 x)
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(* 707281/11664 x)
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(* 707281/11664 x)
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(* 707281/11664 x)
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(* 707281/11664 x)
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(* 707281/11664 x)
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(* 707281/11664 x)
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(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* -29/4 x)
(*.f64 x #s(literal -29/4 binary64))
(* x (- (* -707281/1728 x) 29/4))
(.f64 x (+.f64 #s(literal -29/4 binary64) (.f64 x #s(literal -707281/1728 binary64))))
(* x (- (* x (- (* -17249876309/746496 x) 707281/1728)) 29/4))
(.f64 x (+.f64 #s(literal -29/4 binary64) (.f64 x (+.f64 #s(literal -707281/1728 binary64) (*.f64 x #s(literal -17249876309/746496 binary64))))))
(* x (- (* x (- (* x (- (* -420707233300201/322486272 x) 17249876309/746496)) 707281/1728)) 29/4))
(.f64 x (+.f64 #s(literal -29/4 binary64) (.f64 x (+.f64 #s(literal -707281/1728 binary64) (.f64 x (+.f64 #s(literal -17249876309/746496 binary64) (.f64 x #s(literal -420707233300201/322486272 binary64))))))))
108/841
#s(literal 108/841 binary64)
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108/841
#s(literal 108/841 binary64)
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(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
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(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
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(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
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(* 841/108 x)
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(* 841/108 x)
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4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
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29/4
#s(literal 29/4 binary64)
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4/29
#s(literal 4/29 binary64)
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16/841
#s(literal 16/841 binary64)
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-29/27
#s(literal -29/27 binary64)
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(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
(* x (- 707281/11664 (* 29/27 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
(* x (- 707281/11664 (* 29/27 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))
(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
(* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))
(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
(* -1 (* x (- (* 29/27 (/ 1 x)) 707281/11664)))
(+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64))
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
64/24389
#s(literal 64/24389 binary64)
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(+ 64/24389 (* 594823321/1259712 (pow x 3)))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(* (pow x 3) (+ 594823321/1259712 (* 64/24389 (/ 1 (pow x 3)))))
(+.f64 #s(literal 64/24389 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 594823321/1259712 binary64))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
(* 594823321/1259712 (pow x 2))
(.f64 x (.f64 x #s(literal 594823321/1259712 binary64)))
-4/29
#s(literal -4/29 binary64)
(- (* -841/108 x) 4/29)
(+.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal -4/29 binary64))
(- (* x (- (* -20511149/46656 x) 841/108)) 4/29)
(+.f64 (.f64 x (+.f64 #s(literal -841/108 binary64) (.f64 x #s(literal -20511149/46656 binary64)))) #s(literal -4/29 binary64))
(- (* x (- (* x (- (* -500246412961/20155392 x) 20511149/46656)) 841/108)) 4/29)
(+.f64 (.f64 x (+.f64 #s(literal -841/108 binary64) (.f64 x (+.f64 #s(literal -20511149/46656 binary64) (*.f64 x #s(literal -500246412961/20155392 binary64)))))) #s(literal -4/29 binary64))
(/ 1728/707281 x)
(/.f64 #s(literal 1728/707281 binary64) x)
(/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x)
(/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x)
(/.f64 (+.f64 #s(literal 1728/707281 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 746496/17249876309 binary64) (/.f64 #s(literal 322486272/420707233300201 binary64) x)))) x)
(/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (+ (* 746496/17249876309 (/ 1 x)) (* 139314069504/10260628712958602189 (/ 1 (pow x 3)))))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 322486272/420707233300201 binary64) (/.f64 #s(literal 139314069504/10260628712958602189 binary64) x)))) x)
(/ 1728/707281 x)
(/.f64 #s(literal 1728/707281 binary64) x)
(/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x))
(/.f64 (-.f64 #s(literal 1728/707281 binary64) (/.f64 (+.f64 #s(literal -746496/17249876309 binary64) (/.f64 #s(literal -322486272/420707233300201 binary64) x)) x)) x)
(* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (+ (/ 139314069504/10260628712958602189 (pow x 2)) (* 322486272/420707233300201 (/ 1 x)))) x)) 1728/707281) x))
(/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 (+.f64 #s(literal 746496/17249876309 binary64) (/.f64 (+.f64 #s(literal 322486272/420707233300201 binary64) (/.f64 #s(literal 139314069504/10260628712958602189 binary64) x)) x)) x)) x)

eval179.0ms (2.6%)

Compiler: Compiled 34526 to 2456 computations (92.9% saved)

prune158.0ms (2.3%)

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	1083	3	1086
Fresh	0	3	3
Picked	1	4	5
Done	0	2	2
Total	1084	12	1096

Accuracy

100.0%

Counts

1096 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.0%	(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
✓	68.1%	(/.f64 (-.f64 (.f64 (.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x) x) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
▶	28.1%	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (*.f64 x #s(literal -841/108 binary64)))
▶	52.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
✓	48.1%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64))))
✓	48.8%	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
▶	48.1%	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64))))
▶	99.7%	(-.f64 (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)) (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
▶	28.1%	(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x))) (/.f64 #s(literal -108/841 binary64) x))
✓	52.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	48.3%	#s(literal 4/29 binary64)

Compiler

Compiled 194 to 146 computations (24.7% saved)

simplify158.0ms (2.3%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
✓	cost-diff	256	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (*.f64 x #s(literal -841/108 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
✓	cost-diff	256	(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x))) (/.f64 #s(literal -108/841 binary64) x))
✓	cost-diff	0	(*.f64 x #s(literal -29/27 binary64))
✓	cost-diff	0	(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 108/841 binary64) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
✓	cost-diff	0	(*.f64 x #s(literal 707281/11664 binary64))
✓	cost-diff	128	(/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)
✓	cost-diff	128	(/.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x))
✓	cost-diff	128	(-.f64 (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)) (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))

Rules

1810×	`sum3-define`
1764×	`-lowering-.f32`
1764×	`-lowering-.f64`
1440×	`fnmadd-define`
1156×	`/-lowering-/.f32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	31	140
1	58	133
2	103	132
3	171	129
4	300	127
5	500	125
6	1035	124
7	3102	124
8	7555	124
0	8638	124

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(- (/ (* x 707281/11664) (/ (+ (* x 841/108) -4/29) x)) (/ 16/841 (+ (* x 841/108) -4/29)))
(/ (* x 707281/11664) (/ (+ (* x 841/108) -4/29) x))
(* x 707281/11664)
x
707281/11664
(/ (+ (* x 841/108) -4/29) x)
(+ (* x 841/108) -4/29)
(* x 841/108)
841/108
-4/29
(/ 16/841 (+ (* x 841/108) -4/29))
16/841
(/ 1 (/ 108/841 x))
1
(/ 108/841 x)
108/841
x
(/ 64/24389 (+ 16/841 (* x -29/27)))
64/24389
(+ 16/841 (* x -29/27))
16/841
(* x -29/27)
x
-29/27
(* (+ 16/841 (* -707281/11664 (* x x))) (/ -108/841 x))
(+ 16/841 (* -707281/11664 (* x x)))
16/841
(* -707281/11664 (* x x))
-707281/11664
(* x x)
x
(/ -108/841 x)
-108/841
(/ (+ 16/841 (* -707281/11664 (* x x))) (* x -841/108))
(+ 16/841 (* -707281/11664 (* x x)))
16/841
(* -707281/11664 (* x x))
-707281/11664
(* x x)
x
(* x -841/108)
-841/108

Outputs
(- (/ (* x 707281/11664) (/ (+ (* x 841/108) -4/29) x)) (/ 16/841 (+ (* x 841/108) -4/29)))
(+.f64 (/.f64 (*.f64 x #s(literal 707281/11664 binary64)) (+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))) (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal 4/29 binary64))))
(/ (* x 707281/11664) (/ (+ (* x 841/108) -4/29) x))
(/.f64 (*.f64 x #s(literal 707281/11664 binary64)) (+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x)))
(* x 707281/11664)
(*.f64 x #s(literal 707281/11664 binary64))
x
707281/11664
#s(literal 707281/11664 binary64)
(/ (+ (* x 841/108) -4/29) x)
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
(+ (* x 841/108) -4/29)
(+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))
(* x 841/108)
(/.f64 x #s(literal 108/841 binary64))
841/108
#s(literal 841/108 binary64)
-4/29
#s(literal -4/29 binary64)
(/ 16/841 (+ (* x 841/108) -4/29))
(/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))
16/841
#s(literal 16/841 binary64)
(/ 1 (/ 108/841 x))
(/.f64 x #s(literal 108/841 binary64))
1
#s(literal 1 binary64)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
108/841
#s(literal 108/841 binary64)
x
(/ 64/24389 (+ 16/841 (* x -29/27)))
(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64))))
64/24389
#s(literal 64/24389 binary64)
(+ 16/841 (* x -29/27))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
16/841
#s(literal 16/841 binary64)
(* x -29/27)
(*.f64 x #s(literal -29/27 binary64))
x
-29/27
#s(literal -29/27 binary64)
(* (+ 16/841 (* -707281/11664 (* x x))) (/ -108/841 x))
(+.f64 (/.f64 x #s(literal 108/841 binary64)) (/.f64 #s(literal -1728/707281 binary64) x))
(+ 16/841 (* -707281/11664 (* x x)))
(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
16/841
#s(literal 16/841 binary64)
(* -707281/11664 (* x x))
(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
-707281/11664
#s(literal -707281/11664 binary64)
(* x x)
(*.f64 x x)
x
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
-108/841
#s(literal -108/841 binary64)
(/ (+ 16/841 (* -707281/11664 (* x x))) (* x -841/108))
(+.f64 (/.f64 x #s(literal 108/841 binary64)) (/.f64 #s(literal -1728/707281 binary64) x))
(+ 16/841 (* -707281/11664 (* x x)))
(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
16/841
#s(literal 16/841 binary64)
(* -707281/11664 (* x x))
(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
-707281/11664
#s(literal -707281/11664 binary64)
(* x x)
(*.f64 x x)
x
(* x -841/108)
(/.f64 x #s(literal -108/841 binary64))
-841/108
#s(literal -841/108 binary64)

localize245.0ms (3.6%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
✓	accuracy	99.8%	(*.f64 x #s(literal -841/108 binary64))
✓	accuracy	99.7%	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	accuracy	75.3%	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (*.f64 x #s(literal -841/108 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
✓	accuracy	99.7%	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	accuracy	99.6%	(/.f64 #s(literal -108/841 binary64) x)
✓	accuracy	75.4%	(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x))) (/.f64 #s(literal -108/841 binary64) x))
✓	accuracy	99.9%	(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
✓	accuracy	99.5%	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64))))
✓	accuracy	99.0%	(*.f64 x #s(literal -29/27 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 108/841 binary64) x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
✓	accuracy	99.7%	(/.f64 (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	99.7%	(/.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x))
✓	accuracy	99.5%	(/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)))

Results

177.0ms	255×	0	valid
4.0ms	1×	5	exit

Compiler

Compiled 158 to 32 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

...c/correct-round.rkt:119:19: 34.0ms (48.5% of total)

ival-mult: 16.0ms (22.8% of total)

ival-div: 14.0ms (20% of total)

ival-add: 4.0ms (5.7% of total)

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

backward-pass: 1.0ms (1.4% of total)

const: 0.0ms (0% of total)

series7.0ms (0.1%)

Counts

17 → 204

Calls

Call 1

Inputs
#<alt (- (/ (* x 707281/11664) (/ (+ (* x 841/108) -4/29) x)) (/ 16/841 (+ (* x 841/108) -4/29)))>
#<alt (/ (* x 707281/11664) (/ (+ (* x 841/108) -4/29) x))>
#<alt (/ (+ (* x 841/108) -4/29) x)>
#<alt (* x 707281/11664)>
#<alt (/ 1 (/ 108/841 x))>
#<alt (/ 108/841 x)>
#<alt (/ 64/24389 (+ 16/841 (* x -29/27)))>
#<alt (+ 16/841 (* x -29/27))>
#<alt (* x -29/27)>
#<alt (* (+ 16/841 (* -707281/11664 (* x x))) (/ -108/841 x))>
#<alt (+ 16/841 (* -707281/11664 (* x x)))>
#<alt (* -707281/11664 (* x x))>
#<alt (* x x)>
#<alt (/ (+ 16/841 (* -707281/11664 (* x x))) (* x -841/108))>
#<alt (/ 16/841 (+ (* x 841/108) -4/29))>
#<alt (/ -108/841 x)>
#<alt (* x -841/108)>

Outputs
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* -20511149/46656 (pow x 2))>
#<alt (* (pow x 2) (- (* -500246412961/20155392 x) 20511149/46656))>
#<alt (* (pow x 2) (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656))>
#<alt (* (pow x 2) (- (* x (- (* x (- (* -297558232675799463481/3761479876608 x) 12200509765705829/8707129344)) 500246412961/20155392)) 20511149/46656))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x)))))>
#<alt (* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 4/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3)))))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 4/29 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 4/29 (* 1728/707281 (/ 1 x))) x)) 841/108)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 4/29 (+ (/ 746496/17249876309 (pow x 2)) (* 1728/707281 (/ 1 x)))) x)) 841/108)))>
#<alt (/ -4/29 x)>
#<alt (/ (- (* 841/108 x) 4/29) x)>
#<alt (/ (- (* 841/108 x) 4/29) x)>
#<alt (/ (- (* 841/108 x) 4/29) x)>
#<alt 841/108>
#<alt (- 841/108 (* 4/29 (/ 1 x)))>
#<alt (- 841/108 (* 4/29 (/ 1 x)))>
#<alt (- 841/108 (* 4/29 (/ 1 x)))>
#<alt 841/108>
#<alt (- 841/108 (* 4/29 (/ 1 x)))>
#<alt (- 841/108 (* 4/29 (/ 1 x)))>
#<alt (- 841/108 (* 4/29 (/ 1 x)))>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 707281/11664 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (* 841/108 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt (/ 108/841 x)>
#<alt 4/29>
#<alt (+ 4/29 (* 841/108 x))>
#<alt (+ 4/29 (* x (+ 841/108 (* 20511149/46656 x))))>
#<alt (+ 4/29 (* x (+ 841/108 (* x (+ 20511149/46656 (* 500246412961/20155392 x))))))>
#<alt (/ -1728/707281 x)>
#<alt (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x)>
#<alt (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) (pow x 2))) (+ 1728/707281 (* 746496/17249876309 (/ 1 x)))) x)>
#<alt (/ -1728/707281 x)>
#<alt (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x))>
#<alt (* -1 (/ (+ 1728/707281 (* -1 (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) x)) 746496/17249876309) x))) x))>
#<alt 16/841>
#<alt (+ 16/841 (* -29/27 x))>
#<alt (+ 16/841 (* -29/27 x))>
#<alt (+ 16/841 (* -29/27 x))>
#<alt (* -29/27 x)>
#<alt (* x (- (* 16/841 (/ 1 x)) 29/27))>
#<alt (* x (- (* 16/841 (/ 1 x)) 29/27))>
#<alt (* x (- (* 16/841 (/ 1 x)) 29/27))>
#<alt (* -29/27 x)>
#<alt (* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))>
#<alt (* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))>
#<alt (* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (* -29/27 x)>
#<alt (/ -1728/707281 x)>
#<alt (/ (- (* 841/108 (pow x 2)) 1728/707281) x)>
#<alt (/ (- (* 841/108 (pow x 2)) 1728/707281) x)>
#<alt (/ (- (* 841/108 (pow x 2)) 1728/707281) x)>
#<alt (* 841/108 x)>
#<alt (* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))>
#<alt (* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))>
#<alt (* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))>
#<alt (* 841/108 x)>
#<alt (* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))>
#<alt (* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))>
#<alt (* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))>
#<alt 16/841>
#<alt (+ 16/841 (* -707281/11664 (pow x 2)))>
#<alt (+ 16/841 (* -707281/11664 (pow x 2)))>
#<alt (+ 16/841 (* -707281/11664 (pow x 2)))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (* -707281/11664 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ -1728/707281 x)>
#<alt (/ (- (* 841/108 (pow x 2)) 1728/707281) x)>
#<alt (/ (- (* 841/108 (pow x 2)) 1728/707281) x)>
#<alt (/ (- (* 841/108 (pow x 2)) 1728/707281) x)>
#<alt (* 841/108 x)>
#<alt (* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))>
#<alt (* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))>
#<alt (* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))>
#<alt (* 841/108 x)>
#<alt (* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))>
#<alt (* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))>
#<alt (* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))>
#<alt -4/29>
#<alt (- (* -841/108 x) 4/29)>
#<alt (- (* x (- (* -20511149/46656 x) 841/108)) 4/29)>
#<alt (- (* x (- (* x (- (* -500246412961/20155392 x) 20511149/46656)) 841/108)) 4/29)>
#<alt (/ 1728/707281 x)>
#<alt (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)>
#<alt (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x)>
#<alt (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (+ (* 746496/17249876309 (/ 1 x)) (* 139314069504/10260628712958602189 (/ 1 (pow x 3)))))) x)>
#<alt (/ 1728/707281 x)>
#<alt (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (+ (/ 139314069504/10260628712958602189 (pow x 2)) (* 322486272/420707233300201 (/ 1 x)))) x)) 1728/707281) x))>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (/ -108/841 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>
#<alt (* -841/108 x)>

Calls

51 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(* (+ 16/841 (* -707281/11664 (* x x))) (/ -108/841 x))
0.0ms	x	@	0	(* (+ 16/841 (* -707281/11664 (* x x))) (/ -108/841 x))
0.0ms	x	@	-inf	(* (+ 16/841 (* -707281/11664 (* x x))) (/ -108/841 x))
0.0ms	x	@	0	(/ 108/841 x)
0.0ms	x	@	-inf	(* x -29/27)

rewrite637.0ms (9.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4662×	`-lowering-.f32`
4662×	`-lowering-.f64`
4028×	`/-lowering-/.f32`
4028×	`/-lowering-/.f64`
1594×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	101
1	169	95
2	1572	91
0	8513	91

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 685

Calls

Call 1

Inputs
(- (/ (* x 707281/11664) (/ (+ (* x 841/108) -4/29) x)) (/ 16/841 (+ (* x 841/108) -4/29)))
(/ (* x 707281/11664) (/ (+ (* x 841/108) -4/29) x))
(/ (+ (* x 841/108) -4/29) x)
(* x 707281/11664)
(/ 1 (/ 108/841 x))
(/ 108/841 x)
(/ 64/24389 (+ 16/841 (* x -29/27)))
(+ 16/841 (* x -29/27))
(* x -29/27)
(* (+ 16/841 (* -707281/11664 (* x x))) (/ -108/841 x))
(+ 16/841 (* -707281/11664 (* x x)))
(* -707281/11664 (* x x))
(* x x)
(/ (+ 16/841 (* -707281/11664 (* x x))) (* x -841/108))
(/ 16/841 (+ (* x 841/108) -4/29))
(/ -108/841 x)
(* x -841/108)

Outputs
(+.f64 (/.f64 (.f64 (.f64 x #s(literal 707281/11664 binary64)) x) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (/.f64 #s(literal -16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(+.f64 (/.f64 (-.f64 (.f64 (.f64 x #s(literal 707281/11664 binary64)) x) #s(literal 16/841 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (+.f64 (*.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) #s(literal 16/841 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(+.f64 (/.f64 (-.f64 (.f64 (.f64 x #s(literal 707281/11664 binary64)) x) #s(literal 16/841 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (fma.f64 #s(literal -16/841 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(+.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (/.f64 (.f64 (.f64 x #s(literal 707281/11664 binary64)) x) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(+.f64 (fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (neg.f64 (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64))))
(+.f64 (fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) #s(literal -16/841 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal -16/841 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) #s(literal -16/841 binary64))))
(+.f64 (fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (neg.f64 (.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 16/841 binary64) (+.f64 #s(literal -64/24389 binary64) (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64))))))) (fma.f64 (neg.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64))))) (/.f64 #s(literal 16/841 binary64) (+.f64 #s(literal -64/24389 binary64) (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64)))) (.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))) (/.f64 #s(literal 16/841 binary64) (+.f64 #s(literal -64/24389 binary64) (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64)))))))
(+.f64 (fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (neg.f64 (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)))))) (fma.f64 (neg.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64)) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 707281/11664 binary64) (*.f64 x x)) #s(literal -16/841 binary64))))))
(+.f64 (fma.f64 #s(literal 707281/11664 binary64) (.f64 x (/.f64 x (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (neg.f64 (.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 1 binary64))))
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(/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))
(/.f64 #s(literal 16/841 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -16/841 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(/.f64 #s(literal -16/841 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))))
(pow.f64 (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 16/841 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(*.f64 #s(literal -16/841 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 16/841 binary64))
(.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 #s(literal -64/24389 binary64) (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64)))) (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (-.f64 #s(literal 16/841 binary64) (.f64 x #s(literal -29/27 binary64)))))
(.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 707281/11664 binary64) (*.f64 x x)) #s(literal -16/841 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 x #s(literal -108/841 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 108/841 binary64) x))
(neg.f64 (/.f64 #s(literal 108/841 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x #s(literal -108/841 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x #s(literal 108/841 binary64))))
(/.f64 #s(literal 108/841 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 108/841 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 #s(literal -108/841 binary64) x)
(/.f64 #s(literal -108/841 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal -1 binary64) (/.f64 x #s(literal 108/841 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (/.f64 x #s(literal 108/841 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -841/108 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 841/108 binary64))
(pow.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (neg.f64 (/.f64 x #s(literal 108/841 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -108/841 binary64) x))
(*.f64 #s(literal 108/841 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 #s(literal 108/841 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -108/841 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 108/841 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -108/841 binary64))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal 108/841 binary64)))
(/.f64 x #s(literal -108/841 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -108/841 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 108/841 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 108/841 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal -108/841 binary64))
(pow.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -108/841 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal -841/108 binary64))
(*.f64 #s(literal -841/108 binary64) x)

simplify279.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

2286×	`fma-lowering-fma.f32`
2286×	`fma-lowering-fma.f64`
1992×	`-lowering-.f32`
1992×	`-lowering-.f64`
1990×	`fmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	172	1047
1	484	935
2	1205	914
3	2820	883
4	5651	881
0	8690	881

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(+ 4/29 (* 841/108 x))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* -20511149/46656 (pow x 2))
(* (pow x 2) (- (* -500246412961/20155392 x) 20511149/46656))
(* (pow x 2) (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656))
(* (pow x 2) (- (* x (- (* x (- (* -297558232675799463481/3761479876608 x) 12200509765705829/8707129344)) 500246412961/20155392)) 20511149/46656))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x)))))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 4/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3)))))))
(* 841/108 x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (+ 4/29 (* 1728/707281 (/ 1 x))) x)) 841/108)))
(* -1 (* x (- (* -1 (/ (+ 4/29 (+ (/ 746496/17249876309 (pow x 2)) (* 1728/707281 (/ 1 x)))) x)) 841/108)))
(/ -4/29 x)
(/ (- (* 841/108 x) 4/29) x)
(/ (- (* 841/108 x) 4/29) x)
(/ (- (* 841/108 x) 4/29) x)
841/108
(- 841/108 (* 4/29 (/ 1 x)))
(- 841/108 (* 4/29 (/ 1 x)))
(- 841/108 (* 4/29 (/ 1 x)))
841/108
(- 841/108 (* 4/29 (/ 1 x)))
(- 841/108 (* 4/29 (/ 1 x)))
(- 841/108 (* 4/29 (/ 1 x)))
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 707281/11664 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(* 841/108 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
(/ 108/841 x)
4/29
(+ 4/29 (* 841/108 x))
(+ 4/29 (* x (+ 841/108 (* 20511149/46656 x))))
(+ 4/29 (* x (+ 841/108 (* x (+ 20511149/46656 (* 500246412961/20155392 x))))))
(/ -1728/707281 x)
(* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x)
(/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) (pow x 2))) (+ 1728/707281 (* 746496/17249876309 (/ 1 x)))) x)
(/ -1728/707281 x)
(* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))
(* -1 (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x))
(* -1 (/ (+ 1728/707281 (* -1 (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) x)) 746496/17249876309) x))) x))
16/841
(+ 16/841 (* -29/27 x))
(+ 16/841 (* -29/27 x))
(+ 16/841 (* -29/27 x))
(* -29/27 x)
(* x (- (* 16/841 (/ 1 x)) 29/27))
(* x (- (* 16/841 (/ 1 x)) 29/27))
(* x (- (* 16/841 (/ 1 x)) 29/27))
(* -29/27 x)
(* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))
(* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))
(* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(* -29/27 x)
(/ -1728/707281 x)
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(* 841/108 x)
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(* 841/108 x)
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
16/841
(+ 16/841 (* -707281/11664 (pow x 2)))
(+ 16/841 (* -707281/11664 (pow x 2)))
(+ 16/841 (* -707281/11664 (pow x 2)))
(* -707281/11664 (pow x 2))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* -707281/11664 (pow x 2))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(* -707281/11664 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ -1728/707281 x)
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(* 841/108 x)
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(* 841/108 x)
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
-4/29
(- (* -841/108 x) 4/29)
(- (* x (- (* -20511149/46656 x) 841/108)) 4/29)
(- (* x (- (* x (- (* -500246412961/20155392 x) 20511149/46656)) 841/108)) 4/29)
(/ 1728/707281 x)
(/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)
(/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x)
(/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (+ (* 746496/17249876309 (/ 1 x)) (* 139314069504/10260628712958602189 (/ 1 (pow x 3)))))) x)
(/ 1728/707281 x)
(/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x))
(* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (+ (/ 139314069504/10260628712958602189 (pow x 2)) (* 322486272/420707233300201 (/ 1 x)))) x)) 1728/707281) x))
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(/ -108/841 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)
(* -841/108 x)

Outputs
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* -20511149/46656 (pow x 2))
(.f64 #s(literal -20511149/46656 binary64) (.f64 x x))
(* (pow x 2) (- (* -500246412961/20155392 x) 20511149/46656))
(.f64 (.f64 x x) (+.f64 #s(literal -20511149/46656 binary64) (*.f64 x #s(literal -500246412961/20155392 binary64))))
(* (pow x 2) (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656))
(.f64 (.f64 x x) (+.f64 #s(literal -20511149/46656 binary64) (.f64 x (+.f64 #s(literal -500246412961/20155392 binary64) (.f64 x #s(literal -12200509765705829/8707129344 binary64))))))
(* (pow x 2) (- (* x (- (* x (- (* -297558232675799463481/3761479876608 x) 12200509765705829/8707129344)) 500246412961/20155392)) 20511149/46656))
(.f64 (.f64 x x) (+.f64 #s(literal -20511149/46656 binary64) (.f64 x (+.f64 #s(literal -500246412961/20155392 binary64) (.f64 x (+.f64 #s(literal -12200509765705829/8707129344 binary64) (*.f64 x #s(literal -297558232675799463481/3761479876608 binary64))))))))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x)))))
(+.f64 #s(literal 4/29 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal 1728/707281 binary64) x)))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 4/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3)))))))
(+.f64 #s(literal 4/29 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) (.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)))))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(* -1 (* x (- (* -1 (/ (+ 4/29 (* 1728/707281 (/ 1 x))) x)) 841/108)))
(-.f64 (*.f64 #s(literal 841/108 binary64) x) (+.f64 #s(literal -4/29 binary64) (/.f64 #s(literal -1728/707281 binary64) x)))
(* -1 (* x (- (* -1 (/ (+ 4/29 (+ (/ 746496/17249876309 (pow x 2)) (* 1728/707281 (/ 1 x)))) x)) 841/108)))
(-.f64 (*.f64 #s(literal 841/108 binary64) x) (+.f64 #s(literal -4/29 binary64) (/.f64 (+.f64 #s(literal -1728/707281 binary64) (/.f64 #s(literal -746496/17249876309 binary64) x)) x)))
(/ -4/29 x)
(/.f64 #s(literal -4/29 binary64) x)
(/ (- (* 841/108 x) 4/29) x)
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
(/ (- (* 841/108 x) 4/29) x)
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
(/ (- (* 841/108 x) 4/29) x)
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
841/108
#s(literal 841/108 binary64)
(- 841/108 (* 4/29 (/ 1 x)))
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
(- 841/108 (* 4/29 (/ 1 x)))
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
(- 841/108 (* 4/29 (/ 1 x)))
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
841/108
#s(literal 841/108 binary64)
(- 841/108 (* 4/29 (/ 1 x)))
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
(- 841/108 (* 4/29 (/ 1 x)))
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
(- 841/108 (* 4/29 (/ 1 x)))
(+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
(/ 108/841 x)
(/.f64 #s(literal 108/841 binary64) x)
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x))
(+ 4/29 (* x (+ 841/108 (* 20511149/46656 x))))
(+.f64 #s(literal 4/29 binary64) (.f64 x (+.f64 #s(literal 841/108 binary64) (.f64 x #s(literal 20511149/46656 binary64)))))
(+ 4/29 (* x (+ 841/108 (* x (+ 20511149/46656 (* 500246412961/20155392 x))))))
(+.f64 #s(literal 4/29 binary64) (.f64 x (+.f64 #s(literal 841/108 binary64) (.f64 x (+.f64 #s(literal 20511149/46656 binary64) (*.f64 x #s(literal 500246412961/20155392 binary64)))))))
(/ -1728/707281 x)
(/.f64 #s(literal -1728/707281 binary64) x)
(* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -1728/707281 binary64) (/.f64 #s(literal -746496/17249876309 binary64) x)) x)
(/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x)
(/.f64 (+.f64 #s(literal -1728/707281 binary64) (/.f64 (+.f64 #s(literal -746496/17249876309 binary64) (/.f64 #s(literal -322486272/420707233300201 binary64) x)) x)) x)
(/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) (pow x 2))) (+ 1728/707281 (* 746496/17249876309 (/ 1 x)))) x)
(/.f64 (+.f64 #s(literal -1728/707281 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -322486272/420707233300201 binary64) (/.f64 #s(literal -139314069504/10260628712958602189 binary64) x)) x) #s(literal -746496/17249876309 binary64)) x)) x)
(/ -1728/707281 x)
(/.f64 #s(literal -1728/707281 binary64) x)
(* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -1728/707281 binary64) (/.f64 #s(literal -746496/17249876309 binary64) x)) x)
(* -1 (/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x))
(/.f64 (-.f64 #s(literal -1728/707281 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 746496/17249876309 binary64) (/.f64 #s(literal 322486272/420707233300201 binary64) x)))) x)
(* -1 (/ (+ 1728/707281 (* -1 (/ (- (* -1 (/ (+ 322486272/420707233300201 (* 139314069504/10260628712958602189 (/ 1 x))) x)) 746496/17249876309) x))) x))
(/.f64 (+.f64 #s(literal -1728/707281 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -322486272/420707233300201 binary64) (/.f64 #s(literal -139314069504/10260628712958602189 binary64) x)) x) #s(literal -746496/17249876309 binary64)) x)) x)
16/841
#s(literal 16/841 binary64)
(+ 16/841 (* -29/27 x))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(+ 16/841 (* -29/27 x))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(+ 16/841 (* -29/27 x))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* x (- (* 16/841 (/ 1 x)) 29/27))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(* x (- (* 16/841 (/ 1 x)) 29/27))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(* x (- (* 16/841 (/ 1 x)) 29/27))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(* -1 (* x (- 29/27 (* 16/841 (/ 1 x)))))
(+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64)))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(* -29/27 x)
(*.f64 x #s(literal -29/27 binary64))
(/ -1728/707281 x)
(/.f64 #s(literal -1728/707281 binary64) x)
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
16/841
#s(literal 16/841 binary64)
(+ 16/841 (* -707281/11664 (pow x 2)))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(+ 16/841 (* -707281/11664 (pow x 2)))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(+ 16/841 (* -707281/11664 (pow x 2)))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 (.f64 x x) #s(literal -707281/11664 binary64)))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(* -707281/11664 (pow x 2))
(.f64 (.f64 x x) #s(literal -707281/11664 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ -1728/707281 x)
(/.f64 #s(literal -1728/707281 binary64) x)
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(/ (- (* 841/108 (pow x 2)) 1728/707281) x)
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* x (- 841/108 (* 1728/707281 (/ 1 (pow x 2)))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
(* -1 (* x (- (* 1728/707281 (/ 1 (pow x 2))) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) (/.f64 #s(literal -1728/707281 binary64) x))
-4/29
#s(literal -4/29 binary64)
(- (* -841/108 x) 4/29)
(+.f64 #s(literal -4/29 binary64) (*.f64 x #s(literal -841/108 binary64)))
(- (* x (- (* -20511149/46656 x) 841/108)) 4/29)
(+.f64 #s(literal -4/29 binary64) (.f64 x (+.f64 #s(literal -841/108 binary64) (.f64 x #s(literal -20511149/46656 binary64)))))
(- (* x (- (* x (- (* -500246412961/20155392 x) 20511149/46656)) 841/108)) 4/29)
(+.f64 #s(literal -4/29 binary64) (.f64 x (+.f64 #s(literal -841/108 binary64) (.f64 x (+.f64 #s(literal -20511149/46656 binary64) (*.f64 x #s(literal -500246412961/20155392 binary64)))))))
(/ 1728/707281 x)
(/.f64 #s(literal 1728/707281 binary64) x)
(/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x)
(/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (* 746496/17249876309 (/ 1 x)))) x)
(/.f64 (+.f64 #s(literal 1728/707281 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 746496/17249876309 binary64) (/.f64 #s(literal 322486272/420707233300201 binary64) x)))) x)
(/ (+ 1728/707281 (+ (/ 322486272/420707233300201 (pow x 2)) (+ (* 746496/17249876309 (/ 1 x)) (* 139314069504/10260628712958602189 (/ 1 (pow x 3)))))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 322486272/420707233300201 binary64) (/.f64 #s(literal 139314069504/10260628712958602189 binary64) x)))) x)
(/ 1728/707281 x)
(/.f64 #s(literal 1728/707281 binary64) x)
(/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (* 322486272/420707233300201 (/ 1 x))) x)) 1728/707281) x))
(/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 (+.f64 #s(literal 746496/17249876309 binary64) (/.f64 #s(literal 322486272/420707233300201 binary64) x)) x)) x)
(* -1 (/ (- (* -1 (/ (+ 746496/17249876309 (+ (/ 139314069504/10260628712958602189 (pow x 2)) (* 322486272/420707233300201 (/ 1 x)))) x)) 1728/707281) x))
(/.f64 (-.f64 #s(literal 1728/707281 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -322486272/420707233300201 binary64) (/.f64 #s(literal -139314069504/10260628712958602189 binary64) x)) x) #s(literal -746496/17249876309 binary64)) x)) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(/ -108/841 x)
(/.f64 #s(literal -108/841 binary64) x)
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))
(* -841/108 x)
(*.f64 x #s(literal -841/108 binary64))

eval180.0ms (2.7%)

Compiler: Compiled 21724 to 1790 computations (91.8% saved)

prune103.0ms (1.5%)

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	960	2	962
Fresh	1	0	1
Picked	4	1	5
Done	0	6	6
Total	965	9	974

Accuracy

100.0%

Counts

974 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.1%	(/.f64 (-.f64 (.f64 (.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x) x) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
	52.7%	(/.f64 x #s(literal 108/841 binary64))
✓	48.1%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64))))
✓	48.8%	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
✓	48.1%	(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64))))
	99.8%	(-.f64 (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
✓	52.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	48.3%	#s(literal 4/29 binary64)

Compiler

Compiled 401 to 162 computations (59.6% saved)

regimes24.0ms (0.4%)

Counts

25 → 1

Calls

Call 1

Inputs
#s(literal 4/29 binary64)
(*.f64 #s(literal 841/108 binary64) x)
(/.f64 x #s(literal 108/841 binary64))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (*.f64 x #s(literal -29/27 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 29/4 binary64) (*.f64 x #s(literal -707281/1728 binary64))))
(+.f64 (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) (/.f64 #s(literal 4 binary64) #s(literal 29 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))))
(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x))) (/.f64 #s(literal -108/841 binary64) x))
(/.f64 #s(literal 64/24389 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (*.f64 x #s(literal -841/108 binary64)))
(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
(/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
(.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (.f64 x #s(literal -841/108 binary64)))))
(-.f64 (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 #s(literal 841/108 binary64) (/.f64 #s(literal -4/29 binary64) x))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))
(-.f64 (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 (+.f64 (.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64)) x)) (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 594823321/1259712 binary64) (.f64 x (.f64 x x))) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x #s(literal 594823321/1259712 binary64)) x) x) #s(literal -64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))))
(/.f64 (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64)) (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64))) (+.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64))))
(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))

Outputs
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))

Calls

3 calls:

9.0ms	x
7.0ms	(*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x)
7.0ms	(+.f64 (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) (/.f64 #s(literal 4 binary64) #s(literal 29 binary64)))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(+.f64 (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) (/.f64 #s(literal 4 binary64) #s(literal 29 binary64)))`
99.9%	1	`(*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x)`

Compiler

Compiled 18 to 15 computations (16.7% saved)

regimes2.0ms (0%)

Counts

3 → 3

Calls

Call 1

Inputs
#s(literal 4/29 binary64)
(*.f64 #s(literal 841/108 binary64) x)
(/.f64 x #s(literal 108/841 binary64))

Outputs
(*.f64 #s(literal 841/108 binary64) x)
#s(literal 4/29 binary64)
(*.f64 #s(literal 841/108 binary64) x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
97.3%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 4/29 binary64)

Outputs
#s(literal 4/29 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
48.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch29.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	4.475494311443444e-5	0.30518365890838833
13.0ms	-19.912070981437754	-0.015598077727842581

Results

15.0ms

256×

valid

Compiler

Compiled 142 to 124 computations (12.7% saved)

Precisions

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

ival-div: 4.0ms (51.3% of total)

ival-mult: 2.0ms (25.7% of total)

ival-add: 1.0ms (12.8% of total)

const: 1.0ms (12.8% of total)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	16	19

Stop Event

1×

saturated

Calls

Call 1

Inputs

(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))

(if (<=.f64 x #s(literal -5188146770730811/288230376151711744 binary64)) (*.f64 #s(literal 841/108 binary64) x) (if (<=.f64 x #s(literal 1224979098644775/72057594037927936 binary64)) #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x)))

#s(literal 4/29 binary64)

Outputs

(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))

(if (<=.f64 x #s(literal -5188146770730811/288230376151711744 binary64)) (*.f64 #s(literal 841/108 binary64) x) (if (<=.f64 x #s(literal 1224979098644775/72057594037927936 binary64)) #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x)))

#s(literal 4/29 binary64)

soundness16.0ms (0.2%)

Rules

44×	`-lowering-.f32`
44×	`-lowering-.f64`
40×	`fma-define`
28×	`fma-lowering-fma.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	15	4
0	15	4
0	10	88
1	25	79
2	46	79
3	68	79
4	68	79
5	83	79
6	91	79
7	97	79
8	99	79
0	99	79

Stop Event

1×	fuel
1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Compiler

Compiled 54 to 38 computations (29.6% saved)

preprocess47.0ms (0.7%)

Compiler: Compiled 64 to 40 computations (37.5% saved)

Iter	Nodes	Cost
0	15	15
1	32	13
2	67	12
3	153	12
4	262	12
5	385	12
6	477	12
7	501	12
8	515	12
9	519	12
0	11	4
1	14	4
2	15	4
0	15	4

Iter	Nodes	Cost
0	11	4
1	14	4
2	15	4
0	15	4
0	10	88
1	25	79
2	46	79
3	68	79
4	68	79
5	83	79
6	91	79
7	97	79
8	99	79
0	99	79

Iter	Nodes	Cost
0	15	15
1	32	13
2	67	12
3	153	12
4	262	12
5	385	12
6	477	12
7	501	12
8	515	12
9	519	12
0	11	4
1	14	4
2	15	4
0	15	4

Iter	Nodes	Cost
0	11	4
1	14	4
2	15	4
0	15	4
0	10	88
1	25	79
2	46	79
3	68	79
4	68	79
5	83	79
6	91	79
7	97	79
8	99	79
0	99	79

analyze0.0ms (0%)

sample771.0ms (11.4%)

preprocess24.0ms (0.4%)

explain95.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize45.0ms (0.7%)

series2.0ms (0%)

rewrite533.0ms (7.9%)

simplify10.0ms (0.1%)

eval23.0ms (0.3%)

prune56.0ms (0.8%)

simplify214.0ms (3.1%)

localize235.0ms (3.5%)

series14.0ms (0.2%)

rewrite417.0ms (6.1%)

simplify232.0ms (3.4%)

eval391.0ms (5.8%)

prune104.0ms (1.5%)

simplify289.0ms (4.3%)

localize482.0ms (7.1%)

series12.0ms (0.2%)

rewrite451.0ms (6.6%)

simplify311.0ms (4.6%)

eval179.0ms (2.6%)

prune158.0ms (2.3%)

simplify158.0ms (2.3%)

localize245.0ms (3.6%)

series7.0ms (0.1%)

rewrite637.0ms (9.4%)

simplify279.0ms (4.1%)

eval180.0ms (2.7%)

prune103.0ms (1.5%)

regimes24.0ms (0.4%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch29.0ms (0.4%)

simplify8.0ms (0.1%)

soundness16.0ms (0.2%)

preprocess47.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	15
1	32	13
2	67	12
3	153	12
4	262	12
5	385	12
6	477	12
7	501	12
8	515	12
9	519	12
0	11	4
1	14	4
2	15	4
0	15	4

Iter	Nodes	Cost
0	11	4
1	14	4
2	15	4
0	15	4
0	10	88
1	25	79
2	46	79
3	68	79
4	68	79
5	83	79
6	91	79
7	97	79
8	99	79
0	99	79