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)

sample688.0ms (10.5%)

Results

489.0ms	8251×	0	valid
0.0ms	3×	2	valid
0.0ms	2×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 295.0ms

ival-div: 134.0ms (45.5% of total)

ival-mult: 97.0ms (32.9% of total)

ival-add: 42.0ms (14.3% of total)

const: 18.0ms (6.1% of total)

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

Bogosity

preprocess25.0ms (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)

explain75.0ms (1.2%)

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

39.0ms

512×

valid

Compiler

Compiled 64 to 29 computations (54.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-div: 8.0ms (50.5% of total)

ival-mult: 4.0ms (25.3% of total)

ival-add: 3.0ms (18.9% of total)

const: 1.0ms (6.3% 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)

simplify6.0ms (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)

localize27.0ms (0.4%)

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

20.0ms

256×

valid

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 (66.6% of total)

ival-mult: 2.0ms (16.7% of total)

ival-add: 1.0ms (8.3% of total)

const: 0.0ms (0% of total)

backward-pass: 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)

rewrite313.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4122×	`/-lowering-/.f32`
4122×	`/-lowering-/.f64`
3520×	`-lowering-.f32`
3520×	`-lowering-.f64`
1716×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	23	7
2	156	7
3	1396	7
0	8162	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 193

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 #s(literal 707281/11664 binary64) (.f64 x x)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 #s(literal 0 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 #s(literal 841/108 binary64) x))) (neg.f64 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (-.f64 #s(literal 4/29 binary64) (.f64 #s(literal 841/108 binary64) x)))))
(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 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 #s(literal 0 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 #s(literal 0 binary64) (/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal 4/29 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.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 841/108 binary64) x) #s(literal 4/29 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal 0 binary64) (+.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 #s(literal 16/841 binary64) (-.f64 #s(literal 4/29 binary64) (.f64 #s(literal 841/108 binary64) x))) (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (-.f64 #s(literal 4/29 binary64) (.f64 #s(literal 841/108 binary64) x))))
(-.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 #s(literal 707281/11664 binary64) (.f64 x x)) #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 #s(literal 707281/11664 binary64) (.f64 x x)) #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 #s(literal 707281/11664 binary64) (.f64 x x)) #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 #s(literal 707281/11664 binary64) (.f64 x x)) #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 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal 16/841 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 #s(literal 707281/11664 binary64) (.f64 x x)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 #s(literal 707281/11664 binary64) (.f64 x x))))) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 #s(literal 707281/11664 binary64) (.f64 x x)))) (+.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 -4/29 binary64)) #s(literal 16/841 binary64))) (/.f64 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 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 -4/29 binary64)) #s(literal 16/841 binary64)))) (+.f64 (/.f64 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 #s(literal 707281/11664 binary64) (.f64 x x)))) (+.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 -4/29 binary64)) #s(literal 16/841 binary64))) (/.f64 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 #s(literal 707281/11664 binary64) (.f64 x x)))) (+.f64 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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 -4/29 binary64)) #s(literal 16/841 binary64))) (+.f64 (/.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (+.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))) (-.f64 #s(literal 0 binary64) (/.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))) (-.f64 #s(literal 0 binary64) (/.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))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(fma.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 #s(literal 0 binary64) (/.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))) (-.f64 #s(literal 0 binary64) (/.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 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #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 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #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 #s(literal 841/108 binary64) x))))
(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)))

simplify20.0ms (0.3%)

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)

eval26.0ms (0.4%)

Compiler: Compiled 7075 to 563 computations (92% saved)

prune36.0ms (0.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	208	9	217
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	208	10	218

Accuracy

100.0%

Counts

218 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
▶	98.9%	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
	66.7%	(/.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 841/108 binary64) x) #s(literal -4/29 binary64))) (+.f64 (.f64 #s(literal 707281/11664 binary64) (*.f64 x x)) #s(literal 16/841 binary64)))
	78.3%	(/.f64 (/.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 707281/11664 binary64) (*.f64 x x)) #s(literal -16/841 binary64))))
▶	69.0%	(/.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)))))
▶	79.2%	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 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))))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
	46.9%	(*.f64 #s(literal 841/108 binary64) x)
▶	54.2%	#s(literal 4/29 binary64)

Compiler

Compiled 278 to 197 computations (29.1% saved)

simplify162.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 707281/11664 binary64))
✓	cost-diff	0	(/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	cost-diff	128	(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
✓	cost-diff	6784	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
✓	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 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 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

1986×	`fmsub-define`
1934×	`fnmsub-define`
1766×	`fma-lowering-fma.f32`
1766×	`fma-lowering-fma.f64`
1618×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	165
1	85	162
2	169	162
3	295	162
4	499	162
5	984	162
6	2141	162
7	4277	162
8	6781	162
0	8042	162

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
(/ (+ (* 707281/11664 (* x x)) -16/841) (+ (* 841/108 x) -4/29))
(+ (* 707281/11664 (* x x)) -16/841)
(* 707281/11664 (* x x))
707281/11664
(* x x)
x
-16/841
(+ (* 841/108 x) -4/29)
(* 841/108 x)
841/108
-4/29
(/ (- (* 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
(+ (* x (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))) (- 0 (/ 16/841 (+ (* 841/108 x) -4/29))))
x
(/ (* x 707281/11664) (+ (* 841/108 x) -4/29))
(* x 707281/11664)
707281/11664
(+ (* 841/108 x) -4/29)
(* 841/108 x)
841/108
-4/29
(- 0 (/ 16/841 (+ (* 841/108 x) -4/29)))
0
(/ 16/841 (+ (* 841/108 x) -4/29))
16/841

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)
(/ (+ (* 707281/11664 (* x x)) -16/841) (+ (* 841/108 x) -4/29))
(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
(+ (* 707281/11664 (* x x)) -16/841)
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #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
-16/841
#s(literal -16/841 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)
-4/29
#s(literal -4/29 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)
(+ (* x (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))) (- 0 (/ 16/841 (+ (* 841/108 x) -4/29))))
(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
x
(/ (* x 707281/11664) (+ (* 841/108 x) -4/29))
(/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
(* x 707281/11664)
(*.f64 x #s(literal 707281/11664 binary64))
707281/11664
#s(literal 707281/11664 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)
-4/29
#s(literal -4/29 binary64)
(- 0 (/ 16/841 (+ (* 841/108 x) -4/29)))
(/.f64 #s(literal -16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
0
#s(literal 0 binary64)
(/ 16/841 (+ (* 841/108 x) -4/29))
(/.f64 #s(literal -16/841 binary64) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
16/841
#s(literal 16/841 binary64)

localize212.0ms (3.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	99.0%	(/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	accuracy	98.7%	(/.f64 (.f64 x #s(literal 707281/11664 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	99.7%	(.f64 #s(literal 594823321/1259712 binary64) (.f64 x (*.f64 x x)))
✓	accuracy	99.4%	(.f64 x (+.f64 (.f64 x #s(literal 707281/11664 binary64)) #s(literal -29/27 binary64)))
✓	accuracy	69.8%	(/.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	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)
✓	accuracy	99.7%	(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
✓	accuracy	79.1%	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	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)
✓	accuracy	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))))
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)))

Results

152.0ms

256×

valid

Compiler

Compiled 207 to 34 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

...c/correct-round.rkt:119:19: 30.0ms (33% of total)

ival-sub: 23.0ms (25.3% of total)

ival-mult: 15.0ms (16.5% of total)

ival-div: 10.0ms (11% of total)

ival-add: 9.0ms (9.9% of total)

compiled-spec: 4.0ms (4.4% of total)

const: 1.0ms (1.1% of total)

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

series18.0ms (0.3%)

Counts

19 → 228

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 (/ (+ (* 707281/11664 (* x x)) -16/841) (+ (* 841/108 x) -4/29))>
#<alt (+ (* 707281/11664 (* x x)) -16/841)>
#<alt (* 707281/11664 (* x x))>
#<alt (* x x)>
#<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 (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))) (- 0 (/ 16/841 (+ (* 841/108 x) -4/29))))>
#<alt (- 0 (/ 16/841 (+ (* 841/108 x) -4/29)))>
#<alt (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))>
#<alt (* x 707281/11664)>
#<alt (+ (* 841/108 x) -4/29)>
#<alt (* x (+ (* x 707281/11664) -29/27))>
#<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 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 (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (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 (* 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 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 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 (* -20511149/46656 x)>
#<alt (* x (- (* -500246412961/20155392 x) 20511149/46656))>
#<alt (* x (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656))>
#<alt (* x (- (* x (- (* x (- (* -297558232675799463481/3761479876608 x) 12200509765705829/8707129344)) 500246412961/20155392)) 20511149/46656))>
#<alt 841/108>
#<alt (+ 841/108 (* 4/29 (/ 1 x)))>
#<alt (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x))))>
#<alt (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 4/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3))))))>
#<alt 841/108>
#<alt (+ 841/108 (* 4/29 (/ 1 x)))>
#<alt (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x))))>
#<alt (+ 841/108 (* -1 (/ (- (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)) 4/29) 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 -4/29>
#<alt (- (* 841/108 x) 4/29)>
#<alt (- (* 841/108 x) 4/29)>
#<alt (- (* 841/108 x) 4/29)>
#<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 (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<alt (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<alt (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<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 -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

57 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(+ (* x (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))) (- 0 (/ 16/841 (+ (* 841/108 x) -4/29))))
1.0ms	x	@	inf	(+ (* x (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))) (- 0 (/ 16/841 (+ (* 841/108 x) -4/29))))
1.0ms	x	@	-inf	(+ (* x (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))) (- 0 (/ 16/841 (+ (* 841/108 x) -4/29))))
1.0ms	x	@	0	(/ (- (* 594823321/1259712 (* x (* x x))) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))
1.0ms	x	@	inf	(/ (- (* 594823321/1259712 (* x (* x x))) -64/24389) (+ 16/841 (* x (+ (* x 707281/11664) -29/27))))

rewrite644.0ms (9.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3230×	`-lowering-.f32`
3230×	`-lowering-.f64`
2108×	`+-lowering-+.f64`
2108×	`+-lowering-+.f32`
2090×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	102
1	224	99
2	1937	99
0	8626	99

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 1976

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)
(/ (+ (* 707281/11664 (* x x)) -16/841) (+ (* 841/108 x) -4/29))
(+ (* 707281/11664 (* x x)) -16/841)
(* 707281/11664 (* x x))
(* x x)
(/ (- (* 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 (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))) (- 0 (/ 16/841 (+ (* 841/108 x) -4/29))))
(- 0 (/ 16/841 (+ (* 841/108 x) -4/29)))
(/ (* x 707281/11664) (+ (* 841/108 x) -4/29))
(* x 707281/11664)
(+ (* 841/108 x) -4/29)
(* x (+ (* x 707281/11664) -29/27))
(/ 16/841 (+ (* 841/108 x) -4/29))

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 1 binary64) (.f64 #s(literal 841/108 binary64) x)))
(+.f64 #s(literal 4/29 binary64) (.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 1 binary64)))
(+.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))) #s(literal 16/841 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 841/108 binary64) x) #s(literal 4/29 binary64)) (fma.f64 #s(literal -16/841 binary64) (/.f64 #s(literal 1 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 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 #s(literal 0 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 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 841/108 binary64) x)) #s(literal 4/29 binary64))
(+.f64 (.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 1 binary64)) #s(literal 4/29 binary64))
(+.f64 (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 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal -16/841 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))) #s(literal -16/841 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal -16/841 binary64))))
(+.f64 (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 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))) #s(literal 16/841 binary64)))) (fma.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))) #s(literal 16/841 binary64) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))) #s(literal 16/841 binary64))))
(+.f64 (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 (/.f64 #s(literal -16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal -1 binary64)))) (fma.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 #s(literal -16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal -1 binary64))))
(+.f64 (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 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 256/707281 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 #s(literal 4096/594823321 binary64) (.f64 (+.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)))))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 256/707281 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 #s(literal 4096/594823321 binary64) (.f64 (+.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 #s(literal 1 binary64) (/.f64 #s(literal 256/707281 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 #s(literal 4096/594823321 binary64) (.f64 (+.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 (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 (/.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 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 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))))) (fma.f64 (neg.f64 (/.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 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 #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 #s(literal 256/707281 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 (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 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal -16/841 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))) #s(literal -16/841 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal -16/841 binary64))))
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(pow.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal -1 binary64))
(pow.f64 (neg.f64 (/.f64 (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) #s(literal 16/841 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (/.f64 #s(literal 256/707281 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))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(.f64 #s(literal -16/841 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(.f64 #s(literal -16/841 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(.f64 #s(literal 16/841 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
(.f64 #s(literal 16/841 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(.f64 #s(literal -1 binary64) (/.f64 #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 (.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 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)))
(.f64 (/.f64 #s(literal 4096/594823321 binary64) (.f64 (+.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 #s(literal 1 binary64) (/.f64 #s(literal 256/707281 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 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 16/841 binary64))
(.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 594823321/1259712 binary64))) #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 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)))

simplify530.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

2656×	`-lowering-.f32`
2656×	`-lowering-.f64`
1716×	`+-lowering-+.f64`
1716×	`+-lowering-+.f32`
1362×	`sum4-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	1197
1	591	1111
2	1430	1101
3	3333	1095
4	7423	1095
0	8374	1095

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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

eval377.0ms (5.7%)

Compiler: Compiled 97223 to 3314 computations (96.6% saved)

prune189.0ms (2.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	2335	5	2340
Fresh	3	1	4
Picked	3	2	5
Done	0	1	1
Total	2341	9	2350

Accuracy

100.0%

Counts

2350 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.5%	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
▶	79.2%	(/.f64 (+.f64 (.f64 (.f64 (.f64 #s(literal 841/108 binary64) x) x) #s(literal 841/108 binary64)) #s(literal -16/841 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	79.2%	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
	77.5%	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (.f64 (+.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)))))
▶	26.0%	(/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
▶	46.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
▶	46.9%	(*.f64 #s(literal 841/108 binary64) x)
✓	54.2%	#s(literal 4/29 binary64)

Compiler

Compiled 172 to 126 computations (26.7% saved)

simplify417.0ms (6.4%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 #s(literal 841/108 binary64) x) x)
✓	cost-diff	128	(.f64 (.f64 (*.f64 #s(literal 841/108 binary64) x) x) #s(literal 841/108 binary64))
✓	cost-diff	128	(+.f64 (.f64 (.f64 (*.f64 #s(literal 841/108 binary64) x) x) #s(literal 841/108 binary64)) #s(literal -16/841 binary64))
✓	cost-diff	128	(/.f64 (+.f64 (.f64 (.f64 (.f64 #s(literal 841/108 binary64) x) x) #s(literal 841/108 binary64)) #s(literal -16/841 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	cost-diff	0	(+.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	0	(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
✓	cost-diff	256	(/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 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 #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 x #s(literal 707281/11664 binary64))
✓	cost-diff	128	(/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	cost-diff	6528	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))

Rules

7720×	`-lowering-.f32`
7720×	`-lowering-.f64`
2820×	`cube-prod`
2148×	`/-lowering-/.f32`
2148×	`/-lowering-/.f64`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	22	119
1	45	117
2	73	115
3	115	115
4	220	115
5	380	112
6	589	112
7	802	108
8	1721	108
9	3153	108
10	3765	108
11	4420	108
12	5316	108
13	6001	108
14	6440	108
15	7062	108
16	7374	108
17	7460	108
18	7780	108
19	7893	108
20	7968	108
0	8600	108

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(+ (* x (/ (* x 707281/11664) (+ (* 841/108 x) -4/29))) 4/29)
(+.f64 (/.f64 x (+.f64 #s(literal 108/841 binary64) (/.f64 #s(literal -46656/20511149 binary64) x))) #s(literal 4/29 binary64))
x
(/ (* x 707281/11664) (+ (* 841/108 x) -4/29))
(/.f64 #s(literal 841/108 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -432/24389 binary64) x)))
(* x 707281/11664)
(/.f64 x #s(literal 11664/707281 binary64))
707281/11664
#s(literal 707281/11664 binary64)
(+ (* 841/108 x) -4/29)
(+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))
(* 841/108 x)
(/.f64 x #s(literal 108/841 binary64))
841/108
#s(literal 841/108 binary64)
-4/29
#s(literal -4/29 binary64)
4/29
#s(literal 4/29 binary64)
(* 841/108 x)
(/.f64 x #s(literal 108/841 binary64))
841/108
#s(literal 841/108 binary64)
x
(/ 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
(/ (* x (* x 707281/11664)) (+ (* 841/108 x) -4/29))
(/.f64 x (+.f64 #s(literal 108/841 binary64) (/.f64 #s(literal -46656/20511149 binary64) x)))
(* x (* x 707281/11664))
(/.f64 x (/.f64 #s(literal 11664/707281 binary64) x))
x
(* x 707281/11664)
(/.f64 x #s(literal 11664/707281 binary64))
707281/11664
#s(literal 707281/11664 binary64)
(+ (* 841/108 x) -4/29)
(+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))
(* 841/108 x)
(/.f64 x #s(literal 108/841 binary64))
841/108
#s(literal 841/108 binary64)
-4/29
#s(literal -4/29 binary64)
(/ (+ (* (* (* 841/108 x) x) 841/108) -16/841) (+ (* 841/108 x) -4/29))
(/.f64 (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal -16/841 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))
(+ (* (* (* 841/108 x) x) 841/108) -16/841)
(+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal -16/841 binary64))
(* (* (* 841/108 x) x) 841/108)
(/.f64 x (/.f64 #s(literal 11664/707281 binary64) x))
(* (* 841/108 x) x)
(/.f64 x (/.f64 #s(literal 108/841 binary64) x))
(* 841/108 x)
(/.f64 x #s(literal 108/841 binary64))
841/108
#s(literal 841/108 binary64)
x
-16/841
#s(literal -16/841 binary64)
(+ (* 841/108 x) -4/29)
(+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))
-4/29
#s(literal -4/29 binary64)

localize183.0ms (2.8%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.8%	(.f64 (.f64 #s(literal 841/108 binary64) x) x)
✓	accuracy	99.7%	(.f64 (.f64 (*.f64 #s(literal 841/108 binary64) x) x) #s(literal 841/108 binary64))
✓	accuracy	79.1%	(/.f64 (+.f64 (.f64 (.f64 (.f64 #s(literal 841/108 binary64) x) x) #s(literal 841/108 binary64)) #s(literal -16/841 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	99.8%	(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	79.0%	(/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
✓	accuracy	99.5%	(/.f64 #s(literal 108/841 binary64) x)
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.9%	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	98.7%	(/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))

Results

112.0ms

256×

valid

Compiler

Compiled 134 to 22 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 19.0ms (31.5% of total)

...c/correct-round.rkt:119:19: 19.0ms (31.5% of total)

ival-div: 14.0ms (23.2% of total)

ival-add: 4.0ms (6.6% of total)

compiled-spec: 4.0ms (6.6% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Counts

13 → 156

Calls

Call 1

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

Outputs
#<alt 4/29>
#<alt (+ 4/29 (* -20511149/46656 (pow x 2)))>
#<alt (+ 4/29 (* (pow x 2) (- (* -500246412961/20155392 x) 20511149/46656)))>
#<alt (+ 4/29 (* (pow x 2) (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656)))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 8/29 (/ 1 x))))>
#<alt (* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 8/29 (/ 1 x)))))>
#<alt (* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 8/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3)))))))>
#<alt (* 841/108 x)>
#<alt (* x (+ 841/108 (* 8/29 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 8/29 (* 1728/707281 (/ 1 x))) x)) 841/108)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 8/29 (+ (/ 746496/17249876309 (pow x 2)) (* 1728/707281 (/ 1 x)))) x)) 841/108)))>
#<alt (* -20511149/46656 x)>
#<alt (* x (- (* -500246412961/20155392 x) 20511149/46656))>
#<alt (* x (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656))>
#<alt (* x (- (* x (- (* x (- (* -297558232675799463481/3761479876608 x) 12200509765705829/8707129344)) 500246412961/20155392)) 20511149/46656))>
#<alt 841/108>
#<alt (+ 841/108 (* 4/29 (/ 1 x)))>
#<alt (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x))))>
#<alt (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 4/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3))))))>
#<alt 841/108>
#<alt (+ 841/108 (* 4/29 (/ 1 x)))>
#<alt (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x))))>
#<alt (+ 841/108 (* -1 (/ (- (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)) 4/29) 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 -4/29>
#<alt (- (* 841/108 x) 4/29)>
#<alt (- (* 841/108 x) 4/29)>
#<alt (- (* 841/108 x) 4/29)>
#<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 (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<alt (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<alt (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<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 (* 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 (* -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 (* 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 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 (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (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 (* 707281/11664 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>
#<alt (* 841/108 (pow x 2))>

Calls

39 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/ 108/841 x)
0.0ms	x	@	inf	(/ 108/841 x)
0.0ms	x	@	inf	(* (* 841/108 x) x)
0.0ms	x	@	-inf	(/ 108/841 x)
0.0ms	x	@	-inf	(/ (* x (* x 707281/11664)) (+ (* 841/108 x) -4/29))

rewrite596.0ms (9.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4784×	`-lowering-.f32`
4784×	`-lowering-.f64`
3166×	`/-lowering-/.f32`
3166×	`/-lowering-/.f64`
1276×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	81
1	122	71
2	910	70
0	8645	70

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 614

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
(+.f64 #s(literal 4/29 binary64) (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(+.f64 (/.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal -16/841 binary64) (+.f64 (/.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))) #s(literal 4/29 binary64)))))
(-.f64 #s(literal 4/29 binary64) (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64))) (/.f64 #s(literal -16/841 binary64) (+.f64 (/.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))) #s(literal 4/29 binary64))))
(-.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 #s(literal 4/29 binary64) (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))))) (/.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 #s(literal 4/29 binary64) (/.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))))))
(fma.f64 x (/.f64 (*.f64 x #s(literal -707281/11664 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))) #s(literal 4/29 binary64))
(fma.f64 (/.f64 (*.f64 x #s(literal -707281/11664 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))) x #s(literal 4/29 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal -707281/11664 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))) #s(literal 4/29 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 4/29 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 707281/11664 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) x) #s(literal 4/29 binary64))
(fma.f64 (*.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))
(fma.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64)) #s(literal -64/24389 binary64))) (+.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 16/841 binary64)) (*.f64 x #s(literal 29/27 binary64))) #s(literal 4/29 binary64))
(fma.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64)) #s(literal 4/29 binary64))
(neg.f64 (/.f64 (+.f64 (/.f64 (.f64 #s(literal 353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal 64/24389 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 #s(literal 16/841 binary64) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 4/29 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))))))))
(neg.f64 (/.f64 (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) #s(literal -16/841 binary64)) (+.f64 (/.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))) #s(literal 4/29 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal 64/24389 binary64))) (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 #s(literal 16/841 binary64) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 4/29 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64))))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) #s(literal -16/841 binary64))) (+.f64 (/.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 4/29 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 16/841 binary64) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64)) (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))))) (+.f64 (/.f64 (.f64 #s(literal 353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal 64/24389 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4/29 binary64) (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64))))) (-.f64 #s(literal 16/841 binary64) (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (*.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 4/29 binary64)))))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal 64/24389 binary64)) (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 #s(literal 16/841 binary64) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 4/29 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))))))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal 64/24389 binary64)) (+.f64 #s(literal 16/841 binary64) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64)) (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 x (.f64 x #s(literal 707281/11664 binary64)))))))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) #s(literal -16/841 binary64)) (+.f64 (/.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal 64/24389 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 #s(literal 16/841 binary64) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 4/29 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal 64/24389 binary64))) (neg.f64 (+.f64 #s(literal 16/841 binary64) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64)) (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 x (.f64 x #s(literal 707281/11664 binary64))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) #s(literal -16/841 binary64))) (+.f64 (/.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))) #s(literal 4/29 binary64)))
(/.f64 (-.f64 #s(literal 16/841 binary64) (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) (+.f64 #s(literal 4/29 binary64) (/.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64))) (.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64)) #s(literal 16/841 binary64))) (.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64)) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal -4/29 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))) #s(literal 64/24389 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (.f64 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))) (+.f64 #s(literal 16/841 binary64) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal 4/29 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))))))))
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(.f64 #s(literal 707281/11664 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(*.f64 #s(literal 841/108 binary64) (/.f64 x (/.f64 #s(literal 108/841 binary64) x)))
(*.f64 #s(literal 841/108 binary64) (/.f64 (/.f64 x #s(literal 108/841 binary64)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 841/108 binary64) (/.f64 (/.f64 x #s(literal -108/841 binary64)) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 x #s(literal 108/841 binary64)) (/.f64 x #s(literal 108/841 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 707281/11664 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal 2 binary64)))
(*.f64 (/.f64 x (/.f64 #s(literal 108/841 binary64) x)) #s(literal 841/108 binary64))
(.f64 (.f64 x (*.f64 x #s(literal 707281/11664 binary64))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal -707281/11664 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -707281/11664 binary64)))
(.f64 (.f64 x #s(literal -707281/11664 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 x x) #s(literal 707281/11664 binary64))
(*.f64 #s(literal -707281/11664 binary64) (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(*.f64 #s(literal -707281/11664 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 x #s(literal -108/841 binary64)) (/.f64 x #s(literal -108/841 binary64)))
(*.f64 (/.f64 x #s(literal -108/841 binary64)) (/.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) #s(literal -707281/11664 binary64))
(.f64 (.f64 x #s(literal 707281/11664 binary64)) x)
(*.f64 #s(literal -841/108 binary64) (/.f64 (/.f64 x #s(literal 108/841 binary64)) (/.f64 #s(literal -1 binary64) x)))
(*.f64 #s(literal -841/108 binary64) (/.f64 (/.f64 x #s(literal -108/841 binary64)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -841/108 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 108/841 binary64) x)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) #s(literal 707281/11664 binary64))
(*.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -1 binary64)) (/.f64 x #s(literal -108/841 binary64)))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 707281/11664 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal 108/841 binary64)))
(*.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 108/841 binary64)) x)
(*.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 108/841 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -108/841 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -108/841 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) (/.f64 #s(literal 1 binary64) x)) #s(literal 841/108 binary64))
(*.f64 (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 108/841 binary64) x)))
(*.f64 (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 108/841 binary64) x)) (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) #s(literal 108/841 binary64)) (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) #s(literal 108/841 binary64)))
(*.f64 (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) #s(literal -108/841 binary64)) (/.f64 (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 #s(literal -841/108 binary64) (/.f64 #s(literal 108/841 binary64) x)) (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)))
(.f64 (.f64 (/.f64 x #s(literal 108/841 binary64)) (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)))
(.f64 (neg.f64 (.f64 x (-.f64 #s(literal 0 binary64) x))) #s(literal 707281/11664 binary64))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 707281/11664 binary64))
(.f64 (.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -841/108 binary64)) (-.f64 #s(literal 0 binary64) x))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -108/841 binary64) x)) (/.f64 x (/.f64 #s(literal -108/841 binary64) x)))
(neg.f64 (/.f64 x (/.f64 #s(literal -108/841 binary64) x)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 108/841 binary64) x)))
(neg.f64 (*.f64 (/.f64 x #s(literal -108/841 binary64)) x))
(neg.f64 (*.f64 x (/.f64 x #s(literal -108/841 binary64))))
(neg.f64 (/.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 108/841 binary64) x)))
(/.f64 x (/.f64 #s(literal 108/841 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 108/841 binary64) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -108/841 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -108/841 binary64) x) (*.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -108/841 binary64) x))
(/.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -108/841 binary64) x))
(/.f64 (neg.f64 (*.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 108/841 binary64) x))
(*.f64 x (/.f64 x #s(literal 108/841 binary64)))
(.f64 #s(literal 841/108 binary64) (.f64 x x))
(*.f64 #s(literal 841/108 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 x #s(literal 108/841 binary64)) x)
(*.f64 (/.f64 x #s(literal 108/841 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 108/841 binary64) x)))
(*.f64 (/.f64 x (/.f64 #s(literal 108/841 binary64) x)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x #s(literal -108/841 binary64)))
(.f64 (.f64 x x) #s(literal 841/108 binary64))
(*.f64 (/.f64 x #s(literal -108/841 binary64)) (-.f64 #s(literal 0 binary64) x))
(*.f64 (/.f64 x #s(literal -108/841 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 x #s(literal -108/841 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 x #s(literal -1 binary64)) (/.f64 x #s(literal -108/841 binary64)))
(*.f64 #s(literal -841/108 binary64) (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 x #s(literal -108/841 binary64)))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 841/108 binary64))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 841/108 binary64))
(.f64 (.f64 x (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1/2 binary64)))

simplify207.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1696×	`-lowering-.f32`
1696×	`-lowering-.f64`
1682×	`fma-lowering-fma.f32`
1682×	`fma-lowering-fma.f64`
1616×	`fnmadd-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	837
1	345	816
2	881	765
3	2258	745
4	5140	735
0	8306	735

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
4/29
(+ 4/29 (* -20511149/46656 (pow x 2)))
(+ 4/29 (* (pow x 2) (- (* -500246412961/20155392 x) 20511149/46656)))
(+ 4/29 (* (pow x 2) (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656)))
(* 841/108 x)
(* x (+ 841/108 (* 8/29 (/ 1 x))))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 8/29 (/ 1 x)))))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 8/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3)))))))
(* 841/108 x)
(* x (+ 841/108 (* 8/29 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (+ 8/29 (* 1728/707281 (/ 1 x))) x)) 841/108)))
(* -1 (* x (- (* -1 (/ (+ 8/29 (+ (/ 746496/17249876309 (pow x 2)) (* 1728/707281 (/ 1 x)))) x)) 841/108)))
(* -20511149/46656 x)
(* x (- (* -500246412961/20155392 x) 20511149/46656))
(* x (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656))
(* x (- (* x (- (* x (- (* -297558232675799463481/3761479876608 x) 12200509765705829/8707129344)) 500246412961/20155392)) 20511149/46656))
841/108
(+ 841/108 (* 4/29 (/ 1 x)))
(+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x))))
(+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 4/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3))))))
841/108
(+ 841/108 (* 4/29 (/ 1 x)))
(+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x))))
(+ 841/108 (* -1 (/ (- (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)) 4/29) 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)
-4/29
(- (* 841/108 x) 4/29)
(- (* 841/108 x) 4/29)
(- (* 841/108 x) 4/29)
(* 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)
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(* 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)
(* 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)
(* -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)))
(* 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))
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
(- (* 707281/11664 (pow x 2)) 16/841)
(- (* 707281/11664 (pow x 2)) 16/841)
(- (* 707281/11664 (pow x 2)) 16/841)
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (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))
(* 707281/11664 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))
(* 841/108 (pow x 2))

Outputs
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* -20511149/46656 (pow x 2)))
(+.f64 #s(literal 4/29 binary64) (.f64 #s(literal -20511149/46656 binary64) (.f64 x x)))
(+ 4/29 (* (pow x 2) (- (* -500246412961/20155392 x) 20511149/46656)))
(+.f64 #s(literal 4/29 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -20511149/46656 binary64) (*.f64 x #s(literal -500246412961/20155392 binary64)))))
(+ 4/29 (* (pow x 2) (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656)))
(+.f64 #s(literal 4/29 binary64) (.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)))))))
(* 841/108 x)
(*.f64 x #s(literal 841/108 binary64))
(* x (+ 841/108 (* 8/29 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal 8/29 binary64))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 8/29 (/ 1 x)))))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) (+.f64 #s(literal 8/29 binary64) (/.f64 #s(literal 1728/707281 binary64) x)))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (+ (* 8/29 (/ 1 x)) (* 746496/17249876309 (/ 1 (pow x 3)))))))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) (-.f64 (/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x) #s(literal -8/29 binary64)))
(* 841/108 x)
(*.f64 x #s(literal 841/108 binary64))
(* x (+ 841/108 (* 8/29 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal 8/29 binary64))
(* -1 (* x (- (* -1 (/ (+ 8/29 (* 1728/707281 (/ 1 x))) x)) 841/108)))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) (+.f64 #s(literal 8/29 binary64) (/.f64 #s(literal 1728/707281 binary64) x)))
(* -1 (* x (- (* -1 (/ (+ 8/29 (+ (/ 746496/17249876309 (pow x 2)) (* 1728/707281 (/ 1 x)))) x)) 841/108)))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) (-.f64 (/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x) #s(literal -8/29 binary64)))
(* -20511149/46656 x)
(*.f64 #s(literal -20511149/46656 binary64) x)
(* x (- (* -500246412961/20155392 x) 20511149/46656))
(.f64 x (+.f64 #s(literal -20511149/46656 binary64) (.f64 x #s(literal -500246412961/20155392 binary64))))
(* x (- (* x (- (* -12200509765705829/8707129344 x) 500246412961/20155392)) 20511149/46656))
(.f64 x (+.f64 #s(literal -20511149/46656 binary64) (.f64 x (+.f64 #s(literal -500246412961/20155392 binary64) (*.f64 x #s(literal -12200509765705829/8707129344 binary64))))))
(* x (- (* x (- (* x (- (* -297558232675799463481/3761479876608 x) 12200509765705829/8707129344)) 500246412961/20155392)) 20511149/46656))
(.f64 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
#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 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x))))
(+.f64 #s(literal 841/108 binary64) (/.f64 (+.f64 #s(literal 4/29 binary64) (/.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 841/108 binary64) (/.f64 (+.f64 #s(literal 4/29 binary64) (/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x)) 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 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x))))
(+.f64 #s(literal 841/108 binary64) (/.f64 (+.f64 #s(literal 4/29 binary64) (/.f64 #s(literal 1728/707281 binary64) x)) x))
(+ 841/108 (* -1 (/ (- (* -1 (/ (+ 1728/707281 (* 746496/17249876309 (/ 1 x))) x)) 4/29) x)))
(+.f64 #s(literal 841/108 binary64) (/.f64 (+.f64 #s(literal 4/29 binary64) (/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x)) 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))
-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))
(- (* 841/108 x) 4/29)
(+.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))
(* x (- 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))
(* x (- 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))
(* x (- 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))
(* 841/108 x)
(*.f64 x #s(literal 841/108 binary64))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(+.f64 (*.f64 x #s(literal 841/108 binary64)) #s(literal -4/29 binary64))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(+.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 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))
(* 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))
(/ 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)
(* -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 x #s(literal 841/108 binary64))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(* x (+ 841/108 (+ (/ 1728/707281 (pow x 2)) (* 4/29 (/ 1 x)))))
(+.f64 #s(literal 4/29 binary64) (+.f64 (*.f64 x #s(literal 841/108 binary64)) (/.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 (*.f64 x #s(literal 841/108 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x)))
(* 841/108 x)
(*.f64 x #s(literal 841/108 binary64))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(* -1 (* x (- (* -1 (/ (+ 4/29 (* 1728/707281 (/ 1 x))) x)) 841/108)))
(+.f64 #s(literal 4/29 binary64) (+.f64 (*.f64 x #s(literal 841/108 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 x #s(literal 841/108 binary64)) (+.f64 #s(literal 4/29 binary64) (/.f64 (+.f64 #s(literal 1728/707281 binary64) (/.f64 #s(literal 746496/17249876309 binary64) x)) x)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(+ 4/29 (* 841/108 x))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(* 841/108 x)
(*.f64 x #s(literal 841/108 binary64))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(* 841/108 x)
(*.f64 x #s(literal 841/108 binary64))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal 841/108 binary64)))
-16/841
#s(literal -16/841 binary64)
(- (* 707281/11664 (pow x 2)) 16/841)
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(- (* 707281/11664 (pow x 2)) 16/841)
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(- (* 707281/11664 (pow x 2)) 16/841)
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))
(* 841/108 (pow x 2))
(.f64 x (.f64 x #s(literal 841/108 binary64)))

eval176.0ms (2.7%)

Compiler: Compiled 21074 to 1988 computations (90.6% saved)

prune139.0ms (2.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1093	1	1094
Fresh	0	1	1
Picked	4	1	5
Done	0	3	3
Total	1097	6	1103

Accuracy

100.0%

Counts

1103 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	79.2%	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
▶	77.5%	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (.f64 (+.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)))))
▶	46.8%	(/.f64 x #s(literal 108/841 binary64))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
✓	46.9%	(*.f64 #s(literal 841/108 binary64) x)
✓	54.2%	#s(literal 4/29 binary64)

Compiler

Compiled 54 to 41 computations (24.1% saved)

simplify245.0ms (3.7%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
✓	cost-diff	0	(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
✓	cost-diff	128	(.f64 (+.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))))
✓	cost-diff	1152	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (.f64 (+.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)))))
✓	cost-diff	0	(/.f64 x #s(literal 108/841 binary64))

Rules

3916×	`+-lowering-+.f64`
3916×	`+-lowering-+.f32`
2216×	`-lowering-.f32`
2216×	`-lowering-.f64`
1204×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	97
1	40	70
2	59	66
3	125	66
4	311	66
5	1499	66
6	5513	66
7	7916	66
0	8024	66

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize92.0ms (1.4%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)))
✓	accuracy	80.0%	(.f64 (+.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))))
✓	accuracy	79.1%	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (.f64 (+.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)))))
✓	accuracy	99.5%	(/.f64 x #s(literal 108/841 binary64))

Results

68.0ms

256×

valid

Compiler

Compiled 96 to 20 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 19.0ms (39.9% of total)

...c/correct-round.rkt:119:19: 16.0ms (33.6% of total)

ival-div: 6.0ms (12.6% of total)

ival-add: 6.0ms (12.6% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Counts

6 → 72

Calls

Call 1

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

Outputs
#<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 -4/29>
#<alt (- (* 841/108 x) 4/29)>
#<alt (- (* 841/108 x) 4/29)>
#<alt (- (* 841/108 x) 4/29)>
#<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 (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<alt (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<alt (* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))>
#<alt -16/841>
#<alt (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (- (* 707281/11664 (pow x 2)) 16/841)>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* 707281/11664 (pow x 2))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (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 (* 707281/11664 (pow x 2))>
#<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))>

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(* (+ (* x (* x 707281/11664)) -16/841) (/ 1 (+ (* 841/108 x) 4/29)))
1.0ms	x	@	0	(/ x 108/841)
0.0ms	x	@	0	(* (+ (* x (* x 707281/11664)) -16/841) (/ 1 (+ (* 841/108 x) 4/29)))
0.0ms	x	@	inf	(* (+ (* x (* x 707281/11664)) -16/841) (/ 1 (+ (* 841/108 x) 4/29)))
0.0ms	x	@	-inf	(/ x 108/841)

rewrite446.0ms (6.8%)

Algorithm

1×	batch-egg-rewrite

Rules

5200×	`-lowering-.f32`
5200×	`-lowering-.f64`
3972×	`/-lowering-/.f32`
3972×	`/-lowering-/.f64`
970×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	110	27
2	692	27
0	8494	27

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 690

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 108/841 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -108/841 binary64)))
(neg.f64 (/.f64 x #s(literal -108/841 binary64)))
(neg.f64 (*.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal 1 binary64)))
(/.f64 x #s(literal 108/841 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
(/.f64 #s(literal 841/108 binary64) (/.f64 #s(literal 1 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))
(pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal 841/108 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 108/841 binary64)))
(*.f64 #s(literal 841/108 binary64) x)
(*.f64 #s(literal 841/108 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 x #s(literal -108/841 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -841/108 binary64))
(*.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1/2 binary64)))
(+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64))
(+.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64)))
(+.f64 #s(literal 4/29 binary64) (*.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal -1 binary64)))
(+.f64 (/.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal -16/841 binary64) (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64))))))
(+.f64 (/.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.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 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x))) (.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 (/.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 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x))))
(+.f64 (*.f64 (/.f64 x #s(literal -108/841 binary64)) #s(literal -1 binary64)) #s(literal 4/29 binary64))
(+.f64 (*.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 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64))) #s(literal -1 binary64))))
(-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal -108/841 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -4/29 binary64) (/.f64 x #s(literal 108/841 binary64))))
(-.f64 (/.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (/.f64 #s(literal -16/841 binary64) (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64)))))
(-.f64 (/.f64 #s(literal 16/841 binary64) (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64)))) (/.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) (/.f64 (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal 16/841 binary64)))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (/.f64 (/.f64 #s(literal -256/707281 binary64) (+.f64 (/.f64 x (/.f64 #s(literal -11664/707281 binary64) x)) #s(literal -16/841 binary64))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(-.f64 (/.f64 (/.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.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 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64)))) (-.f64 #s(literal -4/29 binary64) (/.f64 x #s(literal 108/841 binary64))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal 16/841 binary64)))) (/.f64 #s(literal 256/707281 binary64) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal 16/841 binary64)))))
(fma.f64 x #s(literal 841/108 binary64) #s(literal 4/29 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64))
(fma.f64 #s(literal 841/108 binary64) x #s(literal 4/29 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -841/108 binary64) #s(literal 4/29 binary64))
(neg.f64 (-.f64 #s(literal -4/29 binary64) (/.f64 x #s(literal 108/841 binary64))))
(/.f64 (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal -16/841 binary64)) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))
(/.f64 #s(literal 1 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 (+.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 (.f64 x x)) #s(literal 1259712/594823321 binary64)) #s(literal 64/24389 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)))))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) (+.f64 #s(literal -4096/594823321 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)))))) (/.f64 (+.f64 #s(literal -4096/594823321 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -4/29 binary64) (/.f64 x #s(literal 108/841 binary64)))))
(/.f64 (-.f64 #s(literal -4/29 binary64) (/.f64 x #s(literal 108/841 binary64))) #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 16/841 binary64) (/.f64 x (/.f64 #s(literal -11664/707281 binary64) x))) (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64))))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64)) #s(literal 64/24389 binary64)) (-.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.f64 #s(literal -16/841 binary64) (*.f64 x #s(literal 29/27 binary64)))))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64)) #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 x (.f64 x x)) #s(literal 1259712/594823321 binary64)) #s(literal 64/24389 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.f64 #s(literal -16/841 binary64) (*.f64 x #s(literal 29/27 binary64)))))))
(/.f64 (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64)) #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 x)) #s(literal 1259712/594823321 binary64)) #s(literal 64/24389 binary64)) (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.f64 #s(literal -16/841 binary64) (.f64 x #s(literal 29/27 binary64)))))))
(/.f64 (+.f64 #s(literal -4096/594823321 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)))) (.f64 (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64)))))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(/.f64 (+.f64 #s(literal -4096/594823321 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64))))))))
(/.f64 (+.f64 #s(literal -4096/594823321 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)))) (.f64 (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64)))))))))
(/.f64 (+.f64 #s(literal -4096/594823321 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64)) #s(literal -841/729 binary64))))))
(/.f64 (+.f64 #s(literal -4096/594823321 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)))) (.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)))))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(/.f64 (+.f64 #s(literal -4096/594823321 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64)))) (.f64 (-.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) (+.f64 #s(literal -16/841 binary64) (.f64 x #s(literal 29/27 binary64)))) (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 binary64)) #s(literal -64/24389 binary64))))
(/.f64 (+.f64 #s(literal -4096/594823321 binary64) (.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 (.f64 x (*.f64 x x)) #s(literal 1259712/594823321 binary64)) #s(literal -64/24389 binary64))))
(/.f64 (/.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 x (/.f64 #s(literal -11664/707281 binary64) x)))))
(/.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)))) #s(literal -256/707281 binary64)) (*.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal 16/841 binary64))))
(/.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)))) #s(literal -256/707281 binary64)) (*.f64 (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64))) (+.f64 (/.f64 x (/.f64 #s(literal -11664/707281 binary64) x)) #s(literal -16/841 binary64))))
(/.f64 (*.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64)) (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal 16/841 binary64))) (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal 16/841 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal -4/29 binary64) (/.f64 x #s(literal 108/841 binary64))) (+.f64 (/.f64 x (/.f64 #s(literal 11664/707281 binary64) x)) #s(literal 16/841 binary64))) (+.f64 (/.f64 x (/.f64 #s(literal -11664/707281 binary64) x)) #s(literal -16/841 binary64)))
(/.f64 (+.f64 #s(literal 4096/594823321 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))))) (neg.f64 (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64)))))))))
(/.f64 (+.f64 #s(literal 4096/594823321 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))))) (neg.f64 (.f64 (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64)))))) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(/.f64 (+.f64 #s(literal 4096/594823321 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))))) (.f64 (-.f64 #s(literal 4/29 binary64) (/.f64 x #s(literal 108/841 binary64))) (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64))))))))
(/.f64 (+.f64 #s(literal 4096/594823321 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 353814783205469041/1586874322944 binary64))))) (.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 841/729 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64)))))))))
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simplify285.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

2280×	`fma-lowering-fma.f32`
2280×	`fma-lowering-fma.f64`
1944×	`fmsub-define`
1808×	`fmm-def`
1762×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	366
1	254	345
2	578	343
3	1388	341
4	3639	341
0	8399	341

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* 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))))
-4/29
(- (* 841/108 x) 4/29)
(- (* 841/108 x) 4/29)
(- (* 841/108 x) 4/29)
(* 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)
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
-16/841
(- (* 707281/11664 (pow x 2)) 16/841)
(- (* 707281/11664 (pow x 2)) 16/841)
(- (* 707281/11664 (pow x 2)) 16/841)
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* 707281/11664 (pow x 2))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (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))
(* 707281/11664 (pow x 2))
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))

Outputs
(* 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)
4/29
#s(literal 4/29 binary64)
(+ 4/29 (* 841/108 x))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(+ 4/29 (* 841/108 x))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(+ 4/29 (* 841/108 x))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
(* x (+ 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
-4/29
#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) 4/29)
(+.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)
(* x (- 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))
(* x (- 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))
(* x (- 841/108 (* 4/29 (/ 1 x))))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))
(* 841/108 x)
(*.f64 #s(literal 841/108 binary64) x)
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))
(* -1 (* x (- (* 4/29 (/ 1 x)) 841/108)))
(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))
-16/841
#s(literal -16/841 binary64)
(- (* 707281/11664 (pow x 2)) 16/841)
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(- (* 707281/11664 (pow x 2)) 16/841)
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(- (* 707281/11664 (pow x 2)) 16/841)
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(* (pow x 2) (- 707281/11664 (* 16/841 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(* 707281/11664 (pow x 2))
(.f64 #s(literal 707281/11664 binary64) (.f64 x 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)

eval146.0ms (2.2%)

Compiler: Compiled 27265 to 2124 computations (92.2% saved)

prune140.0ms (2.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	761	1	762
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	762	6	768

Accuracy

100.0%

Counts

768 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	79.2%	(/.f64 (+.f64 (.f64 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	46.8%	(/.f64 x #s(literal 108/841 binary64))
	54.2%	(/.f64 #s(literal -16/841 binary64) (.f64 (+.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)))))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
✓	46.9%	(*.f64 #s(literal 841/108 binary64) x)
✓	54.2%	#s(literal 4/29 binary64)

Compiler

Compiled 276 to 107 computations (61.2% saved)

regimes34.0ms (0.5%)

Counts

18 → 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 (*.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 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 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 #s(literal 841/108 binary64) x) x) #s(literal 841/108 binary64)) #s(literal -16/841 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
(/.f64 #s(literal -16/841 binary64) (.f64 (+.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 #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 707281/11664 binary64) (*.f64 x x)) #s(literal -16/841 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 #s(literal 707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)) (.f64 (+.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 #s(literal 500246412961/136048896 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal -256/707281 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (+.f64 (.f64 #s(literal 707281/11664 binary64) (*.f64 x x)) #s(literal 16/841 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))) #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))) (-.f64 #s(literal 0 binary64) (/.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))) (-.f64 #s(literal 0 binary64) (/.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:

21.0ms	(*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x)
6.0ms	x
5.0ms	(+.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
97.4%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (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:

2.0ms

Results

Accuracy	Segments	Branch
54.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch30.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.00013975277456022188	2.3363961498030656
13.0ms	-734250.6677821883	-0.00022089140164111118

Results

17.0ms

272×

valid

Compiler

Compiled 150 to 131 computations (12.7% saved)

Precisions

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

ival-div: 4.0ms (47.5% of total)

ival-mult: 2.0ms (23.7% of total)

ival-add: 1.0ms (11.9% of total)

const: 1.0ms (11.9% 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 5188146770730811/288230376151711744 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 5188146770730811/288230376151711744 binary64)) #s(literal 4/29 binary64) (*.f64 #s(literal 841/108 binary64) x)))

#s(literal 4/29 binary64)

soundness20.0ms (0.3%)

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)

preprocess24.0ms (0.4%)

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%)

sample688.0ms (10.5%)

preprocess25.0ms (0.4%)

explain75.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize27.0ms (0.4%)

series2.0ms (0%)

rewrite313.0ms (4.8%)

simplify20.0ms (0.3%)

eval26.0ms (0.4%)

prune36.0ms (0.5%)

simplify162.0ms (2.5%)

localize212.0ms (3.2%)

series18.0ms (0.3%)

rewrite644.0ms (9.8%)

simplify530.0ms (8.1%)

eval377.0ms (5.7%)

prune189.0ms (2.9%)

simplify417.0ms (6.4%)

localize183.0ms (2.8%)

series4.0ms (0.1%)

rewrite596.0ms (9.1%)

simplify207.0ms (3.2%)

eval176.0ms (2.7%)

prune139.0ms (2.1%)

simplify245.0ms (3.7%)

localize92.0ms (1.4%)

series5.0ms (0.1%)

rewrite446.0ms (6.8%)

simplify285.0ms (4.3%)

eval146.0ms (2.2%)

prune140.0ms (2.1%)

regimes34.0ms (0.5%)

regimes2.0ms (0%)

regimes3.0ms (0%)

bsearch30.0ms (0.5%)

simplify8.0ms (0.1%)

soundness20.0ms (0.3%)

preprocess24.0ms (0.4%)

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