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)

sample944.0ms (21.9%)

Results

743.0ms	8249×	0	valid
1.0ms	4×	2	valid
0.0ms	3×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 275.0ms

ival-div: 151.0ms (54.9% of total)

ival-mult: 57.0ms (20.7% of total)

ival-add: 43.0ms (15.6% of total)

const: 20.0ms (7.3% of total)

backward-pass: 3.0ms (1.1% of total)

Bogosity

preprocess31.0ms (0.7%)

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)

explain93.0ms (2.2%)

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

62.0ms

512×

valid

Compiler

Compiled 64 to 29 computations (54.7% saved)

Precisions

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

ival-div: 15.0ms (67.5% of total)

ival-mult: 4.0ms (18% of total)

ival-add: 3.0ms (13.5% of total)

const: 1.0ms (4.5% 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)

simplify8.0ms (0.2%)

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)

localize33.0ms (0.8%)

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

26.0ms

256×

valid

Compiler

Compiled 13 to 6 computations (53.8% saved)

Precisions

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

...c/correct-round.rkt:119:19: 7.0ms (50.4% of total)

ival-add: 4.0ms (28.8% of total)

ival-mult: 2.0ms (14.4% 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	@	0	(* 841/108 x)
0.0ms	x	@	-inf	(* 841/108 x)
0.0ms	x	@	inf	(* 841/108 x)
0.0ms	x	@	0	(+ (* 841/108 x) 4/29)

rewrite327.0ms (7.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 185

Calls

Call 1

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

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

simplify10.0ms (0.2%)

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)

eval47.0ms (1.1%)

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

prune27.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	202	7	209
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	202	8	210

Accuracy

100.0%

Counts

210 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(fma.f64 (.f64 x #s(literal 707281/11664 binary64)) (/.f64 x (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
	99.4%	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
▶	73.0%	(/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
▶	73.0%	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
▶	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))
▶	51.5%	(*.f64 #s(literal 841/108 binary64) x)
▶	49.8%	#s(literal 4/29 binary64)

Compiler

Compiled 174 to 123 computations (29.3% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

74×	`-lowering-.f32`
74×	`-lowering-.f64`
56×	`fma-define`
48×	`fma-lowering-fma.f32`
48×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	99
1	48	93
2	72	93
3	84	93
4	91	93
5	111	93
6	117	93
0	117	93

Stop Event

1×	iter limit
1×	saturated

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

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

localize144.0ms (3.4%)

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	73.0%	(/.f64 (+.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) #s(literal -16/841 binary64)) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
✓	accuracy	99.8%	(*.f64 x #s(literal -841/108 binary64))
✓	accuracy	99.6%	(.f64 #s(literal -707281/11664 binary64) (.f64 x x))
✓	accuracy	73.0%	(/.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (+.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64))))
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	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 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64)))
✓	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))))

Results

111.0ms

256×

valid

Compiler

Compiled 118 to 26 computations (78% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

...c/correct-round.rkt:119:19: 27.0ms (50% of total)

ival-mult: 11.0ms (20.4% of total)

ival-div: 9.0ms (16.7% of total)

ival-add: 6.0ms (11.1% of total)

const: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Counts

13 → 156

Calls

Call 1

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

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

Calls

39 calls:

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

rewrite315.0ms (7.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3012×	`/-lowering-/.f32`
3012×	`/-lowering-/.f64`
2884×	`-lowering-.f32`
2884×	`-lowering-.f64`
1216×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	52
1	139	50
2	1085	50
0	8768	50

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 897

Calls

Call 1

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

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 #s(literal 4/29 binary64) (.f64 #s(literal 841/108 binary64) x))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
(exp.f64 (log.f64 (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))) #s(literal 1 binary64)))
(-.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))
(-.f64 #s(literal 4/29 binary64) (*.f64 x #s(literal -841/108 binary64)))
(-.f64 #s(literal 4/29 binary64) (/.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal -4/29 binary64)))
(-.f64 (/.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) (-.f64 #s(literal 4/29 binary64) (.f64 #s(literal 841/108 binary64) x))) (/.f64 #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 4/29 binary64) (.f64 #s(literal 841/108 binary64) x))) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal -4/29 binary64)))
(-.f64 (/.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 1 binary64)) #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 (.f64 x x) #s(literal 707281/11664 binary64)) (-.f64 #s(literal 4/29 binary64) (.f64 #s(literal 841/108 binary64) x))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (+.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal -4/29 binary64)))
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(/.f64 (+.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 4096/594823321 binary64)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64)) (neg.f64 (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))))))
(/.f64 (+.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 4096/594823321 binary64)) (+.f64 #s(literal -256/707281 binary64) (neg.f64 (.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) (+.f64 (.f64 #s(literal -707281/11664 binary64) (*.f64 x x)) #s(literal -16/841 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) #s(literal -256/707281 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64)))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) #s(literal -256/707281 binary64)) (neg.f64 (+.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))))
(/.f64 (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64))) (+.f64 #s(literal -16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64)) #s(literal 256/707281 binary64)) (+.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)))
(/.f64 (+.f64 #s(literal -4096/594823321 binary64) (neg.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64)))))
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(/.f64 (+.f64 #s(literal -256/707281 binary64) (neg.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64)))) (-.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64)) #s(literal 256/707281 binary64))) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))))
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(/.f64 (neg.f64 (+.f64 #s(literal -256/707281 binary64) (neg.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64))))) (+.f64 #s(literal -16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64)))) (+.f64 (.f64 (/.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) (/.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64)))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) (/.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))) (.f64 #s(literal 0 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64)))) (.f64 (/.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) (/.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))) (/.f64 #s(literal 256/707281 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))) (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x))))) (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 707281/11664 binary64)) #s(literal -16/841 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 707281/11664 binary64)) #s(literal -16/841 binary64)))
(.f64 #s(literal -1 binary64) (+.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x))))
(.f64 (+.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -4096/594823321 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 x x) #s(literal 841/729 binary64))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 500246412961/136048896 binary64))))))
(.f64 (+.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -4096/594823321 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) (+.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))))))
(.f64 (+.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 4096/594823321 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64)) (neg.f64 (+.f64 #s(literal 256/707281 binary64) (.f64 (*.f64 x x) #s(literal 841/729 binary64)))))))
(.f64 (+.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 4096/594823321 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -256/707281 binary64) (neg.f64 (.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) (+.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)))))))
(.f64 (+.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 4096/594823321 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) (+.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64)))))))
(.f64 (+.f64 (.f64 (*.f64 x x) #s(literal 707281/11664 binary64)) #s(literal -16/841 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 500246412961/136048896 binary64))) #s(literal -256/707281 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 707281/11664 binary64)) #s(literal 16/841 binary64))))
(.f64 (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x)))))
(.f64 (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x))))))
(.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64)) #s(literal 256/707281 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -707281/11664 binary64) (*.f64 x x)) #s(literal -16/841 binary64))))
(.f64 (+.f64 #s(literal -4096/594823321 binary64) (neg.f64 (.f64 #s(literal -353814783205469041/1586874322944 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 256/707281 binary64) (.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) (+.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)) #s(literal -16/841 binary64))))))
(.f64 (+.f64 #s(literal -256/707281 binary64) (neg.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -500246412961/136048896 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16/841 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x)))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 841/108 binary64) x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal -841/108 binary64))) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
(neg.f64 (.f64 #s(literal -707281/11664 binary64) (.f64 x x)))
(pow.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 2 binary64))
(pow.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 841/108 binary64) (.f64 x (*.f64 #s(literal 841/108 binary64) x)))
(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
(.f64 x (.f64 #s(literal -841/108 binary64) (*.f64 x #s(literal -841/108 binary64))))
(.f64 x (.f64 #s(literal 841/108 binary64) (*.f64 #s(literal 841/108 binary64) x)))
(.f64 (.f64 #s(literal 841/108 binary64) x) (*.f64 #s(literal 841/108 binary64) x))
(.f64 #s(literal -707281/11664 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (.f64 x x) #s(literal 707281/11664 binary64))
(.f64 #s(literal -841/108 binary64) (.f64 x (*.f64 x #s(literal -841/108 binary64))))
(.f64 (.f64 x #s(literal -841/108 binary64)) (*.f64 x #s(literal -841/108 binary64)))
(.f64 #s(literal 707281/11664 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 707281/11664 binary64)) x)
(.f64 #s(literal -1 binary64) (.f64 #s(literal -707281/11664 binary64) (*.f64 x x)))
(.f64 (.f64 x #s(literal -707281/11664 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -707281/11664 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -707281/11664 binary64)))
(.f64 (.f64 (*.f64 x #s(literal -841/108 binary64)) x) #s(literal -841/108 binary64))
(.f64 (.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal -841/108 binary64)) x)
(.f64 (.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 841/108 binary64)) x)
(.f64 (.f64 (*.f64 #s(literal 841/108 binary64) x) x) #s(literal 841/108 binary64))
(.f64 (pow.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 (pow.f64 (.f64 x #s(literal -841/108 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 x #s(literal -841/108 binary64)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -707281/11664 binary64)))
(neg.f64 (*.f64 x #s(literal -707281/11664 binary64)))
(*.f64 x #s(literal 707281/11664 binary64))
(*.f64 #s(literal -707281/11664 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 #s(literal 707281/11664 binary64) x)
(.f64 #s(literal -1 binary64) (.f64 x #s(literal -707281/11664 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -707281/11664 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal 841/108 binary64) x))
(neg.f64 (*.f64 #s(literal 841/108 binary64) x))
(*.f64 #s(literal 841/108 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 x #s(literal -841/108 binary64))
(*.f64 #s(literal -841/108 binary64) x)
(.f64 #s(literal -1 binary64) (.f64 #s(literal 841/108 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 841/108 binary64))

simplify270.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

2286×	`fma-lowering-fma.f32`
2286×	`fma-lowering-fma.f64`
1958×	`fmsub-define`
1822×	`fmm-def`
1772×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	721
1	245	606
2	543	604
3	1243	602
4	3444	602
0	8071	602

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

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 (/.f64 (+.f64 #s(literal 20155392/500246412961 binary64) (/.f64 #s(literal -8707129344/12200509765705829 binary64) x)) x) #s(literal -46656/20511149 binary64)) 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 (/.f64 (+.f64 #s(literal 20155392/500246412961 binary64) (/.f64 #s(literal -8707129344/12200509765705829 binary64) x)) x) #s(literal -46656/20511149 binary64)) 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)
(*.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))
16/841
#s(literal 16/841 binary64)
(+ 16/841 (* -707281/11664 (pow x 2)))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
(+ 16/841 (* -707281/11664 (pow x 2)))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
(+ 16/841 (* -707281/11664 (pow x 2)))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
(* -707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal -707281/11664 binary64)))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
(* -707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal -707281/11664 binary64)))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.f64 x (.f64 x #s(literal -707281/11664 binary64))))
(* (pow x 2) (- (* 16/841 (/ 1 (pow x 2))) 707281/11664))
(+.f64 #s(literal 16/841 binary64) (.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)))
(* -707281/11664 (pow x 2))
(.f64 x (.f64 x #s(literal -707281/11664 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
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))
-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)))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* 707281/11664 x)
(*.f64 x #s(literal 707281/11664 binary64))
(* -841/108 x)
(*.f64 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))

eval137.0ms (3.2%)

Compiler: Compiled 25509 to 1652 computations (93.5% saved)

prune108.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1093	2	1095
Fresh	1	1	2
Picked	3	2	5
Done	0	1	1
Total	1097	6	1103

Accuracy

100.0%

Counts

1103 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
▶	24.4%	(/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
▶	51.3%	(/.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))
✓	51.5%	(*.f64 #s(literal 841/108 binary64) x)
✓	49.8%	#s(literal 4/29 binary64)

Compiler

Compiled 50 to 36 computations (28% saved)

simplify117.0ms (2.7%)

Algorithm

1×	egg-herbie

Localize:

Found 10 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	64	(neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))))
✓	cost-diff	6336	(fma.f64 x (/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64))) (neg.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))))
✓	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	0	(/.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))

Rules

1966×	`fnmadd-define`
1396×	`fma-define`
1026×	`fmsub-define`
998×	`fnmsub-define`
758×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	89
1	44	87
2	71	86
3	136	86
4	282	86
5	531	86
6	1313	86
7	2913	86
8	4263	86
9	5432	86
10	5485	86
11	5605	86
12	5621	86
0	5621	86

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize144.0ms (3.3%)

Localize:

Found 10 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	99.5%	(/.f64 #s(literal 16/841 binary64) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	accuracy	99.1%	(/.f64 (.f64 x #s(literal 707281/11664 binary64)) (+.f64 (.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 707281/11664 binary64)))
✓	accuracy	99.8%	(*.f64 #s(literal 841/108 binary64) x)
✓	accuracy	99.7%	(*.f64 x #s(literal 707281/11664 binary64))
✓	accuracy	72.8%	(/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
✓	accuracy	99.5%	(/.f64 #s(literal 108/841 binary64) x)

Results

115.0ms

256×

valid

Compiler

Compiled 103 to 19 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

...c/correct-round.rkt:119:19: 17.0ms (29.4% of total)

ival-div: 11.0ms (19.1% of total)

compiled-spec: 11.0ms (19.1% of total)

ival-add: 10.0ms (17.3% of total)

ival-mult: 7.0ms (12.1% of total)

ival-neg: 1.0ms (1.7% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Counts

11 → 132

Calls

Call 1

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

33 calls:

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

rewrite370.0ms (8.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3830×	`/-lowering-/.f32`
3830×	`/-lowering-/.f64`
3246×	`-lowering-.f32`
3246×	`-lowering-.f64`
1954×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	67
1	101	53
2	959	53
0	8178	53

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 616

Calls

Call 1

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

Outputs
(exp.f64 (log.f64 (/.f64 x #s(literal 108/841 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -108/841 binary64)))
(neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -108/841 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
(/.f64 x #s(literal 108/841 binary64))
(/.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))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 108/841 binary64))
(/.f64 #s(literal -841/108 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1 binary64))
(pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 108/841 binary64) x) (/.f64 #s(literal 108/841 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 108/841 binary64)))
(*.f64 x #s(literal 841/108 binary64))
(*.f64 #s(literal 841/108 binary64) x)
(*.f64 #s(literal 841/108 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 841/108 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -108/841 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 841/108 binary64))
(*.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 #s(literal 1 binary64) x) #s(literal 841/108 binary64))
(*.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 #s(literal -841/108 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64)))
(exp.f64 (log.f64 (/.f64 #s(literal 108/841 binary64) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 x #s(literal 108/841 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -108/841 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x #s(literal 108/841 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x #s(literal 108/841 binary64)))))
(/.f64 #s(literal 108/841 binary64) x)
(/.f64 #s(literal 108/841 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal 108/841 binary64) (*.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 108/841 binary64) (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x #s(literal 108/841 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -108/841 binary64) x) #s(literal -1 binary64))
(/.f64 #s(literal -108/841 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal -108/841 binary64) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal -108/841 binary64) (neg.f64 (*.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -108/841 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
(*.f64 #s(literal 108/841 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 108/841 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 #s(literal 108/841 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -108/841 binary64) x)) #s(literal -1 binary64)))
(*.f64 #s(literal -108/841 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 108/841 binary64))
(*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
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(pow.f64 (/.f64 (/.f64 (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)) #s(literal 16/841 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(*.f64 #s(literal 16/841 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))))
(*.f64 #s(literal -16/841 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -4/29 binary64))) #s(literal 16/841 binary64))
(.f64 (/.f64 #s(literal 16/841 binary64) (+.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal 1259712/594823321 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 x #s(literal 108/841 binary64)) #s(literal 4/29 binary64)))

simplify245.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

2872×	`fma-lowering-fma.f32`
2872×	`fma-lowering-fma.f64`
1820×	`-lowering-.f32`
1820×	`-lowering-.f64`
1672×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	755
1	430	706
2	1090	657
3	2556	643
4	5938	642
0	8065	642

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

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

eval248.0ms (5.8%)

Compiler: Compiled 26560 to 2145 computations (91.9% saved)

prune116.0ms (2.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	925	1	926
Fresh	0	0	0
Picked	2	1	3
Done	0	3	3
Total	927	5	932

Accuracy

100.0%

Counts

932 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	24.4%	(/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
▶	51.4%	(/.f64 x #s(literal 108/841 binary64))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
✓	51.5%	(*.f64 #s(literal 841/108 binary64) x)
✓	49.8%	#s(literal 4/29 binary64)

Compiler

Compiled 28 to 22 computations (21.4% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

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

Rules

2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
0	3	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x 108/841)
x
108/841

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

localize38.0ms (0.9%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(/.f64 x #s(literal 108/841 binary64))

Results

30.0ms

256×

valid

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

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

...c/correct-round.rkt:119:19: 10.0ms (69.1% of total)

ival-div: 4.0ms (27.6% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (/ x 108/841)>

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)>

Calls

3 calls:

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

rewrite252.0ms (5.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2328×	`-lowering-.f32`
2328×	`-lowering-.f64`
1932×	`/-lowering-/.f32`
1932×	`/-lowering-/.f64`
1460×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	13	3
2	39	3
3	145	3
4	658	3
5	6489	3
0	8031	3

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 236

Calls

Call 1

Inputs
(/ x 108/841)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 x #s(literal 108/841 binary64)))
(+.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 0 binary64))
(exp.f64 (log.f64 (/.f64 x #s(literal 108/841 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 x #s(literal 108/841 binary64))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 11664/707281 binary64) (.f64 x x))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(literal 108/841 binary64) x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 108/841 binary64) x)) #s(literal -1/2 binary64)) (.f64 (log.f64 (/.f64 #s(literal 108/841 binary64) x)) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal 108/841 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal -108/841 binary64) (.f64 x x))) (/.f64 x #s(literal 108/841 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 x #s(literal -108/841 binary64))) (/.f64 x #s(literal 108/841 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (*.f64 x x) #s(literal 11664/707281 binary64))) (/.f64 x #s(literal 108/841 binary64)))
(neg.f64 (/.f64 x #s(literal 108/841 binary64)))
(/.f64 x #s(literal 108/841 binary64))
(/.f64 x #s(literal -108/841 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 108/841 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -108/841 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) #s(literal 11664/707281 binary64)) (/.f64 (.f64 x (*.f64 x x)) #s(literal -1259712/594823321 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal 108/841 binary64)) (/.f64 (*.f64 x x) #s(literal 11664/707281 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))))
(/.f64 #s(literal 841/108 binary64) (/.f64 #s(literal 1 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 #s(literal -841/108 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -841/108 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 x #s(literal 108/841 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 108/841 binary64) (.f64 x x)))
(/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -108/841 binary64) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 108/841 binary64) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal -108/841 binary64) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1 binary64) (.f64 #s(literal 108/841 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal -1 binary64) (.f64 #s(literal -108/841 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1 binary64) (.f64 #s(literal -108/841 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal -1 binary64) (.f64 #s(literal 108/841 binary64) (*.f64 x x))))
(/.f64 (.f64 x x) (.f64 x #s(literal 108/841 binary64)))
(/.f64 (.f64 x x) (.f64 x #s(literal -108/841 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x #s(literal 108/841 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x #s(literal -108/841 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (*.f64 x #s(literal 108/841 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 #s(literal -1 binary64) (*.f64 x #s(literal -108/841 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (*.f64 x #s(literal -108/841 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 #s(literal -1 binary64) (*.f64 x #s(literal 108/841 binary64))))
(/.f64 (pow.f64 (/.f64 #s(literal 108/841 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 108/841 binary64) x)))
(/.f64 (/.f64 (.f64 x (.f64 x x)) #s(literal -1259712/594823321 binary64)) (/.f64 (*.f64 x x) #s(literal 11664/707281 binary64)))
(/.f64 (/.f64 (*.f64 x x) #s(literal 11664/707281 binary64)) (/.f64 x #s(literal 108/841 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 #s(literal -108/841 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 #s(literal 108/841 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal -108/841 binary64)) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal 108/841 binary64)) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 #s(literal -108/841 binary64) (.f64 x x)) (.f64 x (.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal -108/841 binary64)) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 #s(literal 108/841 binary64) (.f64 x x)) (.f64 x (.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x #s(literal 108/841 binary64)) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x x))
(/.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) x)
(/.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal 841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x x))
(/.f64 (.f64 #s(literal 841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) x)
(/.f64 (.f64 #s(literal 841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 841/108 binary64)) (.f64 x x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 841/108 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 841/108 binary64)) x)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 841/108 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) (.f64 x x))
(/.f64 (neg.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (neg.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))) x)
(/.f64 (neg.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal -108/841 binary64)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -108/841 binary64)) x)
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 108/841 binary64)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 108/841 binary64)) x)
(/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -841/108 binary64)) (.f64 x x))
(/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -841/108 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 (.f64 x x) #s(literal -841/108 binary64)) x)
(/.f64 (.f64 (.f64 x x) #s(literal -841/108 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal -841/108 binary64) (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 (.f64 #s(literal -841/108 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal -841/108 binary64) (.f64 x x)) x)
(/.f64 (.f64 #s(literal -841/108 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) (*.f64 x x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) x)
(/.f64 (.f64 #s(literal 841/108 binary64) (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 (.f64 #s(literal 841/108 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 841/108 binary64) (.f64 x x)) x)
(/.f64 (.f64 #s(literal 841/108 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) (*.f64 x x))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) x)
(/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 841/108 binary64)) (.f64 x x))
(/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 841/108 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 (.f64 x x) #s(literal 841/108 binary64)) x)
(/.f64 (.f64 (.f64 x x) #s(literal 841/108 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal 1 binary64)) x)
(/.f64 (.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (*.f64 x x))
(/.f64 (.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal -1 binary64)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) (.f64 x (.f64 x x)))) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 108/841 binary64) (*.f64 x x))) x)
(/.f64 (/.f64 #s(literal 841/108 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 841/108 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 x x))
(/.f64 (/.f64 #s(literal 841/108 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
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(.f64 (/.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x (.f64 x x))) (.f64 x x))
(.f64 (/.f64 (.f64 #s(literal -841/108 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (.f64 x x)) x)
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (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)))

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

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)

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)

eval31.0ms (0.7%)

Compiler: Compiled 2815 to 450 computations (84% saved)

prune49.0ms (1.1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	248	5	253

Accuracy

100.0%

Counts

253 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	24.4%	(/.f64 (.f64 x (.f64 x #s(literal 707281/11664 binary64))) (+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal -4/29 binary64)))
✓	51.4%	(/.f64 x #s(literal 108/841 binary64))
✓	99.9%	(+.f64 (*.f64 #s(literal 841/108 binary64) x) #s(literal 4/29 binary64))
✓	51.5%	(*.f64 #s(literal 841/108 binary64) x)
✓	49.8%	#s(literal 4/29 binary64)

Compiler

Compiled 139 to 66 computations (52.5% saved)

regimes12.0ms (0.3%)

Counts

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

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

Calls

3 calls:

4.0ms	(*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x)
4.0ms	x
4.0ms	(+.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)

regimes17.0ms (0.4%)

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:

17.0ms

Results

Accuracy	Segments	Branch
98.0%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 4/29 binary64)

Outputs
#s(literal 4/29 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
49.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch57.0ms (1.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	1.2914807082229534e-6	0.18975071841882268
15.0ms	-160293553.31117567	-0.0006460340543084757

Results

18.0ms

304×

valid

Compiler

Compiled 166 to 145 computations (12.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 5.0ms (53.7% of total)

ival-add: 2.0ms (21.5% of total)

ival-mult: 2.0ms (21.5% of total)

const: 1.0ms (10.7% of total)

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

simplify8.0ms (0.2%)

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 (0.5%)

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	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
0	11	4
1	14	4
2	15	4
0	15	4

Stop Event

1×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Compiler

Compiled 54 to 38 computations (29.6% saved)

preprocess34.0ms (0.8%)

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	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
0	11	4
1	14	4
2	15	4
0	15	4

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	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
0	11	4
1	14	4
2	15	4
0	15	4

analyze0.0ms (0%)

sample944.0ms (21.9%)

preprocess31.0ms (0.7%)

explain93.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.2%)

localize33.0ms (0.8%)

series2.0ms (0%)

rewrite327.0ms (7.6%)

simplify10.0ms (0.2%)

eval47.0ms (1.1%)

prune27.0ms (0.6%)

simplify11.0ms (0.2%)

localize144.0ms (3.4%)

series7.0ms (0.2%)

rewrite315.0ms (7.3%)

simplify270.0ms (6.3%)

eval137.0ms (3.2%)

prune108.0ms (2.5%)

simplify117.0ms (2.7%)

localize144.0ms (3.3%)

series8.0ms (0.2%)

rewrite370.0ms (8.6%)

simplify245.0ms (5.7%)

eval248.0ms (5.8%)

prune116.0ms (2.7%)

simplify7.0ms (0.2%)

localize38.0ms (0.9%)

series0.0ms (0%)

rewrite252.0ms (5.8%)

simplify16.0ms (0.4%)

eval31.0ms (0.7%)

prune49.0ms (1.1%)

regimes12.0ms (0.3%)

regimes17.0ms (0.4%)

regimes2.0ms (0%)

bsearch57.0ms (1.3%)

simplify8.0ms (0.2%)

soundness20.0ms (0.5%)

preprocess34.0ms (0.8%)

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	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
0	11	4
1	14	4
2	15	4
0	15	4